JAMRIS 2015 Vol 9 No 3

Page 1

VOLUME 9

N째 3

2015

www.jamris.org

pISSN 1897-8649 (PRINT) / eISSN 2080-2145 (ONLINE)

JOURNAL OF AUTOMATION, MOBILE ROBOTICS & INTELLIGENT SYSTEMS

Editor-in-Chief

Associate Editors:

Janusz Kacprzyk

Jacek Salach (Warsaw University of Technology, Poland) Maciej Trojnacki (PIAP, Poland)

(Polish Academy of Sciences, PIAP, Poland)

Statistical Editor: Advisory Board:

Małgorzata Kaliczynska (PIAP, Poland)

Dimitar Filev (Research & Advenced Engineering, Ford Motor Company, USA) Kaoru Hirota (Japan Society for the Promotion of Science, Beijing Office) Jan Jabłkowski (PIAP, Poland) Witold Pedrycz (ECERF, University of Alberta, Canada)

Language Editors: Grace Palmer (USA), Urszula Wiaczek

Typesetting: Ewa Markowska, PIAP

Co-Editors: Roman Szewczyk (PIAP, Warsaw University of Technology)

Webmaster: Piotr Ryszawa, PIAP

Oscar Castillo (Tijuana Institute of Technology, Mexico) Marek Zaremba (University of Quebec, Canada)

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(ECERF, University of Alberta, Canada)

Executive Editor: Anna Ładan aladan@piap.pl

Copyright and reprint permissions Executive Editor The reference version of the journal is e-version. Printed in 300 copies.

Editorial Board: Chairman - Janusz Kacprzyk (Polish Academy of Sciences, PIAP, Poland) Plamen Angelov (Lancaster University, UK) Adam Borkowski (Polish Academy of Sciences, Poland) Wolfgang Borutzky (Fachhochschule Bonn-Rhein-Sieg, Germany) Chin Chen Chang (Feng Chia University, Taiwan) Jorge Manuel Miranda Dias (University of Coimbra, Portugal) Andries Engelbrecht (University of Pretoria, Republic of South Africa) Pablo Estévez (University of Chile) Bogdan Gabrys (Bournemouth University, UK) Fernando Gomide (University of Campinas, São Paulo, Brazil) Aboul Ella Hassanien (Cairo University, Egypt) Joachim Hertzberg (Osnabrück University, Germany) Evangelos V. Hristoforou (National Technical University of Athens, Greece) Ryszard Jachowicz (Warsaw University of Technology, Poland) Tadeusz Kaczorek (Bialystok University of Technology, Poland) Nikola Kasabov (Auckland University of Technology, New Zealand) Marian P. Kazmierkowski (Warsaw University of Technology, Poland) Laszlo T. Kóczy (Szechenyi Istvan University, Gyor and Budapest University of Technology and Economics, Hungary) Józef Korbicz (University of Zielona Góra, Poland) Krzysztof Kozłowski (Poznan University of Technology, Poland) Eckart Kramer (Fachhochschule Eberswalde, Germany) Rudolf Kruse (Otto-von-Guericke-Universität, Magdeburg, Germany) Ching-Teng Lin (National Chiao-Tung University, Taiwan) Piotr Kulczycki (AGH University of Science and Technology, Cracow, Poland) Andrew Kusiak (University of Iowa, USA)

Mark Last (Ben-Gurion University, Israel) Anthony Maciejewski (Colorado State University, USA) Krzysztof Malinowski (Warsaw University of Technology, Poland) Andrzej Masłowski (Warsaw University of Technology, Poland) Patricia Melin (Tijuana Institute of Technology, Mexico) Fazel Naghdy (University of Wollongong, Australia) Zbigniew Nahorski (Polish Academy of Sciences, Poland) Nadia Nedjah (State University of Rio de Janeiro, Brazil) Duc Truong Pham (Cardiff University, UK) Lech Polkowski (Polish-Japanese Institute of Information Technology, Poland) Alain Pruski (University of Metz, France) Rita Ribeiro (UNINOVA, Instituto de Desenvolvimento de Novas Tecnologias, Caparica, Portugal) Imre Rudas (Óbuda University, Hungary) Leszek Rutkowski (Czestochowa University of Technology, Poland) Alessandro Safiotti (Örebro University, Sweden) Klaus Schilling (Julius-Maximilians-University Wuerzburg, Germany) Vassil Sgurev (Bulgarian Academy of Sciences, Department of Intelligent Systems, Bulgaria) Helena Szczerbicka (Leibniz Universität, Hannover, Germany) Ryszard Tadeusiewicz (AGH University of Science and Technology in Cracow, Poland) Stanisław Tarasiewicz (University of Laval, Canada) Piotr Tatjewski (Warsaw University of Technology, Poland) Rene Wamkeue (University of Quebec, Canada) Janusz Zalewski (Florida Gulf Coast University, USA) Teresa Zielinska (Warsaw University of Technology, Poland)

Publisher: Industrial Research Institute for Automation and Measurements PIAP

If in doubt about the proper edition of contributions, please contact the Executive Editor. Articles are reviewed, excluding advertisements and descriptions of products. All rights reserved © Articles

1

JOURNAL OF AUTOMATION, MOBILE ROBOTICS & INTELLIGENT SYSTEMS VOLUME 9, N° 3, 2015 DOI: 10.14313/JAMRIS_3-2015

CONTENTS 3

52

Mathematical Modeling of the Bicycle Robot with the Reaction Wheelults Adam Owczarkowski, Piotr Kozierski, Marcin Lis DOI: 10.14313/JAMRIS_3-2015/19

Evolutionary Learning of Goal-Oriented Communication Strategies in Multi-Agent Systems Alhanoof Althnian, Arvin Agah DOI: 10.14313/JAMRIS_3-2015/24

9

Real-Time Operating Systems for Robotic Applications: A Comparative Survey Piotr Kmiecik, Grzegorz Granosik DOI: 10.14313/JAMRIS_3-2015/20 18

65

Polish Version of the Negative Attitude Toward Robots Scale (NARS-PL) Grzegorz Pochwatko, Jean-Christophe Giger, Monika ! " # $ DOI: 10.14313/JAMRIS_3-2015/25

Visualization of Atmosphere Information for Distance Education System based on Fuzzy Inference Using Customized Knowledge Kazuhiro Ohnishi, Jesus A. Garcia-Sanchez, Yongkang Tang, Fangyan Dong, Kaoru Hirota DOI: 10.14313/JAMRIS_3-2015/21

73

Localization of the Wheeled Mobile Robot Based on Multi-Sensor Data Fusion Piotr Jaroszek, Maciej Trojnacki DOI: 10.14313/JAMRIS_3-2015/26

25

A Novel Approach to the Solution of Matrix Games with Payoffs Expressed by Trapezoidal Intuitionistic Fuzzy Numbers Tina Verma, Amit Kumar, Janusz Kacprzyk DOI: 10.14313/JAMRIS_3-2015/22 47

Design of the Novel Double-ring Dynamical Gravimeter Igor Korobiichuk, Michal Nowicki, Roman Szewczyk DOI: 10.14313/JAMRIS_2-2015/23

2

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6@

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N° 3

2015

;<=>?@<A?B<CDECFE BGC=HIJKJE DFCKG?B<CDEFCKE <=B?DLJE1M>L?B<CDE0N=BJGEO?=JME CDE&>AANE DFJKJDLJE-=<DPE#>=BCG<AJME DCQ@JMPJE Submitted: 12th January 2015; accepted: 13th March 2015

Kazuhiro Ohnishi, Jesus A. Garcia-Sanchez, Yongkang Tang, Fangyan Dong, Kaoru Hirota DOI: 10.14313/JAMRIS_3-2015/21 E A distance education system is designed based on fuzzy inference, where visualized atmosphere information is shared by all learners in a virtual classroom. It provides high aspirations, low isolated feeling, low stress, and high affinity to learners, and offers learner’s psychological information, individual difference information, and hints of system improvement to the system manager. The effect of visualized atmosphere information in the learner’s psychological states is confirmed by T score of POMS test for 15 graduate students using CAI contents, and comparison experiment with traditional distance education. The proposal of atmosphere information presentation of virtual classroom provides a first step in establishing Education Academy beyond Space Time (EAST).

Edistance education, visualization, fuzzy inference, atmosphere, POMS

E Several approaches such as an adaptive system based on the learner’s user model have been proposed for effective distance education [1] [2], where not only system’s adaptation to the learner but also learner’s adaptation is necessary. The best effective

learning is not easy to realize under using only the unilateral system’s adaptation because the learning process depends on learner’s emotion. On the other hand, unilateral learner’s adaptation to the system is also not simple to make enough efficiency for each learner because it requests high motivation of the learner. The motivation of learners becomes an important issue for learners’ performance [3]. The learner’s isolation and stress feelings in distance education are still open research topics. The classroom lecture which has learners’ sufficiency has many interactions among learners and lecturer, where the atmosphere of the lecture is shared by the learners and the lecturer. Therefore, educational environment which has interaction among learners and system such as virtual classroom lecture is necessary to realize effective distance education. A distance education system is proposed to realize indirect interaction among learners and education system, to decrease the learner’s stress and isolated feelings, and to inspire learners, where visualized atmosphere information in a virtual classroom is shared among all learners based on fuzzy inference. The expression of human feeling about atmosphere sometimes has fuzzy words; therefore the fuzzy inference is accepted to extract atmosphere information. A multimodal interface, such as KinectŽ sensor is allocated to each learner’s learning environment in order to capture the learner’s state information, i.e., facial expression, gesture/posture, and sound, for the distance

Fig. 1. Interactions among learners, system, and system manager in proposal 18

Journal of Automation, Mobile Robotics & Intelligent Systems

education system. The learner’s state is mapped into a learner’s emotion in affinity arousal-pleasure space [4]. Atmosphere information in the virtual classroom is obtained as an emotional vector on fuzzy atmosfield [-1, 1]3 [5] [6] by applying rule based fuzzy inference to learner’s emotion information. A visualization program provides the atmosphere information of the virtual classroom to each learner. Each learner studies by communicating with the system and is able to recognize the atmosphere of all other leaners that are supposed to stay in the same virtual classroom at the same time. Each learner gets much more motivation, decreases isolated feelings, reduces stress, and increases the feeling of acceptance of the system via the visualized virtual classroom atmosphere. System manager gets each learner’s mood state, obtains an individual difference of atmosphere recognition by learners, and makes use of educational contents improvement or business strategy. The availability of the atmosphere information is confirmed through a comparison experiment of the proposed distance education with a traditional distance education using CAI contents of computational intelligence [7] by 15 leaners. The evaluation is based on learners’ mood obtained via the Profile of Mood State (POMS) test [8]. A distance education system with atmosphere information is proposed in 2. The definition of customized knowledge, visualization of atmosphere information, and their application to distance education are introduced in 3. The efficiency of the atmosphere information is confirmed by using POMS test and CAI contents in 4.

E E E1 E0 E E 3 E $ A distance education system is designed, where a concept of atmosphere in Education Academy beyond Space Time (EAST) is described. A multimodal interface is settled to each learner’s learning environment, visualized atmosphere information in a virtual classroom of the EAST is indicated on the screen of traditional distance education, and records of atmosphere information about learner are provided to the system manager. The mutual interaction among learners, system, and system manager in the virtual classroom is illustrated in Fig. 1. The EAST consists of several virtual classrooms, which are formed by learners, system, and system manager. EAST provides a new distance education which has both advantages of distance education, such as distance education (as an education beyond space) and e-learning (as an education beyond time), where the learner shares the time and their experience of learning even if they learn the lecture contents whenever and wherever they want. The virtual classroom of EAST has interactions among them, where the locations and learning instances of learners are different one after another generally. A concept of virtual classroom of EAST actualizes new learning environment in such a way that each learner feels as if he/she is

VOLUME 9,

N° 3

2015

learning in a real classroom by sharing the same atmosphere. The atmosphere of virtual classroom is formed mainly by emotions of all learners and a virtual lecturer in the system, and reminds each learner the existence of other learners and a virtual lecturer. A multimodal interface, such as KinectŽ is employed to capture each learner’s state from facial expression, gesture/posture, and sound information. Feelings about atmosphere information by each learner are obtained from each learner’s emotions by using rule based fuzzy inference. They are unified into final atmosphere information in the virtual classroom by using average and standard deviation operations. Finally the atmosphere information in the virtual classroom is visualized/displayed on the screen of each learner’s learning environment as two figures, where one figure indicates average atmosphere with shape-color-length model and another shows standard deviations of three atmosphere components by 1/8 ellipsoidal body model. Each learner is easy to forget other learners’ existence even if he/she basically recognize that the other learners are also learning the same contents, because there is no information about the other learners’ existence in the traditional distance education system. The traditional distance education system provides mainly educational contents only, and accordingly the learner may feel isolation and frustration. The learner may know the existence of other learners if the system proffers real classroom like environment. In the proposed distance education system, it is supposed to exist a classroom in the education environment, called a virtual classroom, and to be located by all learners, system, and system manager. The atmosphere information which is estimated from each learner’s emotional data is visualized on the screen of the learner’s terminal. The visualized atmosphere information indicates other learners’ feelings about the lecture; therefore the isolated feelings of learners may be decreased. The learner’s mood is also reflected immediately to the atmosphere information of the virtual classroom from instance to instance; consequently the learner may relieve the frustration by watching the change of atmosphere information in response to his/her mood. In such a way like this, the proposed system improves affinity of learners gradually to the lecture in the virtual classroom. The atmosphere information in the virtual classroom is recorded for each learning instance. The atmosphere for each screen of learning contents will be changed successively according to the accession by learners. Such history of atmosphere information is stored in the system, including 1) the atmosphere of the virtual classroom at the scene and the accessed learner, and 2) the accessed learner’s feeling of the atmosphere of the scene. The history of atmosphere information in the virtual classroom includes the information, i.e., which contents inspire learners and whether the learning is completed in appropriate atmosphere or not. These can help to improve learning effect of the distance education system and generate business chance for the system manager. Articles

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E E17 E $E; R E 3 E $ E E E9 S E E E T/ 0 Fuzzy atmosfield [5, 6] shown in Fig. 2 has been proposed to represent an atmosphere in multi-agent society which consists of many humans and robots, where the atmosphere is changing one after another. Fuzzy atmosfield is accepted to represent atmosphere in a virtual classroom, where the virtual classroom is recognized as the multi-agent society consisting of learners, system, and system manager as agents.

Fig. 3. Membership functions in affinity arousal-pleasure space [8]

Fig. 2. An example of atmosphere represented in fuzzy atmosfield [6]

E 3 E $ E $E& RR E $ E$ E 3 E1 A concept of virtual classroom is introduced in the proposed distance education system, and its atmosphere is supposed to be changed successively. The Atmosphere in the virtual classroom for each learning instance is estimated by using rule based fuzzy inference. The input of fuzzy inference is 3D emotional vectors in affinity arousal-pleasure space [4], and isŕ ‰captured by learners’ multimodal interface device with neural network and fuzzy set [9]. It should be noticed that the affinity axis is suited to represent the relationship between a learner and learning contents because affinity arousal-pleasure space represents emotion and learner’s impression of the learning contents in a space.

E& RR E $ E EO E E# R E

% Each learner’s feelings of the atmosphere in the virtual classroom are estimated by max-min center of gravity method of the fuzzy inference using a 3D emotional vector of each learner as input information. Because there is an individual difference in feelings of atmosphere [10], some kinds of customized knowledge of each learner is necessary for estimating each learner’s feelings of atmosphere correctly. The relations between learner’s emotion and feeling of atmosphere, which are obtained by questionnaire in virtual classroom lecture for each learner, are used as customized knowledge. The customized knowledge in a database is used to create if-then fuzzy inference rules. 20

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Fig. 4. Membership functions in fuzzy atmosfield [6]

Fuzzy membership functions shown in Fig.3 represent emotions estimated for each learner in affinity arousal-pleasure space [-1, 1]3 (i.e. pleasure-displeasure, arousal-sleep, and affinity-no affinity) [4] and are used in antecedent part of if-then fuzzy inference rules. Each learner’s feelings of atmosphere are represented in fuzzy atmosfield [-1, 1]3 (i.e. FriendlyHostile, Lively-Calm, and Casual-Formal) [6]. The membership functions shown in Fig. 4 are used in consequent part.

E 33 8 E 3 E $E 3 E $ E E1 0 For each learning instance, the atmosphere in the virtual classroom is initially set to zero vector in fuzzy atmosfield. When a new learner accesses the learning instance, the learner’s feelings of atmosphere are provided as a vector in fuzzy atmosfield

Journal of Automation, Mobile Robotics & Intelligent Systems

by using fuzzy inference based on customized knowledge. The atmosphere in the virtual classroom of the learning instance is updated at the new learner’s access by adding (max operation) the provided vector to the former set of vectors, i.e., the atmosphere is expressed by a set of vectors in the same number of accessing learners. Although the atmosphere information is represented by a set of vectors in fuzzy atmosfield, it is complicated and boring if the information about a set of all vectors is presented directly to learners. Instead, easily understandable approximate information may be welcomed by learners. As such an approximate expression, average vector in fuzzy atmosfield [-1, 1]3 and standard deviation vector in [-1, 1]3 on the set of all atmosphere feeling vectors are accepted. These two vectors are visualized, and presented to the learner by displaying the visualized images on the learner’s screen (in the right bottom).

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Fig. 6. Visualized standard deviation vector of atmosphere by 1/8 ellipsoidal body model

" E; R E $E 33 8 E 3 E $ E E; E# Atmosphere information of each learning instance is represented by a fuzzy set (a set of vectors in the same number of accessing learners) in fuzzy atmosfield [-1, 1]3, and changes one learner’s access after another. It is represented approximately by a pair of vectors, i.e., an average vector in [-1,1]3 and a standard deviation vector in [0,1]3. Visualization of approximated atmosphere information is proposed to inform the atmosphere in a virtual classroom to learners.

Fig. 7. An example of visualized atmosphere

is shown in Fig. 7, where the atmosphere is assessed as friendly in uniform, lively with split whether strongly live or not so strong, and a little casual in uniform.

" E E17 E $E; R E 3 E $ E E E9 S E E E T/ 0 " E; R E $E 3 E $ A part of ‘2-3 Fuzzy Logic and Reasoning’ in CAI contents of computational intelligence [7] is accepted for the experiment to 15 learners (graduate students) to confirm the availability of visualized atmosphere information in the virtual classroom. An example of the screen of CAI contents with the visualized atmosphere information (in the right bottom area) is shown in Fig. 8. It should be noticed that the atmo-

Fig. 5. Visualized representation of atmosphere average vector by shape-color-length model [6]

An average vector is illustrated by shape-colorlength model [6] as shown in Fig. 5. A standard deviation vector is illustrated by using 1/8 ellipsoidal body model in [0, 1]3 as shown in Fig. 6, where the surface is colored by the correspondence from [0, 1] to [red, purple]. As an example, visualized approximated atmosphere information in the case of average vector (0.4, 0.7, -0.4) and standard deviation vector (0.1, 0.5, 0.2)

Fig. 8. A scene of CAI contents with visualized atmosphere information Articles

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Tab. 1. Results of POMS Test in Traditional Distance Education

2015

Tab. 2. Results of POMS Test in Proposed Distance Education

Learner

T-A

D

A-H

V

F

C

Learner

T-A

D

A-H

V

F

C

1

55

42

42

45

41

49

1

42

43

39

43

37

42

2

53

60

49

37

66

57

2

56

67

48

30

70

66

3

56

54

58

58

50

51

3

56

53

54

56

43

51

4

54

46

49

50

44

57

4

53

45

50

46

44

53

5

45

49

40

69

40

49

5

39

44

38

69

38

40

6

56

51

50

48

40

45

6

48

51

48

51

46

55

7

45

45

44

63

41

47

7

45

43

44

74

41

47

8

50

43

42

55

50

51

8

45

42

40

53

48

49

9

37

49

40

51

43

64

9

36

41

38

43

43

49

10

34

42

43

63

40

40

10

37

44

37

61

37

38

11

55

62

64

41

66

61

11

60

71

66

53

58

61

12

53

43

47

50

38

49

12

55

46

48

51

48

46

13

53

58

58

58

56

51

13

48

55

47

60

51

44

14

48

56

59

66

50

47

14

45

56

56

66

45

49

15

37

48

40

58

41

44

15

39

44

40

45

41

49

sphere information in the right bottom area in Fig. 8 changes as a new learner accesses to this screen, i.e., from average (0, 0, 0) with standard deviation (0, 0, 0) in the case of no average (0.3, 0.2, 0.2) with standard deviation (0.2, 0.3, 0.2) as shown in Fig. 8 right bottom area when the 15th and the last learner finished studying this screen.

" E0 E17 E E9 SE E- %E T/ 0 A traditional style distance education, i.e., without no atmosphere information, is practiced as a preliminary experiment for 15 learners (4 master and 11 PhD students) on two sections ‘2-1 What is Fuzzy Logic?’ and ‘2-2 Fuzzy Set Operations’ in the 2nd chapter of CAI contents [7]. The contents which are used for the experiment are only theoretical scripts to avoid the influence of an upsurge of emotion. Profile of Mood States (POMS) test [8] is done to obtain learners’ mood for 15 learners after finishing two sections. Then main experiment by proposed distance education with atmosphere information is accomplished using a section ’2-3 Fuzzy Logic and Reasoning’ in the 2nd chapter of CAI contents [7] for the same 15 learners. The POMS test is also carried out to the 15 learners after finishing the study. In both experiments, each learner is expected to input the 5 grade answers to 65 questions in POMS. Table 1 shows T scores for 15 learners in the POMS test for traditional style distance education, where T-A, D, A-H, V, F, and C are Tension-Anxiety, Depression-Dejection, Anger-Hostility, Vigor, Fatigue, and 22

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Confusion, respectively. And T scores for 15 leaners on the POMS test for proposed distance education are listed in Table 2. The difference that T scores in Table 2 minus the scores in Table 1 is summarized in Table 3. Table 3 indicates that the effect of visualized atmosphere information is different one learner after another. The best efficiency is found in Tension-Anxiety of leaner 1 and vigor of learner 15, so it is concluded that learner 1 decreases frustration and learner 11 becomes lively. In the interview after experiments, learner 1 says that he relaxes to see the visualized atmosphere information rather than the case of traditional style distance education with no atmosphere information, and learner 11 mentions that he takes an interest in watching the transition of visualized atmosphere information on proposed distance education, which coincides with lower stress of learner 1 and high affinity of learner 11. Anger-Hostility of learner 13 is comparatively lower than that of others, which means that his angry emotion is reducing. Learner 13 answers in the interview that he learns comfortable by feeling that other learners learn in the same virtual classroom through atmosphere information. It indicates that lower isolate feelings of learner 13. Confusion of learner 9 attains the lowest score in the experiments, which is concluded that learner 9 decreases confusion. In the interview learner 9 says that he read the contents carefully when he feels the difficulty of contents because visualized atmosphere information becomes hostile at that time. It means that high aspiration of learner 9.

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Tab. 3. Difference of T Scores between Traditional and Proposal

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the characteristics of the CAI contents and leads to make a strategy for business.

Learner

T-A

D

A-H

V

F

C

1

-13

1

-3

-2

-4

-7

2

3

7

-1

-7

4

9

3

0

-1

-4

-2

-7

0

4

-1

-1

1

-4

0

-4

5

-6

-5

-2

0

-2

-9

6

-8

0

-2

3

6

10

7

0

-2

0

11

0

0

8

-5

-1

-2

-2

-2

-2

9

-1

-8

-2

-8

0

-15

10

3

2

-6

-2

-3

-2

11

5

9

2

12

-8

0

12

2

3

1

1

10

-3

' E #

13

-5

-3

-11

2

-5

-7

14

-3

0

-3

0

-5

2

15

2

-4

0

-13

0

5

The availability of atmosphere information visualization for each learner is confirmed by simulation using CAI contents on computational intelligence [7]. The effect of the proposed distance education system is validated by 15 graduate students using implemented distance education with CAI contents [7]. The effects of the proposal are shown as high aspiration of learner, decreasing of isolate feelings, and lower confusion by the POMS test. The record of atmosphere information during the learning process of each learner shows that the visualization of atmosphere information improves the atmosphere assessed by the learner, and figures out which contents make the learner interesting. The improvement of the atmosphere during the learning process leads to increase the learner’s performance, such as providing the learner’s high affinity feeling and decreasing the learner’s isolated feelings. The availability of atmosphere information for the system manager is also confirmed by analyzing records of atmosphere information during learning processes of all learners, e.g., the analysis of records of atmosphere information may help the system manager to detect which contents are effective for the learner. The proposal of displaying atmosphere information in a virtual classroom aims to establish an innovative distance education system which exceeds face-to-face traditional education system, in the sense of affinity of classroom atmosphere, e.g., the system detects what the atmosphere is the best for each learner and realizes the effective distance education via controlling atmosphere during their learning processes. No learners dislike studying and feel any stress, such as isolation, confusing, and disgust, because all educational contents customized to each learner inspire all learners and make them interesting. The proposal can also help the system manager to work out his/her strategy of the business by analyzing the records of atmosphere information.

Fig. 9. History of average atmosphere information in the proposed distance education system

The history of atmosphere information with proposed distance education is shown in Fig. 9 (average) and Fig. 10 (standard deviation). Average of Friendly-Hostile in 1st, 2nd, 4th, and 5th page are higher than that of other pages, which indicates that 15 learners study smoothly. The 4th page has higher average of Casual-Formal, which means that 15 leaners are inspired by the contents. It also shows that the 4th page is an appropriate instance to realize effective discussion. Studying by 15 learners is done under appropriate atmosphere in the virtual classroom because whole contents have no prominent atmosphere. The system manager says in the interview that the history of atmosphere information includes

Fig. 10. Standard deviation records of atmosphere information in the proposed distance education system

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- ./ 0 Kazuhiro Ohnishi* – Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama-city 226-8502, Japan, E-mail: kazuhiro.ohnishi@gmail.com. Jesus A. Garcia-Sanchez – Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama-city 226-8502, Japan, E-mail: garciajesusadrian@hotmail.com. Yongkang Tang – Applied Informatics, Faculty of Science and Engineering, Hosei University, Koganei 1848584, Japan, E-mail: tangyk@gmail.com. Fangyan Dong – Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohamacity 226-8502, Japan, E-mail: tou@acls.titech.ac.jp. Kaoru Hirota – Japan Society for the Promotion of Science, Beijing Office, 616, Library of Chinese Academy of Sciences (CAS), 33 Beisihuan Xilu, Zhongguancun, Haidian District, Beijing 100190. E-mail: hirota@jsps.org.cn. *Corresponding author

1&1 12#10 [1]

[2]

[3]

[4]

[5]

[6]

24

J. Kim, A. Lee, and H. Ryu, “Personality and its effects on learning performance: Design guidelines for an adaptive e-learning system based on a user model,” International Journal of Industrial Ergonomic, vol. 43, 2013, 450–461. E. Sung, R. E. Mayer, “Affective impact of navigational and signaling aids to e-learning,” Computers in Human Behavior, vol. 28, no. 2, 2012, 473–483. DOI: 10.1016/j.chb.2011.10.019. D. Zhang, J. L. Zhao, L. Zhou, J. and F. Nunamaker Jr., “Can e-learning replace classroom learning?,” Communications of the ACM, vol. 45, no. 5, 2004, 75–79. DOI: 10.1145/986213.986216. Y. Yamazaki, Y. Hatakeyama, F. Dong, K. Nomoto, and K. Hirota, “Fuzzy Inference based Mentality Expression for Eye Robot in Affinity PleasureArousal Space,” Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), vol. 12, no. 3, 2008, 304–313. K. Hirota, “Toward the Realization of Casual Communication between Humans and Robots,” Plenary Talk, ISME 2010, Kokura, 2010. Z. Liu, M. Wu, D. Li, L. Chen, F. Dong, Y. Yamazaki, and K. Hirota, “Concept of Fuzzy Atmosfield for Representing Communication Atmosphere and its Application to Humans-Robots Interaction,” Journal of Advanced Computational Intelligence

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and Intelligent Informatics (JACIII), vol. 17, no.1, 2013, 7–13. [7] B. Kermanshahi and K. Hirota, “High-Tech CAI Series: Fuzzy Logic, AI, and Neural Networks,” Computer Software Development Co., Ltd., 1997. [8] V. Pollock, D. W. Cho, D. Reker, and J. Volavka, “Profile of Mood States: the Factors and Their Physiological Correlates,” The Journal of Nervous and Mental Disease, vol. 167, no. 10, 1979, 612–614. [9] J. A. Garcia Sanchez, A. Shibata, F. Dong, and K. Hirota, “Deep Level Emotion Understanding based on Customized Knowledge for Agent to Agent Communication,” IWACII 2014 (University of Fukui), IWACII2014-02, 2014, 91–99. [10] K. Ohnishi, F. Dong, and K. Hirota, “Atmosphere Understanding for Humans Robots Interaction Based on SVR and Fuzzy Set,” Journal of Advanced Computational Intelligence and Intelligent Informatics (JACIII), vol. 18, no. 1, 2014, 62–70.

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E2CUJ@E HHKC?LIEBCEBIJE0C@>B<CDECFE ?BK<VE:?GJ=EQ<BIET?NCFF=E1VHKJ==JMEWNE K?HJAC<M?@E DB><B<CD<=B<LE&>AANE2>GWJK= Submitted: 22th April 2015; accepted 26th May 2015

Tina Verma, Amit Kumar, Janusz Kacprzyk DOI: 10.14313/JAMRIS_3-2015/22 Abstract: We propose a novel approach to the solution of fuzzy matrix games with payoffs given as trapezoidal intuitionistic fuzzy numbers. We extend Li’s [36, Chapter 9] work based on a cut-set based method for finding an optimal solution to overcome the fact that the assumptions and properties assumed therein do not guarantee in general, first, the very existence of an optimal solution, and second, its attainment via a mathematical programming formulation proposed. We first briefly mention those problems in Li’s [36] approach, and then propose a new, corrected and general method, called the Mehar mehod, based on a modified mathematical programming formulation of a matrix game with payoffs represented by trapezoid intuitionistic fuzzy numbers. For illustration, we solve Li’s [36] example, and compare his and our results. Keywords: trapezoidal intuitionistic fuzzy numbers, mathematical programming problem, two person zero sum game, cut, cut

E Game theory provide many effective and efficient tools and techniques to mathematically formulate and solve many multiperson (collective, multiagent ‌) with strategic interactions among multiple rational decision makers (cf. von Neumann and Morgenstern [56]); for various kinds of mathematical formulations and solution concepts, cf. [61]. Usually, the classical, i.e. nonfuzzy or crisp in our context, game theory assumes the payoffs of players to be real numbers. In reality, we often need to represent the players’ payoffs by their subjective judgments (or opinions) so that natural language descriptions using terms such as “very largeâ€?, “largerâ€?, “mediumâ€?, “smallâ€?, “smaller thanâ€? may be more adequate. Obviously, they are inherently imprecise and fuzzy sets theory [72] can provide effective and efficient tools and techniques. In fuzzy sets, that imprecision is handled by assigning a degree, from [0,1], called the membership degree, to which an object belongs to a set; the degree to which it does not belong to the same set, the non-membership degree is one minus the membership degree. However, in many human centered/focused real decisions making problems such a simple representation of imprecision is not sufficient to adequately represent judgments by (human) decision makers.

Basically, the human beings often tend to provide arguments “pro�, i.e. somehow taking into account “good� aspects, and “con�, i.e. taking into account “bad� aspects. The arguments in favor of “good� imply the membership degree that the product belongs to a “set of good products�, while the arguments in favor of ‘badness’ imply the non-membership degree of the product in the “set of good products�. Moreover, a human being may have his/her own reservations in classifying the object into one of these two categories, “good� and “bad�, so that the two degrees do not necessarily add up to one. Atanassov [3] proposed an interesting generalization of fuzzy sets called intuitionistic fuzzy sets to capture this aspect of human judgments and behavior. In the intuitionistic fuzzy sets, we have two membership functions, one that describes the degree of belongingness of elements and the other that describes the degree of non-belongingness, and the sum of those degrees is less than or equal to one. Over the last decades both the fuzzy sets and the intuitionistic fuzzy sets theories have enjoyed much popularity, and – which is important for our purposes – they have been applied in various game theoretic contexts, for instance, cf. [1, 2, 4–19, 21–24, 27–55, 57–60, 62–71].

E EO $E 7 E $E 33 E E 2 6 3 7 E: E ET $$ E 3 E E 7 \& RR E2 \ E& RR E2 Games may be classified into two major categories: cooperative and non-cooperative. Though the cooperation of players may be assumed in many games, the existence of non-cooperation is probably more attractive because it is often more realistic, especially upon the competition between players. In the non-cooperative games, an important, from conceptual and application points of view, class of games are matrix games (or two-person zero-sum games). In this section, we will provide a brief review of some recent works, which are relevant for this paper, dealing with non-cooperative games in which payoffs are represented by interval/fuzzy numbers/ intuitionistic fuzzy numbers, with a mathematical programming problem formulation; this will also be assumed here. Li and Cheng [37] transformed the fuzzy linear programming problem representing such fuzzy matrix games in which payoffs are represented by triangular fuzzy numbers, into a crisp linear programming problem and used the crisp optimal solution obtained 25

Journal of Automation, Mobile Robotics & Intelligent Systems

to get the crisp optimal solution and a fuzzy optimal value of the fuzzy constrained matrix game. Bector et al. [7] transformed the fuzzy linear programming problem of such fuzzy matrix games in which payoffs are represented by triangular fuzzy numbers, into a crisp linear programming problem and used the crisp optimal solution obtained toget the fuzzy optimal solution of the fuzzy matrix game. Liu and Kao [46] transformed the fuzzy linear programming problem of such fuzzy matrix games with triangular fuzzy number payoffs into a pair of twolevel mathematical programming problems and obtained, by solving them, the lower and upper bound of the optimal fuzzy value of the fuzzy matrix game. Li [30] transformed the fuzzy linear programming problem of such fuzzy matrix games in with triangular fuzzy number payoffs into two crisp linear programming problems and used the crisp optimal solution, obtained by the lexicographic method, to get the fuzzy optimal solution of the fuzzy matrix games. Liu and Kao [47] transformed the interval linear programming problem of such matrix games in which payoffs are represented by intervals, into a pair of two level mathematical programming problems and obtained, by solving them, the lower and upper bound of the optimal interval value of the interval matrix game. Nan et al. [53] transformed the intuitionistic fuzzy linear programming problem of such intuitionistic fuzzy matrix games with triangular intuitionistic fuzzy number payoffs into two crisp linear programming problems and used the crisp optimal solution, obtained by the lexicographic method, to get the intuitionistic fuzzy optimal solution of the intuitionistic fuzzy matrix games. Li [32] transformed the interval linear programming problem of such matrix games with payoffs represented by intervals, into two crisp linear programming problems and obtained, by solving them, the lower and upper bound of the optimal interval value of the interval matrix game. Li [34] transformed the fuzzy linear programming problem of such fuzzy matrix games with triangular fuzzy number payoffs, into three crisp linear programming problems and used the crisp optimal solutions obtained to get the fuzzy optimal solution of the fuzzy matrix games. Li and Hong [38] transformed the fuzzy linear programming problem of such fuzzy constrained matrix games with triangular fuzzy number payoffs into three crisp linear programming problems and used the crisp optimal solutions obtained to get the fuzzy optimal solution and the fuzzy optimal value of the fuzzy constrained matrix game. Li and Hong [39] transformed the fuzzy linear programming problem of such fuzzy constrained matrix games with trapezoidal fuzzy number payoffs into four crisp linear programming problems and used the crisp optimal solutions obtained to get the fuzzy optimal solution and the fuzzy optimal value of the fuzzy constrained matrix game. Li et al. [41] transformed the fuzzy linear programming problem of such fuzzy matrix games with triangular intutionistic fuzzy number payoffs into a crisp 26

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linear programming problem and used the crisp optimal solutions obtained to get the crisp optimal solution of the fuzzy matrix game. Li [35] transformed the fuzzy linear programming problem of such fuzzy matrix games with trapezoidal fuzzy number payoffs into four crisp linear programming problems and used the crisp optimal solutions obtained to get the fuzzy optimal solution of the fuzzy matrix games. Li and Yang [43] transformed the intuitionistic fuzzy bilinear programming problem of such intuitionistic fuzzy bimatrix games with trapezoidal intutionistic fuzzy number payoffs into a crisp bilinear programming problem and used the crisp optimal solution obtained to get the crisp optimal solution and the intuitionistic fuzzy optimal value of the intutitionistic fuzzy bimatrix games. Nan et al. [54] transformed the intuitionistic fuzzy linear programming problem of such intuitionistic fuzzy matrix games with triangular intuitionistic fuzzy number payoffs into two crisp linear programming problems and used the crisp optimal solutions obtained to get the crisp optimal solution and the intuitionistic fuzzy optimal value of the intuitionistic fuzzy matrix games. Li [36, Chapter 9, Section 9.3] proposed a cut set based method of such intuitionistic fuzzy matrix games with trapezoidal intuitionistic fuzzy number payoffs by transforming the intuitionistic fuzzy linear programming problem into a crisp linear programming problem and used the crisp optimal solution obtained to get the intuitionistic fuzzy optimal solution of the intuitionistic fuzzy matrix games. This paper is basically along the lines of that Li’s [36] work, and a novel method will be proposed to alleviate some shortcomings of his method and provide generality. More specifically, to resolve these shortcomings, a correct mathematical formulation of such matrix games with trapezoidal intuitionistic fuzzy number payoffs is developed and a new method (to be called the Mehar mehod) to find the exact optimal solution is proposed.

E E18 %E Basically, Li [36] proposed the following method to find the optimal solution of matrix games in which payoffs are represented by trapezoidal intuitionistic fuzzy numbers: Step 1: Formulate the problem considered as the following mathematical programming problem: Problem P1 Maximize Subject to: m

∑ a x ij

i

≼ v , j = 1,2, , n;

i =1 m

∑x

i

= 1;

i =1

x i ≼ 0, i = 1,2, , m.

Journal of Automation, Mobile Robotics & Intelligent Systems

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(

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)

Step 2: Since the a ij ’s are known, them by assuming a ij = aij , aijL , aijU , aij ;wa ij , ua ij , problem P1 can be transformed into the following problem P2. Problem P2 Maximize Subject to

∑ ( (a m

ij

i =1 m

∑x

i

)

)

, aijL , aijU , aij ;wa ij , ua ij x i ≥ v , j = 1,2, , n;

= 1;

i =1

i = 1,2, , m.

x i ≥ 0,

()

()

β β Step 3: Using the property a ≥ b ⇒ (a )α ≥ b and (a ) ≥ b , problem P2 can be transformed into the following α biobjective mathematical programming problem:

Problem P3 Maximize (v α ) , Maximize (v β ) Subject to

( (a , a , a , a ) ; w ⎛ ⎜⎝ ∑ ( (a , a , a , a ) ;w ⎛ m ⎜⎝ ∑ i =1

ij

L ij

U ij

ij

L ij

U ij

a ij

ij

a ij , ua ij

m

i =1

m

∑x

i

) )x ⎞⎟⎠

⎞ , ua ij x i ⎟ ≥ v α , j = 1,2, , n; ⎠α

ij

i

β

≥ v β , j = 1,2, , n;

= 1;

i =1

i = 1,2, , m.

x i ≥ 0,

⎡ where, α ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎡

⎤

⎤

{ }⎥⎦⎥ , β ∈⎢⎣⎢max {u } ,1⎥⎦⎥ . 1≤i ≤m 1≤ j ≤n

a ij

β

n n ⎛ n ⎞ ⎛ n ⎞ β Step 4: Since, obviously: ⎜ ∑ a i x i ⎟ = ∑ (a i )α x i and ⎜ ∑ a i x i ⎟ = ∑ (a i ) x i , problem P3 can be transformed into: ⎝ i =1 ⎠ α i =1 ⎝ i =1 ⎠ i =1

Problem P4 Maximize (v α ) , Maximize (v β ) Subject to:

∑ ( (a m

i =1

∑ ( (a

ij

)

, aijL , aijU , aij ;wa ij , ua ij

m

i =1 m

∑x

i

)

L U ij , aij , aij , aij ; w a ij , ua ij

) x ≥ v , j = 1,2, ,n; ) x ≥ v , j = 1,2, ,n; α

i

β

α β

i

= 1;

i =1

x i ≥ 0,

i = 1,2, , m.

⎡ where, α ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎤

⎡

⎤

{ }⎥⎦⎥ , β ∈⎢⎣⎢max {u } ,1⎥⎦⎥ . 1≤i ≤m 1≤ j ≤n

a ij

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Step 5: Using the values

((

)

ai , aiL , aiU , ai ;wa i , ua i

)

((

β

) (

)

ai , aiL , aiU , ai ;wa i , ua i

(

VOLUME 9,

α

(

)

)

⎡ wa − α ai + α aiL wa − α ai + α aiU ⎤ ⎥, , i =⎢ i wa i wa i ⎢ ⎥ ⎣ ⎦

(

)

)

⎡ (1 − β ) aiL + β − ua ai (1 − β ) aiU + β − ua ai ⎤ i i ⎥ and assuming v α = ⎡vαL , vαR ⎤ and , =⎢ ⎣ ⎦ 1 − ua i 1 − ua i ⎢ ⎥ ⎣ ⎦

v β = ⎡⎣vLβ vRβ ⎤⎦ , problem P4 can be transformed into: Problem P5

(

)

(

Maximize ⎡⎣vαL , vαR ⎤⎦ , Maximize ⎡⎣vLβ , vRβ ⎤⎦ Subject to

(

(

)

)

)

⎡ w − α a + α a L w − α a + α aU ⎤ ij ij a ij ij ij ⎢ a ij ⎥ x ≥ ⎡v L , v R ⎤ , j = 1,2, , n; , ∑ ⎢ ⎥ i ⎣ α α⎦ w w i =1 a ij a ij ⎢⎣ ⎥⎦ ⎡ (1 − β ) aL + β − u a (1 − β ) aU + β − u a ⎤ m ij a ij ij ij a ij ij ⎢ ⎥ x ≥ ⎡v β , v β ⎤ , j = 1,2, , n; , ∑ ⎢ ⎥ i ⎣ L R⎦ − − u u 1 1 i =1 a ij a ij ⎢⎣ ⎥⎦ m

(

m

∑x

i

(

)

)

= 1;

i =1

x i ≥ 0,

i = 1,2, , m.

⎡ where, α ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎡

⎤

⎤

{ }⎥⎦⎥ , β ∈⎢⎣⎢max {u } ,1⎥⎦⎥. 1≤i ≤m 1≤ j ≤n

a ij

Step 6: Using the property [a , b] x = [ax , bx ]; x ≥ 0, problem P5 can be transformed into: Problem P6

(

)

(

Maximize ⎡⎣vαL , vαR ⎤⎦ , Maximize ⎡⎣vLβ , vRβ ⎤⎦ Subject to:

(

(

)

)

)

⎡⎛ w − α a + α a L ⎞ ⎛ w − α a + α aU ⎞ ⎤ ij ij ij ij ⎢⎜ a ij ⎟ x , ⎜ aij ⎟ x ⎥ ≥ ⎡v L , v R ⎤ , j = 1,2, , n; ∑ i ⎢⎜ ⎟ ⎜ ⎟ i⎥ ⎣ α α⎦ w w i =1 a ij a ij ⎢⎣⎝ ⎠ ⎝ ⎠ ⎥⎦ m

(

(

)

)

⎡⎛ 1 − β a L + β − u a ⎞ ⎛ 1 − β aU + β − u a ⎞ ⎤ ) ij ( ) ij a ij ij a ij ij ⎢⎜ ( ⎟ x ,⎜ ⎟ x ⎥ ≥ ⎡v β , v β ⎤ , ∑ i ⎢⎜ ⎟ ⎜ ⎟ i⎥ ⎣ L R⎦ − − 1 u 1 u i =1 a ij a ij ⎢⎣⎝ ⎠ ⎝ ⎠ ⎥⎦ m

m

∑x

i

j = 1,2, , n;

= 1;

i =1

x i ≥ 0,

i = 1,2, , m.

⎡ where, α ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎡

⎤

⎤

{ }⎥⎦⎥ , β ∈⎢⎣⎢max {u } ,1⎥⎦⎥ . 1≤i ≤m 1≤ j ≤n

n

⎤

n

∑ [a , b ] = ⎢∑ a , ∑ b ⎥ , problem P6 can be transformed into: i

i =1

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a ij

⎡

n

Step 7: Using the property

28

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⎣ i =1

i

i

i =1

⎦

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Journal of Automation, Mobile Robotics & Intelligent Systems

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Problem P7

(

)

(

)

(

)

Maximize ⎡⎣vαL , vαR ⎤⎦ , Maximize ⎡⎣vLβ , vRβ ⎤⎦ Subject to

(

)

⎡ m ⎛ w − α a + αaL ⎞ ⎛ w − α a + α aU ⎞ ⎤ m ij ij ij ij ⎢ ⎜ a ij ⎟ x , ⎜ aij ⎟ x ⎥ ≥ ⎡v L , v R ⎤ , i ∑ ⎢∑ ⎜ ⎟ ⎜ ⎟ i⎥ ⎣ α α⎦ w w i =1 a ij a ij ⎢⎣ i =1 ⎝ ⎠ ⎝ ⎠ ⎥⎦

(

(

)

j = 1,2, , n;

)

⎡ m ⎛ 1 − β aL + β − u a ⎞ ⎛ (1 − β ) aU + β − u a ⎞ ⎤ m ) ij a ij ij ij a ij ij ⎢ ⎜( ⎟x , ⎜ ⎟ x ⎥ ≥ ⎡v β , v β ⎤ , j = 1,2, , n; i ∑ ⎢∑ ⎜ ⎟ ⎜ ⎟ i⎥ ⎣ L R⎦ − − u u 1 1 i =1 a ij a ij ⎢⎣ i =1 ⎝ ⎠ ⎝ ⎠ ⎥⎦ m

∑x

i

= 1;

i =1

i = 1,2, , m.

x i ≥ 0,

⎡ where, α ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎤

⎡

⎤

{ }⎥⎦⎥ , β ∈⎢⎣⎢max {u } ,1⎥⎦⎥ . 1≤i ≤m 1≤ j ≤n

a ij

Step 8: Using the property [a , b] ≥ [c , d ] ⇒ a ≥ c , b ≥ d , problem P7 can be transformed into: Problem P8

(

)

(

Maximize ⎡⎣vαL , vαR ⎤⎦ , Maximize ⎡⎣vLβ , vRβ ⎤⎦ Subject to:

(

)

j = 1,2, , n;

(

)

j = 1,2, , n;

⎛ w − α a + αaL ⎞ ij ij ⎜ aij ⎟ x ≥ vL , ∑ α ⎜ ⎟ i w i =1 a ij ⎝ ⎠ ⎛ w − α a + α aU ⎞ ij ij ⎜ aij ⎟ x ≥ vR , ∑ α ⎜ ⎟ i w i =1 a ij ⎝ ⎠

m

m

(

)

j = 1,2, , n;

(

)

j = 1,2, , n;

⎛ (1 − β ) aL + β − u a ⎞ ij a ij ij ⎜ ⎟ x ≥ vβ , ∑ L ⎜ ⎟ i − 1 u i =1 a ij ⎝ ⎠ m

⎛ (1 − β ) aU + β − u a ⎞ ij a ij ij ⎜ ⎟ x ≥ vβ , ∑ R ⎜ ⎟ i u − 1 i =1 a ij ⎝ ⎠ m

m

∑x

)

i

= 1;

i =1

x i ≥ 0,

i = 1,2, , m.

⎡ where, α ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎤

⎡

⎤

{ }⎥⎦⎥ , β ∈⎢⎣⎢max {u } ,1⎥⎦⎥ . 1≤i ≤m 1≤ j ≤n

a ij

Step 9: The two interval-valued objective functions in problem P8 may be regarded to be of equal importance, i.e., with weights of 0.5. Therefore, using the linear weighted averaging method of the multi-objective decision making as proposed in [20, 25, 28], problem P8 can be aggregated into the following interval-valued mathematical programming problem: Problem P9 ⎛ ⎡ vαL + vLβ vαR + vRβ ⎤⎞ , Maximize ⎜ ⎢ ⎥ 2 ⎦⎟⎠ ⎝⎣ 2 Articles

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Subject to:

(

)

j = 1,2, , n;

(

)

j = 1,2, , n;

⎛ w − α a + αaL ⎞ ij ij ⎜ aij ⎟ x ≥ vL , ∑ α ⎜ ⎟ i w i =1 a ij ⎝ ⎠ ⎛ w − α a + α aU ⎞ ij ij ⎜ aij ⎟ x ≥ vR , ∑ α ⎜ ⎟ i w i =1 a ij ⎝ ⎠

m

m

(

)

j = 1,2, , n;

(

)

j = 1,2, , n;

⎛ (1 − β ) aL + β − u a ⎞ ij a ij ij ⎜ ⎟ x ≥ vβ , ∑ L ⎜ ⎟ i − 1 u i =1 a ij ⎝ ⎠ m

⎛ (1 − β ) aU + β − u a ⎞ ij a ij ij ⎜ ⎟ x ≥ vβ , ∑ R ⎜ ⎟ i 1 − ua ij i =1 ⎝ ⎠ m

m

∑x

i

= 1;

i =1

x i ≥ 0,

i = 1,2, , m.

⎡ where, α ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎤

⎡

⎤

{ }⎥⎦⎥ , β ∈⎢⎣⎢max {u } ,1⎥⎦⎥ . 1≤i ≤m 1≤ j ≤n

a ij

Step 10: According to Ishibushi and Tanaka [26], the interval-valued objective function [a , b] is equivalent to the

⎡ a + b⎤ biobjective performance (objective) function ⎢a , . So, problem P9 can be transformed into: 2 ⎥⎦ ⎣ Problem P10

⎛ ⎡ v L + vLβ vαL + vLβ + vαR + vRβ ⎤⎞ Maximize ⎜ ⎢ α , ⎥⎟ 4 ⎝⎣ 2 ⎦⎠ Subject to:

(

)

j = 1,2, , n;

(

)

j = 1,2, , n;

⎛ w − α a + αaL ⎞ ij ij ⎜ aij ⎟ x ≥ vL , ∑ α ⎜ ⎟ i w i =1 a ij ⎝ ⎠ ⎛ w − α a + α aU ⎞ ij ij ⎜ aij ⎟ x ≥ vR , ∑ α ⎜ ⎟ i w i =1 a ij ⎝ ⎠

m

m

(

)

j = 1,2, , n;

(

)

j = 1,2, , n;

⎛ (1 − β ) aL + β − u a ⎞ ij a ij ij ⎜ ⎟ x ≥ vβ , ∑ L ⎜ ⎟ i 1 − ua ij i =1 ⎝ ⎠ m

⎛ (1 − β ) aU + β − u a ⎞ ij a ij ij ⎜ ⎟ x ≥ vβ , ∑ R ⎜ ⎟ i u 1 − i =1 a ij ⎝ ⎠ m

m

∑x

i

= 1;

i =1

x i ≥ 0,

i = 1,2, , m.

⎡ where, α ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎤

⎡

⎤

{ }⎥⎦⎥ , β ∈⎢⎣⎢max {u } ,1⎥⎦⎥ .

30

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Step 11: Using the usual linear weighted average, cf. [20, 25, 28], problem P10 can be transformed into: Problem P11

⎛ 1 ⎛ vÎąL + vLβ ⎞ 1 ⎛ vÎąL + vLβ + vÎąR + vRβ ⎞ ⎞ Maximize ⎜ ⎜ âŽ&#x;+ ⎜ âŽ&#x;⎠âŽ&#x; 4 âŽ? 2âŽ? 2 ⎠2âŽ? ⎠Subject to

(

)

j = 1,2, , n;

(

)

j = 1,2, , n;

⎛ w − Îą a + ÎąaL ⎞ ij ij ⎜ aij âŽ&#x; x ≼ vL , ∑ Îą ⎜ âŽ&#x; i wa ij i =1 âŽ? ⎠⎛ w − Îą a + Îą aU ⎞ ij ij ⎜ aij âŽ&#x; x ≼ vR , ∑ Îą ⎜ âŽ&#x; i w i =1 a ij âŽ? âŽ

m

m

(

)

j = 1,2, , n;

(

)

j = 1,2, , n;

⎛ (1 − β ) aL + β − u a ⎞ ij a ij ij ⎜ âŽ&#x; x ≼ vβ , ∑ L ⎜ âŽ&#x; i − 1 u i =1 a ij âŽ? ⎠m

⎛ (1 − β ) aU + β − u a ⎞ ij a ij ij ⎜ âŽ&#x; x ≼ vβ , ∑ R ⎜ âŽ&#x; i u − 1 i =1 a ij âŽ? ⎠m

m

∑x

i

= 1;

i =1

i = 1,2, , m.

x i ≼ 0,

⎥ where, Îą ∈ ⎢0,min wa ij ⎢⎣ 11≤≤ij≤≤mn

⎤

⎥

⎤

{ }⎼⎌⎼ , β âˆˆâŽ˘âŽŁâŽ˘max {u } ,1⎼⎌⎼ . 1≤i ≤m 1≤ j ≤n

a ij

Step 12: Find the optimal solution {vÎąL , vLβ , vÎąR , vRβ , x i ;i = 1,2, , m} of problem P11 for some values of the parameters ⎥ ⎤ ⎥ ⎤ Îą ∈ ⎢0,min wa ij ⎼ and β ∈ ⎢max ua ij ,1⎼ , where 0 ≤ Îą + β ≤ 1 . ⎢⎣ 11≤≤ij≤≤mn ⎼⎌ ⎢⎣ 11≤≤ij≤≤mn ⎼⎌

{ }

{ }

Step 13: Using the optimal solution obtained in Step 12, the Îą − cut and β − cut of the intuitionistic fuzzy optimal value of problem P1 corresponding to the chosen values of Îą and β are ⎥⎣vÎąL , vÎąR ⎤⎌ and ⎥⎣vLβ , vRβ ⎤⎌ , respectively.

" E )E E0 E& E E E18 %E Basically, there are the following flaws in the existing Li’s [36, Chapter 9, Section 9.3.1, pp. 361] method, which is mainly related to the fact that the properties therein used do not hold in general: 1. In Step 4 of Li’s method, described in Section 3, for transforming problem P3 into problem P4, the author has used the mathematical properties β

n n ⎛ n ⎞ ⎛ n ⎞ β ⎜âŽ? ∑ a i âŽ&#x;⎠= ∑ (a i )Îą and ⎜âŽ? ∑ a i âŽ&#x;⎠= ∑ (a i ) . i =1 i =1 i =1 i =1 Îą

However, it is obvious from

and

⎛ n ⎞ = ⎜ ∑ ai , aiL , aiU , ai ;wa i , ua i âŽ&#x; âŽ? i =1 ⎠ι

(

)

n ⎛ n ⎞ ⎛ n ⎞ that, in general, ⎜ ∑ a i âŽ&#x; ≠∑ (a i )Îą since: ⎜ ∑ a i âŽ&#x; âŽ? i =1 ⎠ι i =1 âŽ? i =1 ⎠ι

n n n ⎛ ⎛ n ⎞ = ⎜ ⎜ ∑ ai , ∑ aiL , ∑ aiU , ∑ ai âŽ&#x; ;min wa i ,max ua i 1≤i ≤n ⎠1≤i≤n âŽ? âŽ? i =1 i =1 i =1 i =1

{ }

⎞

{ } âŽ&#x;âŽ

Îą

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Journal of Automation, Mobile Robotics & Intelligent Systems

( { } )

VOLUME 9,

( { } )

n n n n ⎡ ⎤ wa i − α ∑ ai + α ∑ aiL min wa i − α ∑ ai + α ∑ aiU ⎥ ⎢ min 1≤i ≤n 1≤i ≤n i =1 i =1 i =1 i =1 ⎥ , =⎢ ⎢ ⎥ min wa i min wa i 1≤i ≤n 1≤i ≤n ⎢ ⎥ ⎣ ⎦

{ }

{ }

N° 3

2015

(1)

and n

∑ (a )α i

i =1

n

=∑ i =1

( (a , a , a , a ) ; w i

L i

(

U i

i

ai

, uai

(

)

)

α

)

L n ⎡ w wa − α ai + α aiU ⎤ a − α ai + α ai ⎥ = ∑⎢ i , i wa i wa i ⎥ i =1 ⎢ ⎣ ⎦ L ⎡ n ⎛ w − α a + α a ⎞ n ⎛ w − α a + α aU ⎞ ⎤ a i i i a i i i ⎟ ,∑⎜ ⎟⎥ = ⎢∑ ⎜ ⎢ i =1 ⎜ w w ⎟ ⎜ ⎟⎠ ⎥ i = 1 a a i i ⎠ ⎝ ⎣ ⎝ ⎦

(

(

)

)

(2)

2. In the interval [a , b] , the inequality a ≤ b should always be satisfied. However, in Step 12 problem P11 is solved R L β β β β without the restrictions vαR ≥ vαL and vR ≥ vL . So, for the obtained values of vα vα , vR vL the inequalities vαR ≥ vαL β β and vR ≥ vL may or may not be satisfied, in general. Li [36] solves problem P12 (and problem P13) to illustrate his proposed method and obtains the optimal solution as shown in Table 1. Problem P12 Maximize (v ) Subject to

(175,180,190) ;0.6,0.2 x1 + (80,90,100) ;0.9,0.1 x2 ≥ v ; (150,156,158) ;0.6,0.1 x1 + (175,180,190) ;0.6,0.2 x2 ≥ v ; x1 + x2 = 1; x1 , x2 ≥ 0.

Table 1. Maximin strategies and the cut sets for specific values of the ordered pair α β obtained by Li’s method

32

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α ,β

x * (α , β )

v *α ,β

0,1

(0.792,0.208)

[155.2,164.7]

0.1,0.8

(0.792,0.208)

[156.5,163.8]

0.2,0.7

(0.793,0.207)

[157.2,163.3]

0.3,0.6

(0.794,0.206)

[158.1,162.8]

0.4,0.5

(0.817,0.183)

[158.4,161.5]

0.5,0.3

(0.795,0.205)

[160.0,161.5]

0.6,0.2

(0.795,0.205)

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It is obvious from Table 1 that the values of x1 and x2 vary with the change of and which indicates that x1 and x2 should rather be meant, in our context, as intuitionistic fuzzy numbers. However, Li [36] has assumed that x1 and x2 are real numbers which is certainly the simplest assumption but it does not allow capturing the very essence of the x1 and x2. Hence, the mathematical formulation, i.e. problem P1, of such matrix games in which the payoffs are represented by trapezoidal intuitionistic fuzzy numbers, is not valid in general.

( E ET 3 E In this section, a new method, called the Mehar method, is proposed to find the optimal solution of problem P13 which yields the exact mathematical formulation of such matrix games in which payoffs are represented by trapezoidal intuitionistic fuzzy numbers. The steps of the proposed Mehar method are as follows: Problem P13 Maximize (v ) Subject to: m

∑ a x ij

i

≼ v ,

j = 1,2, , n;

i =1 m

∑ x

i

= 1;

i =1

x i ≼ 0,

i = 1,2, , m.

Step 1: Since a ij are known, then by assuming

(

)

(

)

(

)

a ij = aij , aijL , aijU , aij ;wa ij , ua ij , x i = xi , x iL , x iU , x i ;w , u , v = v , v L , vU , v ;w , u , 1 = (1,1,1,1) ;w , u and

{ } and u = max {u } , problem P13 can be transformed into:

0 = (0,0,0,0) ;w , u , where w = min wa ij 1≤i ≤m 1≤ j ≤n

1≤i ≤m 1≤ j ≤n

a ij

Problem P14

( ( v , v , v , v ) ;w , u ) L

Maximize Subject to:

∑ ( (a m

ij

i =1

U

)

, aijL , aijU , aij ;wa ij , ua ij

∑( (x , x m

i

L i

)( ( x , x , x , x );w ,u ) ≼ ( (v ,v ,v ,v );w ,u ) , j = 1,2, ,n; i

L i

U i

) ( (1,1,1,1) ;w ,u ) ;

)

( ( x , x , x , x );w ,u ) ≼ ( (0,0,0,0) ;w ,u ) , L i

U i

U

, x iU , x i ;w , u =

i =1

i

L

i

i

i = 1,2, , m.

Step 2: Using the multiplication

( a , a , a , a ) ;w , u ( b , b , b , b ) ;w , u L

U

L

a

a

U

b

⎧ ⎪ ⎪ ⎪ ⎪ =⎨ ⎪ ⎪ ⎪ ⎪ ⎊

b

(a b , a b , a b , a b ) ;min (w , w ) ,max (u ,u ) , (ab , a b , a b , a b ) ;min (w , w ) ,max (u ,u ) , (ab , a b , a b , a b ) ;min (w , w ) ,max (u ,u ) , (ab , a b , a b , a b ) ;min (w , w ) ,max (u ,u ) , (ab , a b , a b , a b) ;min (w , w ) ,max (u ,u ) , L

L

L

L

L U

L U

L U

U

U

U

U

U

a

b

a

b

a ≼ 0, b ≼ 0,

a

b

a

b

a < 0, a L ≼ 0, b ≼ 0,

a

b

a

b

a L < 0, aU ≼ 0, b ≼ 0,

a

b

a

b

aU < 0, a ≼ 0, b ≼ 0,

a

b

a

b

a < 0, b ≼ 0.

U

U

U

L

L

problem P14 can be transformed into:

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Problem P15

( ( v , v , v , v ) ;w , u ) L

Maximize Subject to: m

∑ i =1

((

U

) ((

)

pij , pijL , pijU , pij ;w , u ≥

∑( (x , x m

i

)

)

v , v L , vU , v ;w , u , j = 1,2, , n;

) ( (1,1,1,1) ;w ,u ) ;

)

, x iU , x i ;w , u =

L i

i =1

( ( x , x , x , x );w ,u ) ≥ ( (0,0,0,0) ,w ,u ) , i

L i

U i

(

where,

i = 1,2, , m.

i

⎧ ⎪ ⎪ ⎪ ⎪ L U pij , pij , pij , pij ;w , u = ⎨ ⎪ ⎪ ⎪ ⎪ ⎩

)

∑ ( (a , a n

Step 3: Since

L i

i

i =1

(a x , a x (a x , a x (a x , a x (a x , a x (a x , a x

) , a x ) ;w , u , , a x ) ;w , u , , a x ) ;w , u , , a x ) ;w , u ,

ij

i

L L ij i

, aijU x iU , aij x i ;w , u ,

aij ≥ 0,

ij

i

L L ij i

, aijU x iU

ij

i

L U ij i

, aijU x iU

ij

i

L U ij i

, aijU x iL

ij

i

L U ij i

, aijU x iL

ij

i

aij < 0, aijL ≥ 0,

ij

i

aij < 0, aijL < 0, aijU ≥ 0,

ij

i

aij < 0, aijL < 0, aijU < 0, aij ≥ 0,

ij

i

aij < 0, aijL < 0, aijU < 0, aij < 0.

n n n ⎛ ⎛ n ⎞ ⎞ , aiU , ai ;w , u = ⎜ ⎜ ∑ ai , ∑ aiL , ∑ aiU , ∑ ai ⎟ ;w , u ⎟ , problem P15 can be transformed into: ⎝ ⎠ ⎝ i =1 i =1 ⎠ i =1 i =1

)

)

Problem P16

( ( v , v , v , v ) ;w , u ) L

Maximize Subject to:

U

m m m ⎛ ⎛ m ⎞ ⎞ L U ⎜ ⎜⎝ ∑ pij , ∑ pij , ∑ pij , ∑ pij ⎟⎠ ;w , u ⎟ ≥ ⎝ i =1 ⎠ i =1 i =1 i =1 m m m ⎛ ⎛ m ⎞ ⎞ L U ⎜ ⎜⎝ ∑ xi , ∑ x i , ∑ x i , ∑ x i ⎟⎠ ;w , u ⎟ = ⎝ i =1 ⎠ i =1 i =1 i =1

( (v ,v ,v ,v );w ,u ) , j = 1,2, ,n; L

( (1,1,1,1) ;w ,u ) ;

( ( x , x , x , x );w ,u ) ≥ ( (0,0,0,0) ;w ,u ) , i

L i

U i

i = 1,2, , m.

i

()

Step 4: Since a ≥ b ⇒ (a )α ≥ b

α

U

()

β β and (a ) ≥ b , problem P16 can be transformed into:

Problem P17 Maximize Subject to:

( ( v , v , v , v ) ;w , u ) L

U

α

, Maximize

m m m ⎛ ⎛ m ⎞ ⎞ L U ⎜ ⎜⎝ ∑ pij , ∑ pij , ∑ pij , ∑ pij ⎟⎠ ;w , u ⎟ ≥ ⎝ i =1 ⎠α i =1 i =1 i =1

β

m m m ⎛ ⎛ m ⎞ ⎞ L U ⎜ ⎜⎝ ∑ pij , ∑ pij , ∑ pij , ∑ pij ⎟⎠ ;w , u ⎟ ≥ ⎝ i =1 ⎠ i =1 i =1 i =1 m m m ⎛ ⎛ m ⎞ ⎞ L U ⎜ ⎜⎝ ∑ xi , ∑ x i , ∑ x i , ∑ x i ⎟⎠ ;w , u ⎟ = ⎝ i =1 ⎠α i =1 i =1 i =1

β

m m m ⎛ ⎛ m ⎞ ⎞ L U ⎜ ⎜⎝ ∑ xi , ∑ x i , ∑ x i , ∑ x i ⎟⎠ ;w , u ⎟ = ⎝ i =1 ⎠ i =1 i =1 i =1

( ( v , v , v , v ) ;w , u ) L

U

( ( v , v , v , v ) ;w , u )

, j = 1,2, , n;

( ( v , v , v , v ) ;w , u )

, j = 1,2, , n;

L

U

α

L

U

( (1,1,1,1) ;w ,u )

;

( (1,1,1,1) ;w ,u )

;

α

β

( ( x , x , x , x );w ,u ) ≥ ( (0,0,0,0) ;w ,u ) ,i = 1,2, ,m; ( ( x , x , x , x );w ,u ) ≥ ( (0,0,0,0) ;w ,u ) ,i = 1,2, ,m. i

i

34

L i L i

Articles

U i U i

i

i

β

α

α

β

β

β

2015

Journal of Automation, Mobile Robotics & Intelligent Systems

where, α ∈[0, w ] , β ∈[u,1] .

((

((

⎡ (1 − β ) aiL =⎢ 1 − ua i ⎢ ⎣

)

)

β

N° 3

2015

( ) ) ( ) + (β − u i ) a (1 − β ) a + (β − u i ) a ⎤ ⎥ , problem P17 can be transformed into: ,

Step 5: Using the values

ai , aiL , aiU , ai ;wa i , ua i

VOLUME 9,

)

ai , aiL , aiU , ai ;wa i , ua i

α

⎡ wa − α ai + α aiL wa − α ai + α aiU ⎤ ⎥ and =⎢ i , i wa i wa i ⎢ ⎥ ⎣ ⎦

a

i

U i

1 − ua i

a

i

⎥ ⎦

Problem P18 L U ⎪⎧ ⎡ (w − α ) v + α v (w − α ) v + α v ⎤ ⎪⎫ , ⎨ Maximize ⎢ ⎥⎬ , w w ⎦ ⎭⎪ ⎩⎪ ⎣

⎧ ⎡ (1 − β ) v L + ( β − u) v (1 − β ) vU + ( β − u) v ⎤ ⎪ ⎫ ⎪ , ⎥⎬ Maximize ⎨ ⎢ 1−u 1−u ⎪ ⎦⎪ ⎩⎣ ⎭

Subject to: m m m m ⎡ L U ⎤ ⎢ (w − α ) ∑ pij + α ∑ pij (w − α ) ∑ pij + α ∑ pij ⎥ i =1 i =1 i =1 i =1 ⎢ ⎥≥ , w w ⎢ ⎥ ⎢ ⎥ ⎣ ⎦

⎡ (w − α ) v + α v L (w − α ) v + α vU ⎤ , ⎢ ⎥ , j = 1,2, , n; w w ⎣ ⎦ m m m m ⎡ ⎤ L U ⎢ (1 − β ) ∑ pij + ( β − u) ∑ pij (1 − β ) ∑ pij + ( β − u) ∑ pij ⎥ i =1 i =1 i =1 i =1 ⎢ ⎥≥ , 1−u 1−u ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ L ⎡ (1 − β ) v + ( β − u) v (1 − β ) vU + ( β − u) v ⎤ , ⎢ ⎥ , j = 1,2, , n; 1−u 1−u ⎣ ⎦ m m m m ⎡ ⎤ L U ⎢ (w − α ) ∑ x i + α ∑ x i (w − α ) ∑ x i + α ∑ x i ⎥ ⎡ (w − α ) + α (w − α ) + α ⎤ i i i i = 1 = 1 = 1 = 1 ⎢ ⎥=⎢ , , ⎥; w w w w ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ m m m m ⎡ ⎤ L U β β β β − + − − + − 1 x u x 1 x u xi ⎥ ( ) ( ) ( ) ( ) ∑ ∑ ∑ ∑ i i i ⎢ ⎡ (1 − β ) + ( β − u) (1 − β ) + ( β − u) ⎤ i =1 i =1 i =1 i =1 ⎢ ⎥=⎢ , , ⎥; 1−u 1−u 1−u 1−u ⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ ⎡ (w − α ) xi + α x iL (w − α ) x i + α x iU ⎤ , ⎢ ⎥ ≥ [0,0] , i = 1,2, , m; w w ⎣ ⎦ ⎡ (1 − β ) x iL + ( β − u) xi (1 − β ) x iU + ( β − u) x i ⎤ , ⎢ ⎥ ≥ [0,0] , i = 1,2, , m. 1−u 1−u ⎣ ⎦

where, α ∈[0, w ] , β ∈[u,1] . Step 6: Using the property [a , b] ≥ [c , d ] ⇒ a ≥ c , b ≥ d , problem P18 can be transformed into: Problem P19 ⎛ ⎡ ( w − α ) v + α v L ( w − α ) v + α v U ⎤⎞ , Maximize ⎜ ⎢ ⎥⎟ w w ⎝⎣ ⎦⎠ ⎛ ⎡ (1 − β ) v L + ( β − u) v (1 − β ) vU + ( β − u) v ⎤⎞ Maximize ⎜ ⎢ , ⎥⎟ 1−u 1−u ⎝⎣ ⎦⎠ Articles

35

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N° 3

2015

Subject to: m

m

(w − α ) ∑ pij + α ∑ pijL (w − α ) v + αv L i =1 i =1 ≥ , w

m

w

j = 1,2, , n;

m

(w − α ) ∑ pij + α ∑ pijU (w − α ) v + αvU i =1 i =1 ≥ , w

w

m

j = 1,2, , n;

m

(1 − β ) ∑ pijL + (β − u) ∑ pij (1 − β ) v L + (β − u) v i =1 i =1 ≥ , j = 1,2, , n; 1−u

1−u

m

m

(1 − β ) ∑ pijU + (β − u) ∑ pij (1 − β ) vU + (β − u) v i =1 i =1 ≥ , j = 1,2, , n; 1−u

m

1−u

m

(w − α ) ∑ xi + α ∑ xiL (w − α ) + α i =1 i =1 = ; w

m

w

m

(w − α ) ∑ xi + α ∑ xiU (w − α ) + α i =1 i =1 = ; w

w

m

m

(1 − β ) ∑ xiL + (β − u) ∑ xi (1 − β ) + (β − u) i =1 i =1 = ; 1−u

1−u

m

m

(1 − β ) ∑ xiU + (β − u) ∑ xi (1 − β ) + (β − u) i =1 i =1 = ; 1−u (w − α ) v + α vU

1−u

(w − α ) v + αv ≥ 0; − w w U (1 − β ) v + (β − u) v − (1 − β ) v L + (β − u) v ≥ 0; 1−u 1−u L

(w − α ) xi + α xiL ≥ 0,

i = 1,2, , m;

≥ 0,

i = 1,2, , m;

w (w − α ) xi + α xiU w

(w − α ) xi + α xiU − (w − α ) xi + α xiL ≥ 0, i = 1,2, , m;

w w L ⎛ (1 − β ) x i + ( β − u) xi ⎞ ⎜ ⎟ ≥ 0, 1−u ⎝ ⎠ ⎛ (1 − β ) x iU + ( β − u) x i ⎞ ⎜ ⎟ ≥ 0, 1−u ⎝ ⎠

i = 1,2, , m; i = 1,2, , m;

⎛ (1 − β ) x iU + ( β − u) x i ⎞ ⎛ (1 − β ) x iL + ( β − u) xi ⎞ ⎜ ⎟ −⎜ ⎟ ≥ 0, i = 1,2, , m. 1−u 1−u ⎝ ⎠ ⎝ ⎠ where, α ∈[0, w ] , β ∈[u,1] . Step 7: The two interval-valued objective functions in problem P19 may be regarded to be of equal importance, i.e., with weights 0.5. Therefore, using the usual linear weighted average (cf. [20, 25, 28]), problem P19 can be transformed into the following interval- valued mathematical programming problem:

36

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Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N° 3

2015

Problem P20 ⎛ ⎡ ⎛ (w − α ) v + α v L ⎞ ⎛ (1 − β ) v L + ( β − u) v ⎞ ⎛ (w − α ) v + α vU ⎞ ⎛ (1 − β ) vU + ( β − u) v ⎞ ⎤⎞ ⎜ ⎢⎜ ⎟ +⎜ ⎟ ⎜ ⎟ +⎜ ⎟ ⎥⎟ w 1−u w 1−u ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎥⎟ ⎜ ⎢⎝ , Maximize ⎜ ⎢ ⎥⎟ 2 2 ⎥⎟ ⎜⎢ ⎜⎝ ⎢ ⎥⎦⎟⎠ ⎣ Subject to: Constraints of problem P19. Step 8: According to Ishibushi and Tanaka [26], the interval-valued objective function [ a b ] is equivalent to the

⎡ a + b⎤ biobjective objective function ⎢a , , and therefore problem P20 can be transformed into: 2 ⎥⎦ ⎣ Problem P21 ⎛ ⎡ ⎛ (w − α ) v + α v L ⎞ ⎛ (1 − β ) v L + ( β − u) v ⎞ ⎤⎞ +⎜ ⎥⎟ ⎜ ⎢⎜ ⎟ ⎟ w 1−u ⎠ ⎝ ⎠ ⎥⎟ ⎜ ⎢⎝ , ⎥⎟ ⎜⎢ 2 ⎥ Maximize ⎜ ⎢ ⎟ L L U U ⎜ ⎢ ⎛ (w − α ) v + α v ⎞ ⎛ (1 − β ) v + ( β − u) v ⎞ ⎛ (w − α ) v + α v ⎞ ⎛ (1 − β ) v + ( β − u) v ⎞ ⎥⎟ + + + ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎥⎟ ⎜ ⎢⎜ w w 1−u 1−u ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎥⎟ ⎜ ⎢⎝ ⎝ ⎣⎢ 4 ⎦⎥⎠

Subject to Constraints of problem P19. Step 9: Using the usual linear weighted average (cf. [20, 25, 28]), problem P21 can be transformed into: Problem P22

⎛ ⎛ ⎛ (w − α ) v + α v L ⎞ ⎛ (1 − β ) v L + ( β − u) v ⎞ ⎞ ⎞ +⎜ ⎜ ⎜⎜ ⎟ ⎟ ⎟ ⎟ w 1−u ⎠ ⎝ ⎠⎟ ⎜ 1⎜ ⎝ ⎟ + ⎜ 2⎜ ⎟ ⎟ 2 ⎜ ⎜ ⎟ ⎟ ⎟⎠ ⎜ ⎜⎝ ⎟ ⎜ ⎟ Maximize ⎜ ⎛ ⎛ (w − α ) v + α v L ⎞ ⎛ (1 − β ) v L + ( β − u) v ⎞ ⎛ (w − α ) v + α vU ⎞ ⎛ (1 − β ) vU + ( β − u) v ⎞ ⎞ ⎟ ⎜ ⎜⎜ ⎟ +⎜ ⎟ +⎜ ⎟ +⎜ ⎟ ⎟⎟ w 1−u w 1−u ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎟⎟ ⎜ 1⎜ ⎝ ⎜ 2⎜ ⎟⎟ 4 ⎜ ⎜ ⎟⎟ ⎟⎠ ⎟⎠ ⎝⎜ ⎝⎜ Subject to: Constraints of problem P19. Step 10: Find the optimal solution {xi = ei , x i = fi , v = q , v = r } of problem P22 by taking =0, =1. Step 11: Find the optimal solution {x iL = gi , x iU = hi , v L = s , vU = t } of the following problem by taking =w and =u: Problem P23

⎛ ⎛ ⎛ (w − α ) v + α v L ⎞ ⎛ (1 − β ) v L + ( β − u) v ⎞ ⎞ ⎞ +⎜ ⎜ ⎜⎜ ⎟ ⎟ ⎟ ⎟ w 1−u ⎠ ⎝ ⎠⎟ ⎜ 1⎜ ⎝ ⎟ + ⎜ 2⎜ ⎟ ⎟ 2 ⎜ ⎜ ⎟ ⎟ ⎟⎠ ⎜ ⎜⎝ ⎟ ⎜ ⎟ Maximize ⎜ ⎛ ⎛ (w − α ) v + α v L ⎞ ⎛ (1 − β ) v L + ( β − u) v ⎞ ⎛ (w − α ) v + α vU ⎞ ⎛ (1 − β ) vU + ( β − u) v ⎞ ⎞ ⎟ ⎜ ⎜⎜ ⎟ +⎜ ⎟ +⎜ ⎟ +⎜ ⎟ ⎟⎟ w 1−u w 1−u ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎟⎟ ⎜ 1⎜ ⎝ ⎜ 2⎜ ⎟⎟ 4 ⎜ ⎜ ⎟⎟ ⎠⎟ ⎠⎟ ⎝⎜ ⎝⎜ Articles

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Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N° 3

2015

Subject to: Constraints of problem P19 with the following additional constraints: x iL ≼ ei ,

i = 1,2, , m;

x ≤ fi , i = 1,2, , m; U i

v L ≼ q; vU ≤ r .

Step 12: Using the optimal solution obtained in Steps 10 and 11, the fuzzy optimal solution of problem P13 is

{v = (v ,v ,v ,v );w ,u , x = ( x , x , x , x );w ,u ;i = 1,2, ,m} . L

U

i

i

L i

U i

i

* E2 E 8 3 Li [36] solved problem P12 to illustrate his proposed method. However, as discussed in Section 5, the correct mathematical formulation of the problem, as chosen by Li [36], is problem P24. In this section, to illustrate the proposed Mehar method, the exact optimal solution of the following problem P24 is obtained: Problem P24 Maximize (v ) Subject to:

(175,180,190) ;0.6,0.2 x 1 + (80,90,100) ;0.9,0.1 x 2 ≼ v ; (150,156,158) ;0.6,0.1 x 1 + (175,180,190) ;0.6,0.2 x 2 ≼ v ; x 1 + x 2 = 1; x , x ≼ 0. 1

2

The exact fuzzy optimal solution of problem P24 can be obtained as follows: Step 1: Since a ij are known, then by assuming x i = ( xi , x i , x i ) ;0.6,0.2 , v = ( v , v , v ) ;0.6,0.2 , 1 = (1,1,1) ;0.6,0.2

{ } and 0.2 = max {u } , problem P24 can be transformed into:

and 0 = (0,0,0) ;0.6,0.2 , where 0.6 = min wa ij 1≤i ≤2 1≤ j ≤2

1≤i ≤2 1≤ j ≤2

a ij

Problem P25

( ( v , v , v ) ;0.6,0.2 )

Maximize Subject to:

(175,180,190) ;0.6,0.2 ( x1 , x1 , x1 ) ;0.6,0.2

+ (80,90,100) ;0.9,0.1

( x2 , x2 , x2 ) ;0.6,0.2

≼

( v , v , v ) ;0.6,0.2 (150,156,158) ;0.6,0.1 ( x1 , x1 , x1 ) ;0.6,0.2

( x1 , x1 , x1 ) ;0.6,0.2 ( x1 , x1 , x1 ) ;0.6,0.2

+ (175,180,190) ;0.6,0.2

( x2 , x2 , x2 ) ;0.6,0.2 ≼ ( v , v , v ) ;0.6,0.2 ;

+ ( x2 , x2 , x2 ) ;0.6,0.2 = (1,1,1) ;0.6,0.2 ; ≼ (0,0,0) ;0.6,0.2 ; ( x2 , x2 , x2 ) ;0.6,0.2 ≼ (0,0,0) ;0.6,0.2 .

Step 2: Problem P25 can be transformed into: Problem P26 Maximize Subject to:

( ( v , v , v ) ;0.6,0.2 )

(175x1 ,180x1 ,190x1 ) ;0.6,0.2 (150x1 ,156x1 ,158x1 ) ;0.6,0.2 38

Articles

;

+ (80x2 ,90x2 ,100x2 ) ;0.6,0.2 ≼ ( v , v , v ) ;0.6,0.2 ; + (175x2 ,180x2 ,190x2 ) ;0.6,0.2 ≼ ( v , v , v ) ;0.6,0.2 ;

Journal of Automation, Mobile Robotics & Intelligent Systems

( x1 , x1 , x1 ) ;0.6,0.2 ( x1 , x1 , x1 ) ;0.6,0.2

N° 3

2015

+ ( x2 , x2 , x2 ) ;0.6,0.2 = (1,1,1) ;0.6,0.2 ; ≥ (0,0,0) ;0.6,0.2 ; ( x2 , x2 , x2 ) ;0.6,0.2 ≥ (0,0,0) ;0.6,0.2 .

⎛ ⎛

⎞

∑ ( (a , a , a ) ;w ,u ) = ⎜⎝ ⎜⎝ ∑ a , ∑ a , ∑ a ⎟⎠ ;w ,u n

Step 3: Since

VOLUME 9,

i

i

n

i

n

i

i =1

i =1

n

i

i =1

i

i =1

⎞ ⎟ , problem P26 can be transformed into: ⎠

Problem P27 Maximize Subject to:

( ( v , v , v ) ;0.6,0.2 )

(175x1 + 80x2 ,180x1 + 90x2 ,190x1 + 100x2 ) ;0.6,0.2 ≥ ( v ,v , v ) ;0.6,0.2 ; (150x1 + 175x2 ,156x1 + 180x2 ,158x1 + 190x2 ) ;0.6,0.2 ≥ ( v ,v , v ) ;0.6,0.2 ; ( x1 + x2 , x1 + x2 , x1 + x2 ) ;0.6,0.2 = (1,1,1) ;0.6,0.2 ; ( x1 , x1 , x1 ) ;0.6,0.2 ≥ (0,0,0) ;0.6,0.2 ; ( x2 , x2 , x2 ) ;0.6,0.2 ≥ (0,0,0) ;0.6,0.2 .

()

()

β β Step 4: Using the properties a ≥ b ⇒ (a )α ≥ b and (a ) ≥ b , problem P27 can be transformed into:

α

Problem P28 Maximize

, Maximize

Subject to:

where, α ∈[0,0.6] and β ∈[0.2,1] . Step 5: Using the values

and

=

problem P28 can be transformed into:

Articles

39

Journal of Automation, Mobile Robotics & Intelligent Systems

Problem P29 Maximize Maximize Subject to:

where: α ∈[0,0.6] and β ∈[0.2,1] . Step 6: Using the property [a , b] ≥ [c , d ] ⇒ a ≥ c , b ≥ d , problem P29 can be transformed into: Problem P30

⎪⎧ ⎡ (0.6 − α ) v + α v (0.6 − α ) v + α v ⎤ ⎪⎫ Maximize ⎨ ⎢ , ⎥⎬ 0.6 0.6 ⎦ ⎪⎭ ⎩⎪ ⎣ ⎧⎪ ⎡ (1 − β ) v + ( β − 0.2) v (1 − β ) v + ( β − 0.2) v ⎤ ⎫⎪ Maximize ⎨ ⎢ , ⎥⎬ 1 − 0.2 1 − 0.2 ⎦ ⎭⎪ ⎩⎪ ⎣ 40

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2015

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

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2015

Subject to

(0.6 − α ) (190x1 + 100x2 ) + α (180x1 + 90x2 ) (0.6 − α ) v + αv ≥ ; 0.6 (1 − β ) (180x1 + 90x2 ) + (β − 0.2) (175x1 + 80x2 )

0.6 (1 − β ) v + (β − 0.2) v

≥ ; 1 − 0.2 1 − 0.2 (1 − β ) (180x1 + 90x2 ) + (β − 0.2) (190x1 + 100x2 ) (1 − β ) v + (β − 0.2) v ≥ ; 1 − 0.2 1 − 0.2

(0.6 − α ) (150x1 + 175x2 ) + α (156x1 + 180x2 ) (0.6 − α ) v + αv ≥ ; 0.6 (0.6 − α ) (158 x1 + 190x2 ) + α (156x1 + 180x2 ) 0.6

w

≥

(0.6 − α ) v + αv ; w

(1 − β ) (156x1 + 180x2 ) + (β − 0.2) (150x1 + 175x2 ) (1 − β ) v + (β − 0.2) v ≥ ; 1 − 0.2 β 1 − 156 + 180 x x ( )( 1 2 ) + ( β − 0.2) (158 x1 + 190 x 2 ) 1 − 0.2 (0.6 − α ) ( x1 + x2 ) + α ( x1 + x2 ) 0.6

=

≥

1 − 0.2 β 1 − ( ) v + (β − 0.2) v 1 − 0.2

(0.6 − α ) + α ;

;

0.6

(0.6 − α ) ( x1 + x2 ) + α ( x1 + x2 ) (0.6 − α ) + α = ; 0.6

0.6

(1 − β ) ( x1 + x2 ) + (β − 0.2) ( x1 + x2 ) (1 − β ) + (β − 0.2) ; = 1 − 0.2 (1 − β ) ( x1 + x2 ) + (β − u) ( x1 + x2 )

1 − 0.2 (1 − β ) + (β − 0.2)

= 1 − 0.2 1 − 0.2 (0.6 − α ) v + αv − (0.6 − α ) v + αv ≥ 0; 0.6 0.6 (1 − β ) v + (β − 0.2) v − (1 − β ) v + (β − 0.2) v ≥ 0; 1 − 0.2 1 − 0.2

;

(0.6 − α ) x1 + α x1 ≥ 0; 0.6 (0.6 − α ) x1 + α x1 0.6 (0.6 − α ) x1 + α x1 0.6

≥ 0; −

(0.6 − α ) x1 + α x1 ≥ 0;

(1 − β ) x1 + (β − 0.2) x1 ≥ 0;

0.6

1 − 0.2

(1 − β ) x1 + (β − 0.2) x1 ≥ 0; 1 − 0.2

(1 − β ) x1 + (β − 0.2) x1 − (1 − β ) x1 + (β − 0.2) x1 ≥ 0; 1 − 0.2 0.6 − α ( ) x2 + α x 2 0.6 (0.6 − α ) x2 + α x2 0.6 (0.6 − α ) x2 + α x2 0.6

1 − 0.2

≥ 0; ≥ 0; −

(0.6 − α ) x2 + α x2 ≥ 0;

(1 − β ) x2 + (β − 0.2) x2 ≥ 0;

0.6

1 − 0.2

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(1 − β ) x2 + (β − 0.2) x2 ≼ 0; 1 − 0.2 (1 − β ) x2 + (β − 0.2) x2 1 − 0.2

−

(1 − β ) x2 + (β − 0.2) x2 ≼ 0. 1 − 0.2

where: Îą ∈[0,0.6] and β ∈[0.2,1] . Step 7: Using the linear weighted average, problem P30 can be transformed into the following interval- valued mathematical programming problem P31: Problem P31

Maximize

Subject to Constraints of problem P30. Step 8: Problem P31 can be transformed into the following problem P32: Problem P32 ⎛ ⎥ ⎛ (0.6 − Îą ) v + Îą v ⎞ ⎛ (1 − β ) v + ( β − 0.2) v ⎞ ⎤⎞ +⎜ ⎼âŽ&#x; ⎜ âŽ˘âŽœ âŽ&#x; âŽ&#x; 0.6 1 − 0.2 ⎠âŽ? ⎠⎼âŽ&#x; ⎜ ⎢âŽ? , ⎢ ⎼ ⎜ âŽ&#x; 2 Maximize ⎼âŽ&#x; âŽœâŽ˘ ⎜ ⎢ ⎛ (0.6 − Îą ) v + Îą v ⎞ + ⎛ (1 − β ) v + ( β − 0.2) v ⎞ + ⎛ (0.6 − Îą ) v + Îą v ⎞ + ⎛ (1 − β ) v + ( β − 0.2) v ⎞ ⎼âŽ&#x; ⎜ ⎢ âŽ?⎜ 0.6 1 − 0.2 0.6 1 − 0.2 ⎠âŽ&#x; âŽ?⎜ ⎠âŽ&#x; âŽ?⎜ ⎠âŽ&#x; âŽ?⎜ ⎠âŽ&#x; ⎼âŽ&#x; ⎼âŽ&#x; âŽœâŽ˘ âŽ?⎣ ⎌⎠4

Subject to Constraints of problem P30. Step 9: Using the linear weighted average, problem P32 can be transformed into: Problem P33

Maximize

Subject to: Constraints of problem P30. Step 10: %& ' ( ' ( #BB * ­\ ¯­6

3725 494 19 19 19 19 ⎍ ⎧ ,v = , x 1 = , x1 = , x 2 = , x 2 = ⎏ ⎨v = 24 3 24 24 24 24 ⎭ . ⎊ Step 11: _ * ­\+[ ¯­6 & ' ( : 42

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Problem P34

Maximize

Subject to Constraints of problem P30 with the following additional constraints

is

.

Step 12: Using the optimal solutions obtained in Step 10 and Step 11, the fuzzy optimal solution of problem P24 is

* E# %E )

1&1 12#10

We have proposed a new mathematical programming based method, called the Mehar method, for solving matrix games in which payoffs are represented by trapezoidal intuitionistic fuzzy numbers. This methods improves Li’s [36] method by being based on assumptions and properties that are valid in a general case so that the new mathematical programming formulation yields a generally valid solution.

[1] Aggarwal A., Mehra A., Chandra S., “Application of linear programming with I-fuzzy sets to matrix games with I-fuzzy goals�, Fuzzy Optimization and Decision Making, vol. 11, no. 4, 2012, 465–480. DOI: 10.1007/s10700-012-9123-z. [2] Aplak H. S., Turkbey O., “Fuzzy logic based game theory applications in multi-criteria decision making process�, Journal of Intelligent & Fuzzy Systems, vol. 25, no. 2, March 2013, 359–371. DOI: 10.3233/IFS-2012-0642. [3] Atanassov K. T., “Intuitionistic fuzzy sets�, Fuzzy Sets and Systems, vol. 20, no. 1, 1986, 87–96. DOI: 10.1016/S0165-0114(86)80034-3. [4] Aubin J.P., “Cooperative fuzzy game�, Mathematics of Operations Research, vol. 6, no. 1, 1981, 1–13. DOI: 10.1287/moor.6.1.1. [5] Bector C. R., Chandra S., “On duality in linear programming under fuzzy environment“, Fuzzy Sets and Systems, vol. 125, no. 3, 2002, 317–325. DOI: 10.1016/S0165-0114(00)00122-6. [6] Bector C. R., Chandra S., Fuzzy Mathematical Programming and Fuzzy Matrix Games, Berlin: Springer, 2005. DOI: 10.1007/3-540-32371-6. [7] Bector C. R., Chandra S., Vijay V., “Duality in linear programming with fuzzy parameters and matrix games with fuzzy payoffs�, Fuzzy Sets and Systems, vol. 146, no. 9, 2004, 253–269. DOI: 10.1016/ S0165-0114(03)00260-4. [8] Bector C. R., Chandra S., Vijay V., “Matrix games with fuzzy goals and fuzzy linear programming duality�, Fuzzy Optimization and Decision Making, vol. 3, no. 3, 2004, 255–269. DOI: 10.1023/B:FODM.0000036866.18909.f1. [9] Branzei R., Dimitrov D., Tijs S., “Convex fuzzy games and participation monotonic alloca-

# 2/ 91 :1 12 0 The first and second author want to acknowledge the adolescent inner blessings of Mehar (lovely daughter of the cousin sister of one of the authors, Dr. Amit Kumar). They believe that Mata Vaishno Devi has appeared on the Earth in the form of Mehar and without her blessings it was not possible to develop the ideas presented in this paper. The first author also acknowledges the financial support given to her by Department of Science and Technology under INSPIRE Programme for research students [IF130759] to complete the doctoral studies.

- ./ 0 Tina Verma*, Amit Kumar – School of Mathematics and Computer Applications, Thapar University, Patiala, India. E-mail:verma.tina21@gmail.com,amitkdma@gmail.com Janusz Kacprzyk – Systems Research Institute Polish Academy of Sciences, Industrial Research Institute for Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, Poland. E-mail: kacprzyk@ibspan.waw.pl *Coresponding author

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J=<PDECFEBIJE2CUJ@E C>W@J6K<DPE ND?G<L?@E:K?U<GJBJKE Submitted: 13th February; accepted 5th May 2015

Igor Korobiichuk, Michal Nowicki, Roman Szewczyk DOI: 10.14313/JAMRIS_3-2015/23 Abstract:

7 7 7 7 7 7 7 7 7 7

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 : 7 7" 7 7 7 7 7 7 7;7 < Keywords: 7 7 7 7

1. Introduction The gravimeter is an instrument used for measurements of local variations in Earth’s gravitational : + %& * 3

tion varies by about 0.5% on the surface of the Earth, due to the planet internal structure, land masses, metallic ores deposits, surface shape etc. The gravimeters operation principle is in essence the same as for other accelerometers, but there is need for exceptional measurement accuracy, due to the extremely small relative changes of the measured value [1]. Gravimeters are used in mineral prospecting, seismology, geodesy, geophysical surveys and research. They display the measured gravitational acceleration value in units of gals (cm2/s), named after the famous Galileo Galilei [2]. Table. 1. Acceleration units conversion Base unit

Gal (cm2/s)

m2/s

Standard gravity g0

Gal (cm2/s)

1

0.01

0.00101972

m2/s

100

1

0.101972

Standard gravity g0

980.665

9.80665

1

Existing gravimeter systems are either relative or absolute. Absolute gravimeter system measures the absolute value of the gravity acceleration, ex. by directly measuring the acceleration of a mass during free fall in a vacuum, when the accelerometer is rigidly attached to the ground, and the falling mass forms one of the arms of the Michelson interferometer. Relative gravimeters measure the ratio of the gravity between different measurement points. They

can be constructed for example as a mass on a spring. Transportable systems would use extremely stable inertial platform to overcome distortions caused by the device’s movement and vibrations [3, 4]. Most of the precise gravimeter systems are heavy, complicated and rigidly attached to the ground. To study the characteristics of the Earth’s gravitational :

' & * & gravimetric system (AGS) is necessary [5, 6]. In the available literature there are descriptions of known gravimeters working principles, and some accelerometers characteristics that are used as gravimeters in AGS’s. However, there are no descriptions of the design, functional diagram and the working principle of the double-ring dynamically tuned gravimeter [7–10]. Accuracy of the Earth gravity anomalies measurement using gravimetric aviation system is largely dependent on the choice of system’s sensing element. Today, the gyroscopic gravimeters are considered to be one of the most effective among the available solutions. Additionally, in [7, 11] it was proved that the double-ring dynamically tuned gravimeter (DG) has much greater accuracy and performance than the standard one-ring one. Therefore, further research and development of the double-ring dynamically tuned gravimeter design is advisable, as the most promising of the known aviation gravimeters. The aim of this paper is to provide a description of the design and lay out the working principle of the double-ring dynamically tuned gravimeter.

2. Design Double-ring dynamically tuned gravimeter development belongs to measurement techniques science, and can be used for moving platform gravimetric measurements in geodesy, geology, and in inertial navigation systems. A dynamically tuned gyroscope (DTG) is a rotor suspended by a universal joint with flexure pivots. The flexure spring stiffness is independent of the rotor spin rate. However, the dynamic inertia, from the gyroscopic reaction effect, from the gimbal suspension provides negative spring stiffness proportional to the square of the spin speed. Therefore, at a particular tuning speed, the two moments cancel each other, freeing the rotor from torque, which is a necessary condition for an ideal gyroscope. The design of the double-ring DTG [12], is shown in Fig. 1. The rotor 1, drive shaft 2 and internal suspension elements are driven by engine 3, which provides a constant rotational speed. Internal Kardanov suspension contains gimbal ring 4, two internal flexure pivots 5, 47

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linking gimbal ring to the rotor and two external flexure pivots 6 connecting gimbal ring with a drive shaft. Axes of the internal and external flexure pivots are perpendicular to each other and perpendicular to the axis of the drive shaft.

Fig. 1. Schematic diagram of the gravimeter construction The reference voltage generator 7 is coupled with the drive shaft. The generator is used to generate control signals that drive the Ms and Ms? moment sensors, affecting the rotor. The two electromagnetic torque sensors are attached to the body of the device. When supplying power to the sensors they create a torque Âł ´ 9 & & & & tor Voltage, is applied between the middle and two extreme points of the windings. The angle sensors As and As are also attached to the body of the device. They convert the rotor plane deviation from the neutral position into electrical signals. In particular, the shown angle sensors respond to the change of the air gap between the windings center and the rotor surface, in device body points that do not revolve around the x and h axis. The basis of the design of double-ring dynamically tuned gravimeter was the known two-stage gyroscope based gravimeter [11, 12]. The common essential feature of the double-ring dynamically tuned gravimeter and the known one is that they contain two-stage gyroscope and the torque sensors. However, unlike the double-ring dynamically tuned gravimeter, in the known gravimeter construction the center of mass of the two-stage gyroscope rotor is located on the axis of rotation, and it contains the sensor of the angular velocity of the gyroscope rotor rotation relative to the base. As a result, the output value of the gravimeter is the angular velocity of rotation of the gyroscope rotor relative to the device’s base. Thus, the known gyroscopic gravimeter require additional signal conversion to determine the gravity acceleration value, which contributes additional errors in measurement result. 48

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Furthermore, there is no measurement errors calculation and compensation in the standard device. Therefore, measurement results obtained using this gravimeter contains * : ( ( + These errors are caused by non-linear distortions of the trajectory of the sensing element; precession oscillations damping through viscous type torques action on the sensor element; non-synchronization of precession oscillations; the discrepancy between the value of the angular precession vibrations frequency used in the estimation algorithms, and the value of the angular precession oscillation frequency of the sensing element; interferences that distort the sens * ( ( ( + %& * : back of the known solution is a low accuracy. Thus, the presented work is focused on redesigning the gravimeter to improve the accuracy of measurements of the acceleration of gravity. The problem is solved by the fact that the center of rotor 2 mass of the dynamically tuned gyroscope 1 (Fig. 2) is shifted relative to its axis of rotation. Additionally, rotation angle sensor 3 and the calculation and measurement errors compensation unit 5 are introduced, where the angle of rotation sensor 3 input is connected to the dynamically tuned gyroscope 1 output and rotation angle sensor 3 output is connected to the input of measurement errors calculation and compensation device 6.

3. Operational Principle Double-ring dynamically tuned gravimeter working principle is as follows. The center of mass C of the rotor 2 is shifted relative to the axis of rotation by the value of l (Fig. 2). With the drive motor (not shown in the Fig. 2, 3 in Fig. 1) rotor 2 rotates at a constant an* 3 ¾+ 1 & 9 rotor 2 rotates in the horizontal plane. In the presence of gravitational acceleration along the axis of gyroscope rotation, the rotor 2 starts to deviate. The result is a signal at the output of the angle of rotation sensor 3 that goes to the input of the device 6, through the low-pass filter 5. The device 6 performs calculations and compensation of measurement errors. Torque sensor 4 is used for measuring compensation method based on dynamically tuned gyroscope. The output value of the double-ring dynamically tuned gravimeter is the output signal of the measurement errors calculation and compensation device 6. If 0z axis is directed vertically, along the acceleration of gravity g, with the other accelerations excluded, there is a moment of the force of gravity Mg that will make the rotor 2 deviate relative to the axis 0x. Moment of the force of gravity Mg is determined by the expression: (1) where: m – rotor mass, l – displacement of the center of rotor mass relative to its axis of rotation, a – angle of rotor deviation. Moment Mœ of the vertical acceleration @ on the axis of sensitivity of the device (Fig. 1) is: (2)

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SIGNAL PROCESSING UNIT

LOW PASS FILTER

T

1

2015

The output signal of the angle of rotation sensor passes through the amplifier (not shown in the drawing) with a gain of 1/S and enters the lowpass filter input. The output signal of the angle of rotation sensor also present errors caused by translational and angular vibrations of the gravimeter carrying aircraft. Therefore, given these circumstances, lowpass filter input is given by:

6

5

N° 3

(9)

2

3 Where: Rx, Ry – translational acceleration of the aircraft projections on the axes 0x, 0y, b – proportionality factor, B – moment of inertia of the rotor, – angular acceleration of the aircraft projections on the axes 0x, 0y, Mi2 – torque related to the instrumental errors of the dynamically tuned gyroscope. Since the DG performs direct measurements of &

* 3 ' : & measurement signal. The frequency spectrum of the signal, which corresponds to the acceleration of gravity, and the signal corresponding to the vertical acceleration, angular and translational vibrations of the aircraft are different (Fig. 3, curve 2 and curve 1, respectively). The bulk of utility component of the measurement signal is focused at frequencies lower than 0.1 rad/s (curve 2, Fig. 3). The majority of the errors and noise in the measurement signal is concentrated

z TORQUE SENSOR

Îł l 0 C

ANGLE SENSOR

x

y

4 J . Gravimeter operating schematic diagram

Elastic torque MT of the rotor’s flexure pivots is: (3) where Cx – Flexure pivots stiffness. The centrifugal moment Mu is: (4) where I – moment of inertia of the rotor, g – angle velocity of the rotor. If we assume that a ¡¡¸6 & 8 (5) where, denoting

, we get: (6)

Denoting put signal:

, we get the low-pass filter in(7)

where: (8) Thus, the angle of rotor deviation is proportional to the acceleration of gravity g and vertical acceleration ¸.

Fig. 3. The spectral density of the vertical acceleration G@$B&J$ &J J J J J J J GÇťJ$B&J$ &J Articles

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at frequencies greater than 0.1 rad/s (curve 1, Fig. 3). _ & & ' : ' & * 3 ( (+ %& : ' ( : * of the measurement signal to eliminate errors caused by vertical accelerations, angular and translational vibrations of the DG carrying aircraft. The signal pro * 3 & : * & `W put signal. ! & : ) * \+\\6@X ~ the majority of the second signal frequency is 0,269 ~ + | ' : & ) \+6 ~ ' ( * : * ( caused by vertical accelerations, angular and transla 3 + 4 ' : & ' can be written [11]: (10) where – lowpass filter weight function. It can be written as [15]:

(11)

where – transfer function of low-pass filter.

(12) In this case – the time interval of the signal processing unit, n¸­¸6 < +++ ^ & ( (' revolutions of the DNG outer frame. The result is an DG output signal, which contains useful information about the gravity acceleration g. The errors in the signal are for the great part filtered out. These errors are caused by: translational acceleration with the dominant frequency of 3140 rad/s; angular acceleration with the dominant frequency of 20 rad/s, which is equal to the frequency of natural DG oscillations (the most dangerous case of resonance); angular acceleration with the dominant frequencies of 40 rad/s and 60 rad/s; angular acceleration, the frequency of which is equal to 6.7 and 10 rad/s (subharmonic oscillations). In addition, the computation time allow for almost entirely DG instrumental error elimination, because for a full rotation of its external frame these errors in turn take equal amplitude positive and negative values, that is, on average, they are zero. Improving the accuracy of measurements in the double-ring dynamically tuned gravimeter is ensured by the fact that the center of mass of the DG rotor is shifted from its axis of rotation, and therefore this gravimeter takes the direct measurement of the acceleration of gravity. These measurements are performed 50

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using the rotation angle sensor, which was incorporated into the device. During the preliminary tests of the proposed invention, the following hardware was used: – Dynamically tuned gyroscope serially produced at “NVK GI Petrovsky Kyiv Automation Factory�, Kyiv, Ukraine); – Signal processing unit – onboard computer AN124. In the factory made gyroscope the said center of mass of the rotor is located on the axis of rotation. %& & ( : ( : 9 * 9 weight to the rotor, the location of which shifted the rotor center of mass relatively to its axis of rotation. As a result of the tests it was determined that DG allows to separate the gravity acceleration signal from the disturbances caused by vertical accelerations, angular and translational vibrations of the aircraft carrying the gravimeter. Thus, the DG output signal is compensated for the impact of a number of measurement errors. However, the results of measuring the gravity acceleration contain systematic errors Ri & * : * & * 3 meter: ! R1: nonlinear distortion of the gravimeter sensing element trajectory, ! R2: precession oscillations damping through viscous type torques action on the sensor element, ! R3: non-synchronization of the precession oscillations, ! R4: the discrepancy between the value of the angular precession vibrations frequency used in the estimation algorithms, and the value of the angular precession oscillation frequency of the sensing element, ! R5: interferences that distort the sensing element mode of motion. Compensation of the systematic measurement errors of gravitational acceleration is performed by their subtraction according to the known formula [16]: (13) where: g – gravimeter output signal after error compensation, R – the output signal of the rotation angle sensor proportional to the acceleration of the force of gravity. Calculation of systematic measurement errors in the device is performed based on the approach outlined in [11]. Without the error compensation for the proposed method, the errors may be equal in magnitude to the signal value, i.e. be unacceptably large. U (' * : creasing of the measurement accuracy of the gravity acceleration. Furthermore, from the literature [7, 8] it is clear that the dynamically tuned gravimeter has the major advantages over other gyroscopic gravimeters: – The absence of friction in the rotor suspension node, – in case when the stiffness of gravimeter’s suspension is close to zero, the sensitivity and the accuracy of the device increases considerably,

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– it has small dimensions (54 46 mm diameter) and low weight (0.35 kg) – less than any other gyroscopic gravimeter, – it has an automated processing of the output signal, thus its performance is much higher than in other types of aircraft gravimeters.

4. Conclusions As a result of the tests it was determined that the double-ring dynamically tuned gravimeter enhances gravitational acceleration measurement accuracy to 10 times compared with other known gyroscopic gravimeters. Improving the accuracy of measurements in the device is ensured by the fact that the center of mass of the DG rotor is shifted relative to the axis of its rotation, and therefore this gravimeter takes the direct measurements of the gravity acceleration, and it became possible to perform measurement signal filtering. The achieved gravitation measurement accuracy is 1 mGal, that is 0.00001 m/s2 or ~1*10-6 g .

# 2/ 91 :1 12 0E This work was partially supported by the Erasmus Mundus project ACTIVE.

- ./ 0 Igor Korobiichuk* – Industrial Research Institute for Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, Poland. E-mail: kiv_Igor@list.ru. – Industrial Research Institute for Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, Poland. e-mail: mnowicki@piap.pl. ! " – Institute of Metrology and Biomedical Engineering, Warsaw University of Technology, Boboli 8, 02-525 Warsaw, Poland. E-mail: r.szewczyk@mchtr.pw.edu.pl. *Corresponding author

1&1 12#10 [1] [2]

[3]

[4]

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[6]

Zhai Z., et al., The accuracy evaluation and analysis of airborne gravimetry in coastal area, Cehui Xuebao/Acta Geodaetica et Cartographica Sinica, vol. 44, issue 1, 2015, 1–5. 5@7 _ 3 Âť >+!+ X# # 8 # Y + # : Z Y Pidruchnyk. Pub.: Lybid, Kyyiv, 2001, 261. (In Ukrainian). 5=7 # Âť' `+;+ Hyroskopycheskye systemy: Élementy hyroskopycheskykh pryborov, 1988, 432. (In Ukrainian). [9] Novykov L.Z., Raykhman O.YU., “Shumova H.M. “Blok hyrotakhometrov, osnovannyy na mynyatyurnykh dynamychesky nastrayvaemykh hyroskopakh, dlya kosmycheskykh prymenenyyâ€?. In: Materyaly III Sankt-Peterburhskoy mezhdunarodnoy konferentsyy po yntehryrovannym navyhatsyonnym systemam. Sankt-P.: Hosudarstvennyy nauchnyy tsentr Rosyyskoy Federatsyy-TSNYY ÉlektropryborÂť, 1996, 218. (In Russian). 56\7 _ 3 Âť >+!+ & 1+ƒ+ ‡` ( & nastroyuvanyy hiroskop dlya vykorystannya v yakosti hravimetra“, Materialy chetvertoyi naukovo-tekhnichnoyi konferentsiyi „Pryladobuduvannya 2005: stan i perspektyvyâ€?, Kyyiv, 2005, 134–135. (In Ukrainian). 5667 E3 Âť 3 3 ÂżB6@\<6 W \6ƒ @~\\+ ^ ‡_ Âť 3 & 3x 6Z@6 ÂżB\+ /1 Ukrainian). [12] Odyntsov A.A., Dynamychesky nastrayvaemye hyroskopy: Uchebnoe posobye. – K.: KPY, 1982, 68. (In Ukrainian). [13] 5 # Y Y8# # 8 Z Y :5 : 4Y 5nyk, ed. by: E.S. Polishchuka,@ BHKVK @ XYZ\^@ V`a@ & a@' . (In Ukrainian). [14] Pavlovskyy M.A., Teoryya hyroskopov. - K.: Vyshcha. shk., 1986, 303. 56X7 q Âť & |+!+ ! & _+`+ # !+"+ Tsyfrovaya obrabotka syhanalov: Uchebnoe posobye dlya vuzov 3 Âť 6ZZ\ <X[+ /1 Ukrainian). 56[7 _ 3 Ă€+ ‡E (' & * roscopic gravimeter measurement errorsâ€?. In:

Y Y 5 Y Y 9 Y ference Mechanics 2004, Rzeszow University of Technology, Poland, 2004, 21–28.

Torge, W., Gravimeter, Walter de Gruyter: New York, NY, USA, 1989. Taylor B. N., Guide for the Use of the International System of Units (SI), NIST Special Publication 811, Appendix B, 1995 . Seigel H.O., A Guide to High Precision Land Gravimeter Surveys, Scintrex Limited: Concord, Canada, 1995. Huang Y., et al., “SGA-WZ: A New Strapdown Airborne Gravimeterâ€?, Sensors, vol. 12, no.7, 2012, 9336-9348. DOI: 10.3390/s120709336. MartĂ­nez-Moreno F.J, et al., “Regional and residual anomaly separation in microgravity maps for cave detection: The case study of Gruta de las Maravillas (SW Spain)â€?, Journal of Applied Geophysics, vol. 114, 2015, 1–11. DOI: 10.1016/j.jappgeo.2015.01.001. Articles

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1UC@>B<CD?KNE9J?KD<DPECFE:C?@6/K<JDBJME#CGG>D<L?B<CDE0BK?BJP<J=EE <DE >@B<6 PJDBE0N=BJG=E Submitted: 8 April 2015; Accepted 28 May

Alhanoof Althnian, Arvin Agah DOI: 10.14313/JAMRIS_3-2015/24 Previous studies in multi-agent systems have observed that varying the type of information that agents communicate, such as goals and beliefs, has a significant impact on the performance of the system with respect to different, usually conflicting, performance metrics, such as speed of solution, communication efficiency, and travel distance/cost. Therefore, when designing a communication strategy for a multi-agent system, it is unlikely that one strategy can perform well with respect to all of performance metrics. Yet, it is not clear in advance, which strategy will be the best with respect to each metric. With multi-agent systems being a common paradigm for building distributed systems in different domains, performance goals can vary from one application to the other according to the domain’s specifications and requirements. To address this issue, this work proposes a genetic algorithm-based approach for learning a goaloriented communication strategy. The approach enables learning an effective communication strategy with respect to flexible, user-defined measurable performance goals. The learned strategy will determine what, when, and to whom information should be communicated during the course of task execution in order to improve the performance of the system with respect to the stated goal. Our preliminary evaluation shows that the proposed approach has promising results and the learned strategies have significant usefulness in improving the performance of the system with respect to the goals.

Emulti-agent system, communication strategy, evolutionary communication, and genetic algorithms

E A number of research efforts investigated the importance of communication and its impact on the performance of multi-agent systems. Studies are usually conducted by varying communication conditions and testing the performance of the system. We consider the work in [1] and [19], where experiments were carried out to study the effect of communicating different types of information when agents are assigned different tasks. As shown in Figure 1.a, the process starts by manually determining the type of information that agents are allowed to communicate - i.e. none, only goals, only beliefs, or both. Then, the average performance of the system over multiple runs is measured with respect to different metrics such as 52

time to complete, interference, communication efficiency, and duplication of efforts. In their work, whenever agents are allowed to communicate information, they broadcast every value update once obtained. Authors concluded that varying the type of information that agents communicate can significantly affect the performance of the multi-agent system with respect to different metrics, especially if no implicit communication present. Moreover, their results showed that more communication does not always guarantee better performance. The latter conclusion has crucial implication. It indicates that even in applications where communication is free, the system designer should not allow full communication and assume that the system is performing at its best level. The progress that the work presented above made in understanding the impact of communication on MAS performance, together with the fact that system designers must choose a performance goal [1], motivated us to propose a genetic algorithm-based approach for learning a goal-oriented communication strategy. Therefore, rather than manually creating different communication conditions (as in Figure 1.a), the system designer can start from selecting his performance goal and feed it to the learning system. The system, then, learns a centralized goal-effective strategy that determines what information instances should be communicated during task execution, when, and to whom in order to achieve the best performance of the system with respect to the selected goal (see Figure 1.b). During task execution, agents execute the evolved strategy in a decentralized manner. At each time-step, each agent consults the strategy to decide whether it needs to communicate or not. Therefore, in this work, agents’ collective behavior, and hence performance, improves as a result of executing a goaloriented communication strategy, evolved offline by the GA. The goal of this work is to propose and preliminary test an evolutionary approach that automatically generates an effective communication strategy with respect to a user-defined performance goal in multi-agent systems. Our ultimate aim is to allow system designers to easily vary the goal and automatically obtain the corresponding communication strategy. Therefore, the system designer does not need to know or analyze the properties of each information instance and its effect on the performance goal of the system. This can eliminate a significant design task in developing a multi-agent system. Moreover, the proposed approach can assist system designers to find

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out the potentially best performance that the system can achieve with respect to a specific goal, such as the minimum time or energy that a task takes to be completed. Therefore, a system designer will be able to choose among the performance of the system with multiple communication strategies of varying goals and select the one that has the best fit to the system’s needs. A multi-agent version of the Wumpus World [16, 22] is used in this work as a testing domain for our approach, where a team of carriers and fighters cooperate to kill wumpuses and collect gold.

b)

Fig. 1. Reversal of the (a) communication-to-performance investigation process to obtain (b) performanceto-communication learning process The remainder of this paper is organized as follows. Section 2 briefly overviews related work. In section 3, we analyze the problem of designing a goaloriented communication strategy for a multi-agent system, and explain why it is a challenge to design one manually. The Wumpus World, our test domain, is explained in section 4. In section 5, we provide detailed information on how we utilize a genetic algorithm to design a learning system that automatically generates an effective goal-oriented communication strategy. We show, in section 6, promising results in preliminary experiments with two performance goals using the Wumpus World domain, and we finally conclude in section 7 and discuss future work.

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E E ) Given the impact of using an effective communication on MAS performance, it is not surprising that approaches for learning all aspects of communication, including language, protocols, and strategies, have been proposed in the literature. We focus in this section on existing work related to communication strategies, which help agents decide what, when, and to whom they communicate. The main contribution of this work is not only learning a communication strategy, but also learning communication strategies with respect to flexible goals. We refer to goals as the criteria or metrics used in the communication decision process to determine whether a specific communication act should take place. A rule of thumb is that information should be communicated only if doing so is beneficial to the system’s performance, [2]. Different metrics have been used in the literature to value communication decisions of agents. Examples include performance-based metrics such as minimum communication cost [10, 22], task progress [20], minimum time [8, 9], and avoiding coordination errors [14]. Also, information-based metrics have been used such as timeliness and relevance [22], information redundancy [6], and KL divergence [20]. As stated above, the advantage of this work over existing ones is that it is designed with no assumptions about the desired system’s performance. Therefore, system designers have the ability to design their own metric, with which they would like to improve the system’s performance. Communication decisions in cooperative MAS can be either centralized, where a coordinator agent that has a full observation of the global state compute a central strategy, or decentralized, where each agent with local observation compute its own strategy. In the latter case, however, cooperative agents need access to their teammates’ states and actions to be able to estimate the overall communication benefits, and hence make communication decisions. Therefore, researchers have designed different approaches to allow agents obtain such information. For example, [10] allowed agents to send feedback about the usefulness of the information they received to senders, [14] allowed agents to take actions based on shared information, and hence know the actions taken by the teammates, and [22] extended agents’ observability to enable agents to track team members’ mental states, and hence infer what teammates know and when. Based on the domain characteristics, some research efforts, such as [14, 15, 18, 20], proposed approaches based on modeling the team’s decision problem using variations of Markov Decision Process (MDP), such as Dec-MDP and Dec-POMDP, to enable agents to estimate the impact of communication, and hence compute their communication policies. The computation, however, is usually based on myopic assumptions, where each agent evaluates the benefit of communication in isolation for 1-step horizon assuming others never communicate. The work in [2, 4] proposed approaches that relax these assumptions, yielding better performance. As mentioned previously, the work presented in this paper addresses this issue by adaptArticles

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ing a centralized learning offline and distributed execution at runtime. Existing work based on MDP framework have proposed approaches to compute a communication policy online [20], offline [8], or in a hybrid manner [5], as part of the solution to the problem, in a centralized [3], distributed, and round-robin fashion [12]. Other efforts have proposed approaches to learning communication strategies include [10], where authors proposed a distributed probabilistic control system that observes the information entering and leaving an agent and learns the classes of information and communication frequency that are beneficial to the agent and its neighbors using their feedback. Moreover, the work in [7] introduces a Hierarchical Reinforcement Learning (HRL) algorithm to allow agents learn a hierarchical communication and action policy, where the main task is decomposed into cooperative and non-cooperative tasks and a communication task is added under each cooperative task. Using the algorithm, agents can decide when to communicate with other agents to obtain their actions. Moreover, reinforcement learning is used in [11] to allow agents learn action policies, which are extended to include communication by adding linguistic state variables in receivers’ state space and linguistic action variables to senders’ action space. Furthermore, [9] used Genetic Programming (GP) to evolve agents’ behavior, represented by parse trees, which include communication actions that enable an agent to request data from another. In research efforts, some researchers applied heuristics to allow agents to reason on-line about when and what to communicate. Examples include using hill-climbing heuristic to find out what information maximizes the expected reward [15]. Another work in [22] used implicit communication to allow agents reason about teammates’ needs and productions, and hence communicate proactively. Most of the works, presented above, address only part of the communication decisions in MAS. For example, [2, 4, 5, 6, 7, 9, 12, 14, 20] address only when agents communicate, [15] addresses what agents communicate, and [8, 11, 18, 22] address what and when agents communicate. Similar to our work, [10] addresses what, when, and to whom agents communicate. However, authors provided agents with only one timing strategy, which is frequency of communication, equivalent to one of our timing strategy, EveryTimeInterval, which will be explained in a later section.

E : 6/ E# E0 %

Results of the work in [19] imply that communicating each information instance that agents obtain during task execution affects the performance of the system with respect to multiple metrics. Therefore, depending on the desired performance goal, it may not be necessary to communicate all available information instances. If it is determined that one should be communicated, determining when (timing) and to whom (recipients) becomes essential as communication incurs cost. 54

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Therefore, it is crucial to consider designing a communication strategy for each information instance. Moreover, if there are multiple types of agents in the system, a separate communication strategy should be designed for each information instance and a recipient type combination. To explain this, consider our test domain, the Wumpus World, where a team of carriers and fighters cooperates to collect gold and kill wumpuses, where carriers are responsible of collecting gold, and fighters kill wumpuses. In this domain, the “wumpus location� information instance means danger to carriers and a spot they should keep themselves away from, while, to fighters, this information means a target and a place that they should run to in order to kill the wumpus and help carriers collect gold in the same location. Moreover, some information instance might be important to only carriers or fighters. For example, “gold location� is only important to carriers. Consequently, the system’s designer must keep in mind the properties of each information instance and how it can possibly affect the performance of each agent type and hence the overall performance. what who

k IS = {ISi k}

In this work, we formulate the communication decisions problem to learning the communication patterns that improve the system performance with respect to flexible, user-defined goals. It is assumed that for each Information instance (ISi), there are n alternatives for when it can be communicated, and m alternatives for who it can be communicated to. Therefore, the total number of Communication Strategies (CommSt) for ISi is computed by: CommSt (ISi) = (n*m

when who k c TotalCommSt = (n*m )k*c

(2)

The total number of possible communication strategies increases exponentially with the number of information instances k and number of agents’ types c. Besides, due to the randomness in multiagent systems, it is usually not clear upfront which communication strategy will be effective with respect to the task and performance goal [1, 12], and it is difficult and time-consuming to manually try all possible communication strategies. Yet, combinations of different sub-strategies for each information instance may result in unexpected performance. This calls for an automated approach for determining an effective communication strategy with respect to a stated performance goal, which is proposed in this paper. We as-

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sume that a communication language already exists, and communication is always reliable.

" E 33 E We have designed and built a multi-agent version of the Wumpus World Problem [16, 22] to use as our test domain. This is done using the Repast Symphony plugin for Eclipse [13], which is an open source Javabased agents modeling and simulation toolkit. We designed the world of our domain to contain several rooms that contain gold and wumpuses. This new feature in the domain allows having multiple different beliefs and goals that provide variety of information instances, which adds a key property that makes it effective for evaluating communication strategies. The considered information instances along with their values are listed in Table 1, and will be explained throughout this section. Our world consists of 12 rooms in a 140x140 grid. One room is the drop-off room, where agents have to drop any gold that they collect, and others either contain gold and/or wumpuses or are empty. Figure 2 shows a screenshot of our world. The long-term goal of the team, carriers and fighters, is to kill wumpuses and collect gold. In our experiments, the world contains 5 carriers, 3 fighters, 5 wumpuses, and 10 pieces of gold, all of which distributed randomly at the beginning of each simulation. Carriers have the information about rooms’ locations, but not their contents. Carriers are capable of finding gold and wumpuses, picking up and dropping off gold, while fighters are capable of shooting wumpuses. Similar to [22], the only way that fighters can know about the location of a wumpus is by getting a message from a carrier that observed it (Wumpus location IS4). When a wumpus is killed, carriers who observed it can determine that the wumpus is dead and the room is safe only by getting a message (Safe room IS8) from the fighter who killed it. In order to facilitate the achievement of the longterm goal and enhance collaboration, each agent also has a short-term goal. Carriers’ and fighters’ goals are listed in Table 1. Initially, all carriers have the “ExploreRoomâ€? goal, and have to decide on a goal room. Each carrier can only hold one piece of gold at a time. Therefore, once a carrier picks up gold, its goal will be “DropOffGoldâ€? as it must go to the drop-off room and drop the gold there. Carriers and fighters states, Sc and Sf, respectively, are defined as follows: Sc = {(s1, s2)} S _= {s1 1, s2 = {0, 1, f}. 1 location, whether inside a room (1), in the hallway (0), or dis * /Ă 0+ E & *& * * & room that they are in, this is abstracted in the state to only three cases to deliver a coherent choice to when an agent can communicate, as we will explain in the timing strategies section. The second element s2 indicates the carrier’s possession of gold, whether it holds * /60 & * /\0 * /Ă 0+

Fig. 2. Screenshot of the Wumpus World

At each time-step, every agent performs (observe, communicate, act) execution cycle. In observe, agents are able to make the observations {IS3, IS4, IS5, IS8}, in Table 1, as well as deciding on a goal room or change goal. In the communicate step, agents refer to their communication strategy to see if they should communicate any information at the current timestep. In the act step, both agent types are able to move UP, DOWN, RIGHT, and LEFT. In addition, carriers are #1U 2# ` ># >44 * : *& able to SHOOT a wumpus. Moreover, each agent maintains a mental model about other agents by communicating goals and goal rooms, if allowed by the assigned communication strategy. The behavior of agents, both carriers and : *& (( 8 • A carrier will choose the closest room that contains gold. If it has no information about gold locations, it will choose the closest room it has never visited to explore. • When a carrier decides to go to a room, which it knows nothing about the content, the carrier must explore the room. • A carrier will not explore a room that is currently being explored by another carrier, unless it has no other options. • If a carrier knows that a room contains gold, it will not need to explore the room; instead the carrier will target the gold and collect it. • A carrier will avoid empty room. • A carrier will escape the room once it observes a wumpus. • A carrier will avoid wumpus rooms unless it receives information that the wumpus is killed, or a carrier tells the agent that it contains gold, which implies that the sender was able to explore the room, and hence the wumpus is killed. • A carrier will choose a different goal room if it receives information that its goal room is empty/ has a wumpus while the agent is moving to it. • Fighters do not move unless they receive information about a wumpus location. • If a fighter receives multiple requests, it will choose the closest one. • A fighter will choose a different wumpus/stay still if it receives information that another fighter has killed the wumpus that the agent is going to kill. Articles

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' E % E 33 We use a steady state Genetic Algorithm (GA) to evolve goal-oriented communication strategies in a multi-agent system. GA is a model of machine learning that simulates the natural phenomenon of evolution. Starting with a number of random solutions for the problem, GA mimics natural selection by favoring fit solutions in selecting parents for producing offsprings. Once parents are selected, crossover and mutation operations are applied and new offsprings are placed in population to form the next generation. This process continues until a termination condition is met. Although GA is not guaranteed to find optimal solutions, it has been successfully applied to problems in different application domains to find near-optimal solutions. $ E T E;

T

Goal (IS1)

“ExploreRoom�, “PickUpGold�, j nqs tuqv^w

Carrier

Goal Room (IS2)

[1-12]

Carrier

uqv^@Bq{|}q~@ #3)

(x,y), 140 > x,y > 0

Carrier

 Â‚s Y@Bq{|}q~@ (IS4)

(x,y), 140 > x,y > 0

Carrier

Empty Room (IS5)

„&% &…@ @VY@^nqs%qt@nqq‚† Carrier

Goal (IS6)

“LookForWumpus�, “KillWumpus�

Goal Room (IS7)

„&% &…@ @VY@^nqs%qt@nqq‚† Fighter

Safe Room (IS8)

„&% &…@ @VY@^nqs%qt@nqq‚† Fighter

Fighter

Table 1. Information instances of the Wumpus World and their values

) ;

2

ISi

[1, k]

k @~ ‚�Xn@q�@V~�qn‚|}q~@ V~Y`|~{XY@V~@`‘X@^q‚|V~

RT

[1, c]

c:@~ ‚�Xn@q�@|’X~`Y“@ `\sXY@V~@`‘X@^q‚|V~

R

P2P (1), # �YX`@„&a@ n-1)], Broadcast (n)

n @`q`|v@~ ‚�Xn@q�@|’X~`Y

T

EveryUpdate (1), –KXn\)V‚X ~`XnK|v@„&a@i], ~#`|`X@„ i+1), (i+s)]

i @‚|˜V‚ ‚@}‚X@V~`XnK|v s @~ ‚�Xn@q�@sqYYV�vX@ |’X~`Y“@Y`|`XY

Table 2. Possible values for each token in a cell/communication strategy The key elements required to apply GA to a problem are to seek a suitable coding for the solution individual (chromosome), to design a fitness function to evaluate solution candidates, and to determine a termination condition. Other parameters such as crossover rate, mutation rate, selection approach, and replacement approach need to be tuned to improve the performance of the algorithm. 56

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The proposed evolutionary approach determines a communication strategy for each information instance, whether goal or observation, that could be obtained by any agent during task execution. Hence, the evolved strategy will consist of a set of sub-strategies for the communicated information instances.

' E0 E 3 Each individual in GA population represents a solution candidate, and in our case, a goal-oriented communication strategy. An individual is made of a vector of cells. We define a cell to be a 4-tuple vector: (ISi, RT, R, T). A cell represents a communication strategy for one information instance. It indicates that an information instance ISi should be communicated to agents R of type RT only at time-steps that conform to T. The possible values that each token can take are listed in Table 2 and explained below. Individuals in a GA population have different lengths because the number of cells in an individual may differ. This is due to the fact that an individual contains only cells corresponding to communication strategies for information instances that should be communicated. If an information instance should not be communicated, it will not be included in the evolved individual. This flexibility allows learning what information instances should be communicated, and hence keeps the communication cost minimum by evolving a strategy that communicates only information instances that contribute to the performance goal. An example of GA individual, i.e. goaloriented communication strategy is shown in Figure 3. 5.1.1 Recipients Strategies The recipients type RT and recipients R in a cell define who an information instance IS should be sent to. The former defines, as the name indicates, the receiving agents type, which in our case takes two values; either carriers or fighters, and the later determines the number of recipients of type RT, which can be (1) Peer-to-Peer, (2) Broadcast, or (3) Subset.

Figure 3: An example of a GA individual (goal-oriented communication strategy) The first strategy, Peer-to-Peer (P2P), allows sending the information to only the closest agent of type RT to the sender, and Broadcast allows sending the information to all agents of type RT. However, Subset allows sending the information to the closest m agents of type RT, where m is the number of recipients, and whose value is evolved by GA (see Figure 4). As explained in a previous section, it is important to determine whether an information instance should be communicated to both carriers and fighters, or only one type. If one information instance (ISi) is communicated to both types, there will be two cells for ISi in an individual, each corresponding to one type of recipients. So with this solution representation, GA will be able to evolve a communication strategy that allows communicating information instances to only

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Figure 4: Recipients strategies

those agents that make use of it. Individuals that contain two cells for the same information instance and same recipients’ type need to go through correction for duplication elimination, which will be explained in details in a later section. 5.1.2 Timing Strategies The last token in a GA individual cell is T, which corresponds to time or when an information instance should be communicated. It determines the timesteps at which an agent is allowed to communicate the information instance. In this work, we consider three strategies for the ‘when’ component. Agents are able to communicate an information instance (1) every update, (2) every time interval, or (3) in a state. Graphical illustration of all timing strategies is shown in Figure 5, which we will refer to frequently in this section. The gray arrow represents the time line of one agent, and blue and red dots represent the timesteps at which communication is allowed or not, respectively.

Figure 5: Timing strategies

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Before we explain these time strategies, we need to distinguish between two types of information instances; (1) single-value and (2) multi-value information instances. The single-value instances are those that, at any time-step, an agent is allowed to have only one value of them, while the multi-value, an agent can possess multiple values of the same information instance. Examples of the single-value are ‘goal’ and ‘goal room’, since an agent can have only one goal and one goal room at any point of time. While “wumpus location” and “gold location” are considered multi-value since an agent may have a list of all locations where it observed wumpuses or gold. As shown in Figure 5, with the first timing strategy, every update, agents are allowed to communicate at all time-steps (all blue dots). Therefore, agents communicate value updates at the same time-step that they obtain them, and hence communicate every value update. If the information instance is single-value, an agent will communicate the information instance every time-step the agent updates it with a different value. If the information instance is multi-value, then whenever a new value is added to the values of the information instance, the agent will communicate only this new value. This strategy is idle for information instances that need immediate response or reaction from others or when lateness is not tolerated. With the second strategy, every time interval, agents have to wait a specific period of time before they are allowed to communicate a value of the information instance. For this time strategy, GA evolves how often agents are allowed to communicate. For instance, if T=3, agents are allowed to communicate this information every 3 time-steps. If the information instance is single-value, an agent will check every 3 time-steps to see if the information instance’s value has been updated since the last time the agent communicated it. If an agent updates its value more than once since the last communication only the last update will be communicated, as shown in Figure 5, green value is not communicated but orange value is communicated. However, if the information instance is multi-value, an agent will check every 3 time-steps to see if it has obtained and added any new value to the values list. All new added values for this information instance will be communicated, and hence both green and orange values are communicated in Figure 5. This strategy is more energy efficient than the previous one because it allows agents to combine multiple values in one message. The possible Articles

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time interval values are determined by the system designer. In this work, we allow time intervals in the range [2, 10]. " s,

s2, i.e.

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cells corresponding to sub-strategies for different information instances, a special crossover operator that swaps a subset of cells between two parents is needed. Allowing crossover point to only take place between cells and never divide a cell can enforce this (see Figure 6). This special crossover operator has been used previously in another work [21], where a cells-like GA individual representation has been used. This has the advantage of producing valid offsprings, as well as preserving GA’s property of maintaining and using successful cells, a.k.a., sub-solutions or sub-strategies, found in previous generations as a building block to discover new valid solutions. In this work, we use one-point crossover, where the crossover point is randomly chosen for each parent. Figure 6 shows an example of two parents going through crossover. 5.3.2. Mutation When two offsprings are produced after crossover, they go through mutation. While crossover helps GA exploit the good solutions found so far, mutation makes sure that GA explores new solutions. In this work, mutation rate is the probability that one element of a cell will be changed.

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5.3.3. Selection Selection in GA corresponds to the criteria to select two parents from the population to produce new offsprings. In this paper, roulette wheel selection is adopted as our selection method. It is a fitness proportionate selection method, in which fitted individuals are more likely to be chosen to produce new offsprings, since they have more potential to produce highly fitted individuals. 5.3.4. Replacement

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2 { |} ~ } Y Where, |: is weight for time metric. : is weight for number of messages metric, where =1-|. The values of the two parameters can be adjusted according to the importance of the associated metrics. For instance, if the two metrics are of equal priority, | can be assigned the value of 0.5. However, if time is more important, then more weight can be added to | such as (|, )=(0.6, 0.4) or (|, )=(0.7, 0.3) based on the designer’s goals.

' E: E/3 5.3.1. Crossover Since each solution candidate consists of multiple 58

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Figure 6: Crossover and correction operations

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7

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A number of GA parameters were assigned values (Table 3), which were empirically found to be effective. Our test domain was set to run until the agents finish the task, i.e., kill wumpuses and collect all the gold present in the environment, or when 2000 timesteps pass by, whichever occurs first. We observed that if the agents could not finish the task in 1400 time-steps, then they would not be able to finish it, and hence 2000 was set up as a maximum time. Minimum amount of communication is required to enable agents to finish the task. Since the only way that fighters can kill wumpuses is to get information from carriers about the wumpuses’ locations, a complete communication strategy has to include a communication strategy for the ‘Wumpus Location’ information instance with fighters as the recipients’ type. No matter how good a communication strategy is with respect to the performance goal, without enabling agents to finish the task, the system will run for a long time and the strategy will receive a bad fitness score. Therefore, in efforts to speed up GA convergence, we decided to provide carriers with a default communication strategy for communicating the “Wumpus Location� information instance to fighters. Hence, during learning, if the communication strategy being evaluated does not include a sub-strategy for communicating the “Wumpus Location� to fighters (referred to incomplete strategies), carriers will use their default strategy to enforce communicating this information instance, along with strategy being evaluated, in order to allow agents finish the task. We emphasize that strategies in GA population will not be altered or modified; rather their fitness score reflect their complete counterpart. Consequently, GA will be able to make use of good but incomplete strategies. During learning, if the communication strategy being evaluated is complete, that is it includes a sub-strategy for communicating the “Wumpus Location� to fighters, carriers will use the provided strategy for this information instance, rather than the default one. After multiple experiments, we determined that the communication strategy for the ‘Wumpus Location’ information instance that has minimum number of messages sent is ‘communicate every update of the information instance to fighters as P2P’. Although the used when strategy, i.e. every update, sends each wumpus observation in a separate message, we found out that delaying communication will make more carriers exposed to the wumpuses, and hence more messages for the same wumpus will be sent to fighters. Figure 7 shows the evolution of time-minimal and energy-minimal communication strategies for the wumpus world domain. The GA termination condition is when a predetermined number of generations, g=100, pass by without improvement in the average population fitness. Our intuition is that as long as GA is able to improve the average fitness of the population by performing crossover and mutation, it is likely that the so-far-best solution will be improved in a future generation. The top line in the Figure shows the fitness value of the worst individual in the population of each genArticles

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Figure 7. Evolution of (a) Energy-Minimal and (b) Time-Minimal communication strategies

eration. The lines in the middle and bottom show the average fitness value and the best fitness in the population of each generation, respectively. A somewhat surprising observation in both figures is that although all communication strategies include the minimum required communication for finishing the task, agents were still unable to finish the task using some communication strategies. This can be seen in Figure 7.b as the worst individual has fitness value of 2000 in the first generation, which is the maximum time the simulation can run. After some investigation of such communication strategies, we learned that some combinations of communication sub-strategies could prevent agents from finishing the task. An example of such strategies is when a carrier broadcasts the location of an observed wumpus to other carriers and communicates it to fighters using any strategy, but concurrently fighters do not communicate the news about killed wumpus. Therefore, the room that contained the wumpus will never be visited by carriers since they all were warned about it but never told about being a safe room. Table 4 shows the evolved communication strategies. Each row corresponds to the communication strategy of one information instance. The column to the left lists all information instances that we consider, and for each we show the learned timing (Â 5 and recipients (Â 5 strategies for each recipient type of carriers and fighters, if applicable. Columns to the right correspond to the learned energy-minimal and time-minimal communication strategies. It is clear that the time-minimal strategy communicates more information than the energy-minimal strategy. This is due to the fact that the fitness function for evolving the time-minimal strategy considers only the number of time-steps that the agents need to complete the task. Therefore, strategies that enable agents to complete the task faster are always favored 60

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no matter how much they cost. The time-minimal strategy communicates all information instances that the energy-minimal strategy communicates but to more receivers, as can be seen in IS2 and IS4. The energy-minimal strategy communicates the carriers’ goal room as P2P every five time-steps, but does not communicate carriers’ goal at all. Since initially all carriers have the ‘ExploreRoom’ goal and each carrier knows that others have this goal in their mental model, not communicating any update of the goal will make each carrier believe that others always have ‘ExploreRoom’ goal. A carrier will not explore a room that is currently explored by another carrier, hence, with this communication strategy, a carrier will never explore a room that is currently explored or even visited by another carrier to pick up gold. It is surprising that GA has enforced such behavior that was not originally implemented in carriers. We believe that the reason for evolving such strategy is because the world has 12 rooms but only 10 pieces of gold; hence each room is more likely to have a small number of gold, usually one, or empty. Bearing this mind, along with the fact that exploring a room takes time and energy, it is probably time and energy efficient to avoid exploring a room that others are exploring or picking gold from. More experiments with larger number of gold will be conducted in the future to observe if such behavior will still evolve. As expected, the time-minimal communication strategy includes strategies for communicating some useless information instances to the recipients (shaded cells) such as sending locations of gold to fighters. Communicating such information only increases the number of messages sent, without affecting the recipients’ behavior or the overall performance with respect to other metrics. Existence of such information instances in the evolved strategy is expected be-

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cause it complies with the fitness function that only considers time. Therefore, two strategies that allow completing the task with minimum time will have the same fitness value, even if one can achieve this with less communication. Figure 8 compares the performances of the multiagent system with the two evolved communication strategies; MinTime and MinEnergy, as well as the minimum and maximum communication strategies, MinComm and MaxComm, respectively. This should give the big picture and enable us to see how the evolved strategies compare to the two communication extremes. As mentioned previously, minimum communication strategy allows only communicating every update of the wumpus location to fighters as P2P, which is the strategy with minimum number of messages that enables agents to complete the task, while maximum communication strategy broadcasts every update of all information instances to both agents’ types. The following performance metrics are considered: ƒ Energy: Measures the total energy consumed by all agents to finish the task. This performance metric can be used if the user needs the task to be completed with minimum energy cost. ƒ Time: Measures the number of time-steps needed to complete the task. The task is determined completed when the last gold piece in the environment is picked up. This metric can be used if the user needs the task to be completed as fast as possible. ƒ Moves: Measures the number of moves of all agents until the task is complete. A move is defined as changing position. This metric can be used

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if the user needs the task to be completed with minimum travel cost/distance. ƒ Messages: Measures the number of messages exchanged until the task is completed. ƒ Energy Variance: Measures the variance of n numbers; where n is the number of agents in the world. Each number represents the amount of energy consumed by one agent. This performance metric can be used if the user needs the task to be completed with minimum energy variance. The lower the variance the closer the amount of energy consumed across all agents. ƒ Load Variance: Load is the amount of work each agent has completed. In Multi-agent systems, it is important to distribute the load evenly among agents with no overloaded/idle agents. This performance metric can be used if the user needs the task to be completed with maximum load balance/minimum load variance. The lower the variance, the more balanced the load is across the agents. o Carriers Load Variance: Measures the variance of n numbers; where n is the number of carriers in the domain. Each number represents the amount of gold picked up by one carrier. o Fighters Load Variance: Measures the variance of m numbers, where m is the number of fighters in the domain. Each number represents the number of wumpuses killed by one fighter. ƒ Work Duplication: Work duplication occurs when two agents target the same goal at the same time.

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Table 4. Evolved goal-oriented communication strategies Articles

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Figure 8. System’s performance with different communication strategies

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o Carrier: Number of times two or more carriers explored a room at the same time and number of times a carrier fails to pick up gold because someone else has already collected it. o Fighters: Number of times two or more fighters target the same wumpus. With maximum communication, agents have a full observation of the world, which allows them to cooperate maximally and make the best decisions. This behavior is reflected in minimum time, energy variance, and load variance, as shown in Figure 8, comparing to other strategies. However, the system did not perform the best with respect to energy, moves, and work duplication, which confirms the conclusion of previous studies that more communication does not guarantee better performance [19]. Energy-minimal communication strategy consumes the minimum amount of energy, compared to other strategies, followed by time-minimal strategy, and then maximum communication strategy, while minimum communication strategy has the highest energy consumption. With only minimum communication, agents cooperate minimally, and hence each agent depends only on its own view of the world, which results in significantly longer time to complete the task, large number of moves, and high work duplication, energy variance, and load variance as can be seen in Figure 8. Comparing to other strategies, the system has the worst performance with the minimum communication strategy, with respect to all metrics except messages. It is not surprising that the energy-minimal and time-minimal strategies have the same performance with respect to time (Figure 8.b). When GA evolves for minimum energy, it implicitly evolves for minimum time since more time always means more energy consumption, but the opposite is not always true, thus the time-minimal strategy consumes more energy (Figure 8.a) due to more moves (Figure 8.c) and communication (Figure 8.d). Both time-minimal and energy-minimal strategies have the same performance with respect to time as the maximum communication strategy, which makes us believe that the GA was able to find the minimum time to complete the task, and hence optimal timeminimal strategy. Moreover, the energy-minimal strategy has the second lowest number of messages after the minimum communication strategy. Yet, it improves the system performance significantly over minimum communication strategy with respect to all other metrics, including energy. In this case, GA was able to evolve a strategy that communicates only the right amount of important information that significantly contributes to improving the performance goal. However, the energy-minimal strategy does not offer the best performance with respect to energy variance and load variance, although it has the next best energy variance after maximum communication strategy. We believe that this is due to the fact that these two metrics conflicts with the goal (i.e. energy metric) since they require more messages to be communicated. For example, the energy-minimal strategy does not allow agents to communicate information about the state of the world (i.e. gold and safe rooms).

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Agents with both maximum and time-minimal communication strategies share their goal and goal room, which helps carriers not to explore a room currently explored by another carrier, hence lower work duplication than minimum communication. However, agents with energy-minimal strategy share only their goal room, which makes agents not to explore a room currently explored or visited by another carrier to pick up gold. Therefore agents have the lowest work duplication amongst all strategies. Furthermore, since the time-minimal strategy includes communicating more information about the state of the world (gold and safe rooms) over energy-minimal strategy. This results in the agents sharing the same belief about the state of the world, which provides all the agents the same opportunity to collect gold, as can be seen in the low load variance (almost as low as maximum communication).

* E# We proposed a GA-based approach for learning an effective goal-oriented communication strategy in multi-agent systems. The usefulness of the proposed approach lies in the fact that it removes a significant designing load from system designers since they do not need prior knowledge about the connection between communicating an information instance and the system performance. The learned communication strategy is a comprehensive one that determines what, when, and to whom agents communicate. We ran preliminary experiments with two performance goals; namely, total energy consumed and time to complete. The results obtained are quite promising and satisfactory, and indicate that the proposed approach has great potential. We observed that, on one hand, evolving an energy-minimal communication strategy implicitly minimizes the number of messages sent, time to complete, number of moves, and work duplication, because they all cost energy and any increase in them increases total energy. On the other hand, evolving time-minimal strategy allows communicating more information, which enhances cooperation that is reflected as low moves, load variance, and work duplication as the maximum communication strategy. There are numerous experiments that we are interested in running with variations of the performance goal and task’s parameters. Next, we aim to examine our approach with other fitness functions and varying goals’ weights. Furthermore, there are multiple parameters that we wish to tune and study their effects on the evolved communication strategies, and hence the system’s performance. Most of these parameters are domain-dependent, as they meant to create variations of the same problem/task. Broadly speaking, we are interested in studying three types of parameters; action and communication costs, agents population, and task complexity. # 2/ 91 :1 12 Althnian would like to acknowledge King Saud University for the scholarship support. Articles

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- ./ 0 Alhanoof Althnian * – Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, Kansas, USA. E-mail: alhanoof@ku.edu Arvin Agah – Department of Electrical Engineering and Computer Science, University of Kansas, Lawrence, Kansas, USA. E-mail: agah@ku.edu * Corresponding author

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Balch T., Arkin R. C. “Communication in Reactive Multiagent Robotic Systems�, Autonomous Robots, Volume 1, 1994, 27-52. DOI: 10.1007/ BF00735341. Becker Raphen, et al., “Analyzing myopic approaches for multi-agent communication�, Computational Intelligence, vol. 25, no. 1, 2009, 31-50. DOI: 10.1111/j.1467-8640.2008.01329.x. Boutilier C., “Sequential optimality and coordination in multiagent systems �, IJCAI, vol. 99, 1999. Carlin A., Zilberstein S., “Myopic and non-myopic communication under partial observability�, Web Intelligence and Intelligent Agent Technologies, 2009. WI-IAT’09. IEEE/WIC/ACM International Joint Conferences on, vol. 2, IET, 2009. DOI: 10.1109/WI-IAT.2009.174. Chakraborty D., Sen S., “Computing effective communication policies in multiagent systems�. In: Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems, 2007, 36. DOI: 10.1145/1329125.1329168. Dutta P. S., Goldman C. V., Jennings N.R. “Communicating effectively in resourceconstrained multi-agent systems�. In: IJCAI, 2007, 1269–1274. Ghavamzadeh M., Mahadevan S., “Learning to communicate and act using hierarchical reinforcement learning�. In: Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, vol. 3, 2004, 1114–1121. Goldman C. V., Zilberstein S., “Optimizing information exchange in cooperative multiagent systems�. In: Proceedings of the second international joint conference on Autonomous agents and multiagent systems, 2003, 137–144. DOI: 10.1145/860575.860598. Iba H., Nozoe T., Ueda, K., “Evolving communicating agents based on genetic programming�. In: IEEE International Conference on Evolutionary Computation, 1997, 297-302. DOI: 10.1109/ICEC.1997.592321. Kinney M., Tsatsoulis C., “Learning communication strategies in multiagent systems�, Applied intelligence, vol. 9, no. 1, 1998,

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71–91. DOI: 10.1023/A:1008251315338. “ �. In: 3 [12] Melo F.S., Spaan M.T., “A POMDP-based Model for Optimizing Communication in Multiagent Systems�. In: Proc. 1st Eur. Workshop on Multiagent Systems, 2011. [13] North M.J., T.R. Howe, N.T. Collier, Vos R.J., “The Repast Simphony Runtime System�. In: Proceedings of the Agent 2005 Conference on Generative Social Processes, Models, and Mechanisms, 2005. [14] Roth, M., Simmons, R., & Veloso, M. “Reasoning about joint beliefs for execution-time communication decisions�. In Proceedings of the fourth international joint conference on Autonomous agents and multi-agent systems, 2005, pp. 786-793. DOI: 10.1145/1082473.1082593. [15] Roth M., Simmons R., Veloso M., “What to communicate? Execution-time decision in multiagent POMDPs�. In: Distributed Autonomous Robotic Systems 7, 2006, 177–186. DOI: 10.1007/4-431-35881-1_18. [16] Russell S., Norvig P., 9 Y 4Y A modern approach, Prentice-Hall: Egnlewood Cliffs, 1995. [17] Thierens D., “Selection schemes, elitist recombination, and selection intensity�. In: Proceedings of the 7th International Conference on Genetic Algorithms, 1997, 152–159. “ " . $ # . / �. In: 3 [19] Wei C., Hindricks K., Jonker C. M., “The Role of Communication in Coordination Protocols for Cooperative Robot Teams�. In: International Y Y Y Y 9 Y , 2014. DOI: 10.5220/0004758700280039. [20] Williamson S., Gerding E., Jennings N., A principled information valuation for communications during multi-agent coordination, 2008, 137–151. [21] Wu A. S., Yu H., Jin S., Lin K. C., Schiavone G., “An incremental genetic algorithm approach to multiprocessor scheduling�, IEEE Transactions on Parallel and Distributed Systems, vol. 15, no. 9, 2004, 824-834. DOI: 10.1109/TPDS.2004.38. [22] Zhang Y., “Observant and Proactive Communication in Multi-Agent Teamwork�. In: IEEE/WIC/ACM International Conference on Intelligent Agent Technology, 2006, 460-466. DOI: 10.1109/IAT.2006.97.

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TC@<=IE;JK=<CDECFEBIJE2JP?B<UJE BB<B>MJE CQ?KME CWCB=E0L?@JEv2 06T9Â… Submitted: 27th May 2015; accepted 14th June 2015

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DOI: 10.14313/JAMRIS_3-2015/25 Abstract: This paper presents the Polish adaptation of the Negative Attitude toward Robots Scale (NARS-PL), primarily created by Nomura et al. (2004). 213 individuals participated in the study (49 professionals and 164 nonprofessionals). The Polish version obtained satisfactory psychometric properties for a two-factor structure. Both subscales, the Negative Attitudes toward Robots that Display Human Traits (NARHT) and the Negative Attitudes toward Interactions with Robots (NATIR) possess good internal consistency. Effects of participant gender and robot’s appearance were found. Theory consistent relationships between attitude toward robots, belief in human nature uniqueness and robots’ human-likeness are discussed. Keywords: social robots, acceptance of robots, anthropomorphism, human uniqueness, human-robot interaction

1. Introduction Thanks to new technical solutions we are coming closer than ever before to integrating social robots into our daily life. Defined as physically embodied agents, social robots are created for human-machine peer-to-peer interaction [1]. They are designed to assist as partners in multiple duties, both at home and at work. User knowledge and attitude toward robots are essential factors in human-robot interaction (HRI) [2], [3]. A special scale, the Negative Attitude towards Robots Scale (NARS), was developed by Nomura, Kan ; 5?7 5X7 ( ' & * 3 ables possibly discouraging people from interacting with social robots. The main purpose of this paper is to present the Polish adaptation of NARS. The factorial structure of the scale was analyzed and compared to the Japanese original and the Portuguese version. The reliability of the emerged subscales (Negative Attitudes toward Robots that Display Human Traits and Negative Attitudes toward Interactions with Robots) was tested. Moreover, the relationships between NARS and related constructs (belief in human nature uniqueness and perceived anthropomorphism of robots) were investigated in order to assess the validity of the scale. The structure of this paper is as follows: Section 1 presents an in-depth overview of different scales and measures, i.e. the Negative Attitude toward Robots,

Belief in Human Nature Uniqueness, and Anthropomorphism scale. Section 2 describes the applied methods and procedure, i.e. modification of the scales, methods of statistical data analysis, and a description of robots used as target stimuli. Section 3 contains the obtained results. Finally, in Section 4 a brief discussion of the results and suggestions for further work are proposed.

1.1. The Negative Attitudes Towards Robots Scale (NARS) The scale [4] measures psychological reactions to humanlike and non-humanlike robots. The main focus is put on the extent to which one would be reluctant to interact with a robot. The original Japanese scale contains 14 items, ordered in three subscales: negative attitudes towards interacting with robots (NARS-interaction), towards the social influence of robots (NARS-Social Influence), and towards emotions in interaction with robots (NARS-Emotion). Satisfying levels of goodness-of-fit indices (GFI=.90, AGFI=.86, RMSEA=0.08, N=240) and Cronbach al'& /­+@@ +@= +[X "E ; 1 "E ; Social Influence, NARS-Emotion, respectively) were ( & 5X7+ The NARS scale has been used in numerous studies, measuring different dimensions of HumanRobot Interaction (HRI) like predicting verbal and behavioral reactions to social robots [6] or the effect of interacting with robots on attitudes towards 5@7+ ; ( & (' groups and cultures on attitude towards robots [8], [9], [10]. Although several attempts of translations were made, only a few studies reported the structural and psychometric properties of NARS. A thorough psychometrical analysis was provided in [11]. Authors used the English version of NARS with a sample of British students and university employees. Three ( /@ = 6?‚ (' % ?+0 & moved from the original scale due to inconsistency and the final three-factor structure differed from the original NARS. Piçarra, Giger, Pochwatko, & Gonçalves [12] carried out a series of four studies to validate the Portuguese version of NARS (PNARS), which showed significant differences from the Japanese scale. A confirmatory factor analysis demonstrated the two-factor structure: the Negative Attitudes to & ` ' q ( % /"E q% ÂŹ 65

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J J- J J J J J J J J J$ J" . . U1)%J JX U2)%J JX U3)

from .80 to .89) and the Negative Attitudes toward 1 & /"E%1  ( +@B +=X0 and reasonable goodness-of-fit indices (CFI=.93, EW41­+Z< !;]E­+\[X0+ %& #"E ; 12 items. Both the British and the Portuguese validations support the conclusion that various cultural variables (e.g. familiarity with the idea of robots) may be responsible for discrepancies between the Japanese and European factors structure [12].

1.2. Belief in Human Nature Uniqueness (BHNU) The essentialist belief that human nature is unique and that human beings share a deep underlying natural essence can influence attitudes toward robots and acceptance of robots as a social category. It has been shown that such psychological essentialism is associated with prejudice, perceived differences between groups, dispositional attributions, and justifying social inequalities [13]. People who believe that humans share a unique essence are more likely to hold stronger negative attitudes toward robots with human-like characteristics. Both BHNU and attitude (measured with NARS) are associated with the level of perceived anthropomorphism of so 56?7 56X7+ %& _q"2 9 3 * of responses to 6 items regarding essentialist beliefs (see Table 2). The higher the results, the stronger the belief in human nature’s uniqueness.

1.3. Anthropomorphism of Robots Epley, Waytz and Cacioppo [16] define anthropomorphism as the attribution of humanlike psychological traits, emotions, intentions, motivations and goals to non-human agents (robots in this case, but it refers also to avatars and agents in virtual environments). Those attributions are based on the robot’s behavior and the homocentric knowledge (i.e. self-knowledge and knowledge about other humans) that is accessible at the moment of judgment. The attribution of human characteristics to robots is considered to be crucial for the quality of HRI. Ex66

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pecting robots to behave in a human way is a good predictor of intention to cooperate with them.

2. Method 2.1. Participants Participants of a convenience sample (N=164) were recruited via ads placed in social networks, various Internet groups and discussion boards. A mailing list of participants of previous studies conducted in VRLAB IPPAS was also used. Additionally, a subsample of professionals (mainly engineers, working in area of robotics) was included (n=49). See Table 1 for the characteristics of the sample.

2.2. Materials The robots: Perceived anthropomorphism of social robots was primed with short movies presenting one of the robots we chose based on the objective level of human-likeness Starting with the lowest level – Care-o-bot (Fig. 1a) is a mobile assistant designed to support hu( 3 3 ( 56@7+ 1 3 ' in Germany by the Fraunhofer Institute for Manufacturing Engineering and Automation IPA. It has been experimentally used in homes and offices, hospitals and airports. It is wheel based, possesses two arms, and has a display with a pair of eyes (that are frequently replaced with necessary data, depending on the current activity). The medium level of human-likeness represents ASIMO /: *+ 6 0 ( 3 ' q Company, designed to be a multifunctional mobile assistant. It has the ability to understand voice commands and to respond in the same way, and it also recognizes faces. One of the applications is to help people who lack full mobility. 1) 2) 3)

Care-o-bot homepage: http://www.care-o-bot.de/ Asimo homepage: http://asimo.honda.com/ Actroid homepage: http://www.kokoro-dreams.co.jp/english/ rt_tokutyu/actroid.html

Journal of Automation, Mobile Robotics & Intelligent Systems

ACTROID (Fig. 1c) developed by Osaka University and manufactured by Kokoro Company Ltd., is a humanoid robot with the highest level of human-likeness [18]. It can mimic such lifelike functions as blinking, speaking, and breathing. The Actroid can also imitate human-like behavior with slight shifts in position, head and eye movements, and the appearance of breathing with its chest. It has been modelled after an average young woman. In our study, it is supposed to activate the highest level of anthropomorphism.

2.3. Measures

2015

Non-professionals

Professionals

Total

N

164

49

213

Age M(SD)

<Z 6\ /Z XB0

B\ B@ /6< ?\0

<Z B[ /6\ 6X0

Gender M/F/n.r.

XZ~@@~<=

21/14/14

80/91/42

Vocational school

3

–

3

High school

12

1

13

Student

X\

6@

[@

College

@6

6@

88

Humanities

30

1

31

Social sciences

24

3

<@

42

31

@B

13

–

13

3

–

3

24

–

24

Education

# :

2.4. Procedures An online study was conducted with the use of the GEX platform4). Participants were informed that no personal data are collected and that they can quit at any stage without consequences. After accepting an informed consent form and reading a brief instruction, participants watched a randomly selected movie presenting one of the three above mentioned robots. Care-o-bot, ASIMO, or Actroid introduced itself as an exemplar of a social robot. It then described its possible usage and functions. In each movie the same female voice recording was applied. After the movie participants responded to the NARS, BHNU, and Anthropomorphism questionnaires. In the last step the socio-demographic data were collected. After completing the task, participants were thanked for their contribution. www.gex.net.pl/vrlab/run/social_robot

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Table 1. Characteristics of the participants

NARS-PL: The English 14Engineering item version of NARS [4] was Life sciences translated to Polish. Participants ' * @ ' Arts /6 ^ * * @ ^ Other strongly agree). Belief in human nature uniqueness scale 56<7 56X78 E [ ( the extent to which humans reserve human nature for their own group and deny the possibility of a human + # ' ' @ ' /6 ^ * @ ^ * 0+ %& English version of the BHNU scale was translated to Polish by the authors. Level of anthropomorphism of robots: The Ep E U '' Ä 56@7 used to measure the level of anthropomorphism as a function of the robot’s appearance. It is a 14-item scale composed of three dimensions: the supportive anthropomorphic traits, the non-supportive anthropomorphic traits, and the behavioral traits. The scale was translated to Polish by the authors. Participants ' @ ' /6 ^ * @ ^ * 0+

4)

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2.5. Quality Indices Principal Components Factor Analysis – (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components [19]. Varimax rotation is an orthogonal rotation of the factor axes to maximize the variance of the squared loadings of a factor on all the variables in a factor matrix. Each factor will tend to have either large or small loadings of any particular variable [20]. Kaiser-Meyer-Olkin (KMO) is the measure of sampling adequacy. The test assesses the appropriateness of using factor analysis on data. Values over 0.8 are considered good [20]. Bartlett test of sphericity is another sampling adequacy measure applied together with factor analysis [20]. It tests the hypothesis that the correlation matrix is an identity matrix, which would indicate that variables are unrelated and therefore unsuitable for structure detection. It should be significant. Reliability Analysis in psychometrics refers to the overall consistency of a measure [20]. Highly reliable measures produce similar results under consistent conditions. One of the common methods of reliability testing is checking internal consistency of a measure. Cronbach’s alpha is a commonly used measure of internal consistency [21]. It is used to assess the consistency of results across items within a test. Values above 0.60 are acceptable for scientific uses of the 3 \+=X ' chological diagnosis. Validity analysis in psychometrics refers to the degree to which evidence and theory support the inArticles

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terpretations of test scores, referred to the proposed 5<67+ 1 * * ‚ many different methods are used. A usual practice is looking for predicted differences and correlations. In other words, if significant differences are observed between groups that are supposed to differ in a certain way, the test is valid [22].

9' X[+<=Ă… 3 + %& consistent with the Portuguese translation results (see Table 4 for details). Unfortunately, the original Japanese structure was not replicated. What is more, factors did not have any content coherence. A couple of items had high loadings in more than one factor. The third factor consisted of only one unique item (14) and all other 3. Results items had stronger loadings in the remaining two. The E& E0 E $E2 06T9 Scree plot suggested a possible two factor solution, All 14 items of the original NARS were used to conand these factors had low internal consistency (Cronduct principal components factor analysis with vari & '& +@@ +?Z ' 3 0+ 1 ( @ 6? max rotation. The Kaiser-Mayer-Olkin (KMO) meashowed very low item-total correlations. Additionally, sure of sampling adequacy reached the required level these items seem to be outdated or inadequate in our (.863), and Bartlett test of sphericity was significant conditions, and it is probable that item 14 is cultur(chi2­6\Z@+B6 ­Z6 '¡+\\60+ %& & ally biased due to the differences in the familiarity with the idea of robots in popuTable 2. English-Polish translation of the Belief in Human Nature Uniqueness Scale lar culture in both countries [12]. The Japanese are used to higher English version Polish version robots exposure and that might lead to a more complex cogniNawet najbardziej zaawansowany tive representation of robots and Even if ultra-sophisticated‌ technicznie: their future role in society than Europeans have. a robot will never be considered as * Æ Consistently with the Portu& ( *‚

+ guese version, it was decided to a robot will never feel the same * Æ ( 3 ( @ 6? emotions as a human being, ( Q Q + the analysis on the remaining 12 a robot will never use language in * Æ ' * items. The principal components & ( & ( *‚ Æ QÆ ( ( Q + analysis with varimax rotation met all minimal requirements a robot will always be a mechanical Æ ( QÇ / !>­+=[6‚ _  '¡+\\60+ ( & & ( *‚

+ The two obtained factors exa robot will never have * ' Ç ' XX+<ZÅ 3 + 4

‚ Ăˆ ( Ăˆ + tor loadings are presented in table 4 (compared with Portu * Æ ( a robot will never have morality. guese and Japanese solutions). ( Ăˆ + Polish and Portuguese factors are loaded with exactly same quesTable 3. English-Polish translation of the Anthropomorphism Scale tions, whereas Japanese subscale structure is substantially differSubscale English version Polish version ent. NATIR consists mostly of thoughtful ( questions loading Japanese S1 factor – negative attitude towards Supportive Anthropomorphic Traits considerate taktowna interaction with robots, but it sympathetic sympatyczna also includes two items from S2 factor – negative attitude towards devious ' * social influence of robots. NARHT embarrassable ' gathers all S3 items – negative Nonsupportive Anthropomorphic Traits attitude towards emotions in jealous zazdrosna interactions with robots and creative twĂłrcza those S1 and S2 items that refer to robots with human traits or aggressive agresywna humanlike functions.

Behavioral Traits

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agile

zwinna

active

aktywna

energetic

energiczna

fearful

strachliwa

lethargic

'

muscular

:

E E $E2 06T9 Differences between professional and non-professional samples were marginally significant /'­+\@0 & reasons (different experiences and knowledge about robots in particular and robotics in general)

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Table 4. Factor structure of NARS-PL (compared to Japanese and Portuguese versions) Polish factor loadings Item Original and translated item*** number

1

U / 0 ( Æ Q * ' Æ ( Q +

Japanese factor Label** loadings (subscales)*

Portugese factor loadings (subscales)**

1

2

0.331

\+@6=

NARHT

s2

NARHT

0.309

\+X?X

NARHT

s2

NARHT

\+X[=

\+?X?

NATIR

s3

NARHT

\+@Z[

\+6@=

NATIR

s1

NATIR

0.809

NARHT

s3

NARHT

\+=@

NARHT

s3

.NARHT

NATIR

s1

NATIR

I would feel uneasy if robots really had emotions. W ( * Ê Æ * + 2

Something bad might happen if robots developed into living beings. U / 0 ( Æ ( QÇ (+

3 I would feel relaxed talking with robots.

4

X

6

U / 0 ( Æ Q * ( / 0 ' Æ Q ( / 0 ( Ê + I would feel uneasy if I was given a job where I had to use robots. W ( Q ( * (~ ( * ( Æ ( ' Q Ë Ê+ If robots had emotions, I would be able to make friends with them. U / 0 ( Æ ' ' QÇ ( obdarzonymi emocjami.

0.106

I feel comforted being with robots that have emotions.

8

9

> / 0 ( Æ ĂŠ ( Ăˆ innych ludzi.

\+@Z6

I would feel nervous operating a robot in front of other people. " ' ( Æ ' ( Q Ăˆ * Q Ç & sytuacjach.

\+BX=

0.49

NARHT

s1

NARHT

\+@X6

\+6<@

NATIR

s1

NATIR

\+X6[

0.301

NATIR

s2

NATIR

0.629

0.428

NATIR

s1

NATIR

\+X<[

\+?XZ

NATIR

s2

NATIR

1 & & & : intelligences were making judgments about things.

10

11

` / 0 ( Æ * ( ( ÇÊ ' (+ I would feel very nervous just standing in front of a robot. ;Ç Æ * ( / 0 Æ

Ăˆ * ( * Æ ĂŠ+ I feel that if I depend on robots too much, something bad might happen. U / 0 ( Æ ( QÇ (+

12 I would feel paranoid talking with a robot.

13

> ( Æ ( * ( Ê ' dzieci. 1 ( & : on children.

* ' 8 ;68 * 3 & ‚ ;<8 * 3 : ‚ ;B8 * 3 ( & + ** # & # * 8 "E q%8 * 3 & & ( ‚ "E%1 8 * 3 attitude towards interaction with robots. *** ( 3 ( + @ ^ ‡; ‡ x ( x /ĂŒ%& ĂŒ x ( & * ( x0 6? ^ U QÆ ' Ăˆ ' Æ ( ' x /ĂŒ1 & & ( x+ Articles

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Fig. 2. Appearance of stimulus robot, participant sex, and expertise level differences in NARS-PL (non-professional sample=non-pro; professional sample=pro) and sample size differences we analyzed the results separately. Below, the results of a large non-professional sample are shown. The results of the professional sample are mentioned in some comparisons, when indicated. Both obtained subscales have good internal consistency. Cronbach’s alpha coefficients are .84 for "E%1 +@Z "E q%+

E; E $E2 06T9 Analysis of variance was conducted with NATIR and NARHT as dependent variables, and participants gender, expertise (professionals and non-professionals), BHNU (high or low, split based on median), and robot’s appearance (low, medium, high human-likeness) as independent factors. Expected differences were found for both NARS–PL subscales accounting for diagnostic and nomological validity (see fig. 2). There was a significant main effect of participant * /( & ( ' 3 & ( ‚ "E%1 '¡+\X‚ "E q% '­+\[X0 & ' als sample. What is more, a significant main effect of robot appearance was found in the professional sample (attitudes towards more anthropomorphic robots ( ' 3 ‚ "E%1 '¡+\6‚ "E q% '¡+\X0+ " interaction effects were found. A significant main effect of the Belief in human nature uniqueness scale was obtained. Participants scoring high in BHNU had significantly lower scores "E ; #| /"E%1 '¡+\\6‚ "E q% '¡+\\60+ 1 more visible for Actroid – a highly anthropomorphic robot. Correlations with BHNU were moderate * 3 /"E%1 ­ +BZ '¡+\\6‚ "E q% ­ +?= '¡+\\60+

4. Conclusions The preliminary study aimed at the adaptation of "E ; 5? X7 (' & #"E ; 56<7 showed that the Polish version of the scale consists of two subscales: 70

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1) The Negative Attitudes toward Interactions with Robots (NATIR), that encompasses the reac & ‚ 2) The Negative Attitudes toward Robots with Human Traits (NARHT), that captures the responses to robots that display human traits like emotions, language, and agency. This is consistent with PNARS structure and suggests that a cross-cultural study may be necessary. NARS-PL is both reliable and valid. High values of internal consistency indices for both subscales were obtained. Theory consistent associations with robot anthropomorphism ratings, participant sex, and their expertise level were also observed. Further studies showing the predictive validity of NARS and its applications to virtual reality agents and avatars are in progress. It is argued that NARS-PL is a useful tool to predict human responses to social robots in HRI studies in Poland. Limitations. One of the drawbacks is the sampling method used in the study. It is posible that it favours participants that have already more positive general attitudes toward technology or robots in particular. It also differs from methods used in the original and Portuguese studies. Replication on a broader sample is necessary. Another issue might be the subjective choice of robots used as attitude activation stimuli. They should represent three levels of human-likeness, but the differences are not only quantitative, but also, if not mainly, qualitative due to the fact that they were designed by different constructors. What is more, the used robots may not cover the full dimention of human-likeness. For example, Care-o-bot as representing low level of human-likeness posesses already quite a few human features. In future studies two solutions should be provided. First, using robots especially designed for the study, and differing minimally in attractiveness, size etc. Second, higher and lower levels of human-likeness could be introduced in the design, namely: very low level repre-

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sented by e.g. factory robots, and very high, not to say ideal level represented by humans themselves [23].

# 2/ 91 :1 12 0 This paper was partly financed by the Institute of Psychology PAS statutory fund. This paper was partially financed by the Foundation for Science and Technology (Portugal) through CIEO funding – PEst-OE/SADG/UI4020/2014.

AUTHORS Grzegorz Pochwatko* – Virtual Reality and Psychophysiology Lab, Institute of Psychology, Polish Acad ( ; \\ B@= # + E-mail: grzegorz.pochwatko@psych.pan.pl. Jean-Christophe Giger – Department of Psychology and Sciences of Education, University of Algarve and Research Centre for Spatial and Organizational Dynamics – CIEO. E-mail: jhgiger@ualg.pt. " # $ – Institute of Automatic Control and Robotics, Faculty of Mechatronics, Warsaw University of Technology, Warsaw, Poland. E-mail: k.kukielka@mchtr.pw.edu.pl. %$ " & – Virtual Reality and Psychophysiology Lab associate, Institute of Psychology, Polish E ( ; \\ B@= # + ] mail: jswidrak@psych.pan.pl. % $ ' " – Institute of Automatic Control and Robotics, Faculty of Mechatronics, Warsaw University of Technology, Warsaw, Poland. E-mail: j.mozaryn@mchtr.pw.edu.pl +' / ;< = $ – Institute of Automatic Control and Robotics, Faculty of Mechatronics, Warsaw University of Technology, Warsaw, Poland. E-mail: m.rozanska@mchtr.pw.edu.pl Nuno Piçarra – University of Algarve, Faro, Portugal. E-mail: nuno.psicologia@outlook.pt *Corresponding author

1&1 12#10 567 4 * %+ " & & 1+ ` & & + ‡E 3 3 x Robotics and Autonomous Systems, vol. 42, no. 3–4, 2003, 143–166. `>18 6\+6\6[~ \Z<6 ==Z\/\<0\\B@< 9+ 5<7 ( %+ + } ( ;+ xq the difference between users’ expectations and perceptions about a robotic agent affect their & 3 �x International Journal of Social Robotics, vol. 4, no. 2, 2012, 109–116. `>18 6\+6\\@~ 6<B[Z \66 \6<< + [3] Stafford R.Q., MacDonald B.A., Li X., Broad ]+ ‡> ' '  '

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3 3 x International Journal of Social Robotics, vol. 6, + < <\6? <=6 <Z@+ `>18 6\+6\\@~ 6<B[Z \6B \<<? Z+ 5?7 " ( %+ %+ ; %+ ‡]9' ( investigation into influence of negative attitudes & ( x+ 1 8 3rd Workshop on Social Intelligence Design, SID, Enschede, 2004. 5X7 " ( %+ %+ ; %+ ‡]9' ( investigation into influence of negative attitudes & ( x E ˆ ; 3 + <\ + < <\\[ 6B=^6X\+ `>18 6\+6\\@~ \\6?[ \\X \\6< @ 5[7 " ( %+ ;& %+ 4 Q + q + ‡]9perimental investigation of relationships between anxiety, negative attitudes, and allow x+ 1 8 Proceedings of the 2nd IASTED International Conference on Human Computer Interaction IASTED-HCI’ <\\@+ 5@7 E+ _ & ' + % & * !+ } & ]+ ‡E * 9' (' & & ( x+ 1 8 AISB Symposium on the New Frontiers in Human-Robot Interaction, Edinburgh, Scotland, 2009 [8] Bartneck C., Nomura T., Kanda T., Suzuki T., Kato + ‡E x+ 1 8 1st International Conference on Usability & Internationalization HCI | ƒ * 2;E <\\X+ 5Z7 q ' `+ +]+ ‡2 3 * '& bia and cyber-dystropianism: The role of gender, technology and religion on attitudes to x+ 1 8 Proceedings of the 7th ACM/ IEEE International Conference on Human-Robot Interaction HRI’12, 2012, 139–140. DOI: 6\+66?X~<6X@[=Z+<6X@@<?+ 56\7 E+ 1* ĂŽ + & `+ % & * !+ x| * ‡ xĂ?x International Journal of Social Robotics, vol. 3, no. 2, 2011, 111–123. `>18 6\+6\\@~ 6<B[Z \6\ \\@[ X+ [11] Syrdal D., Dautenhahn K., Koay K., Walters M., ‡%& * 3 and reactions to robot behavior in a live human x+ 1 8 AISB Symposium on the New Frontiers in Human-Robot Interaction, Edinburgh, Scotland, 2009. [12] Piçarra N., Giger J.-C., Pochwatko G. , Gon$ 3 W+ xƒ & # * 3 sion of the Negative Attitudes towards Robots ; x Revue europĂŠenne de psychologie appliquĂŠe 3 + [X <\6X ZB^6\?+ `>8 6\+6\6[~Q+ erap.2014.11.002.1162-9088. 56B7 ` ( ;+ | + #&+ } ƒ+}+ ‡| & (x Group Processes and Intergroup Relations 3 + Z + 6 <\\[ <X^?<+ `>18 6\+66@@~6B[=?B\<\[\XZ=X[+ 56?7 # $ "+ W * + U+ # & W+ ‡‡} 3 & ( } ! & Ă?x8 _ liefs of Human Nature Uniqueness and social ro ' ' x / ' 0+ 56X7 # $ "+ W * + U+ # & W+ W $ 3 W+ Humanizing robots: Need for cognition, perspecArticles

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tive taking and beliefs in human nature unicity as predictors of anthropomorphization of social robots (submitted). 56[7 ]' "+ E+ U '' +%+ ‡> ; * q man: A Three-Factor Theory of Anthropomor'& (x Psychological Review, vol. 114, no. 4, <\\@ =[?^==[+ `>18 6\+6\B@~\\BB <ZX„+66?+?+=[?+ 56@7 2+ %+ E W+ # U+ ` & & + ‡U > Ă? B ^ ƒ _ x+ 1 8 % '' /] +0 Your Virtual Butler: The Making-of _ ‚ q *8 ;' * <\6B Z@^66[+ [18] Yoshikawa M., Matsumoto Y., Sumitani M., Ishigu q+ ‡` 3 '( ' & * '' ( x+ In: 2011 IEEE International Conference on Robotics and Biomimetics (ROBIO) @ 66 <\66 <B@=^ <B=B+ `>18 6\+66\Z~ >_1>+<\66+[6=6[X? [19] Jolliffe I.T., Principal Component Analysis, Springer Series in Statistics, 2002. [20] Davidshofer K.R., Murphy C.O., Psychological testing: principles and applications, 6th ed., Upper Saddle River, N.J.: Pearson/Prentice Hall. ISBN \ 6B 6=Z6@< B <\\X+ [21] Cozby P.C., Methods in behavioral research, 10th ed., Boston: McGraw-Hill Higher Education, 2009. 5<<7 4 E+ ĂŒ` 3 * * ;#;;x ; * 2009. 5<B7 U ]+ q W+ q ( |+ ; * E+ ‡U ing the uncanny valley: Empirical evidence of a top-down fluency account for affective re ' & ( * x Cognition, 2014, in review.

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9CL?@<A?B<CDECFEBIJE IJJ@JME CW<@JE CWCBEW?=JMECDE >@B<60JD=CKE ?B?E&>=<CDE Submitted: 4 March 2015; accepted 26th May 2015

Piotr Jaroszek, Maciej Trojnacki DOI: 10.14313/JAMRIS_3-2015/26 Abstract: The paper presents a method of localization of a mobile robot which relies on aggregation of data from several sensors. A review of the state of the art regarding methods of localization of ground mobile robots is presented. An overview of design of the four-wheeled mobile robot used for the research is given. The way of representation of robot environment in the form of maps is described. The localization algorithm which uses the Monte Carlo localization method is described. The simulation environment and results of simulation investigations are discussed. The measurement and control equipment of the robot is described and the obtained results of experimental investigations are presented. The obtained results of simulation and experimental investigations confirm the validity of the developed robot localization method. They are the foundation of further research, where additional sensors supporting the localization process could be used. Keywords: wheeled mobile robot, localization, environment map, laser scanner, Inertial Measurement Unit, odometry, data fusion, Monte Carlo localization method

E Introduction One of the elements necessary for autonomous realization of robot motion is its localization in the global reference system [1]. The problem of robot localization is widely studied in scientific publications [2]–[4], because of its key significance. The knowledge of position and orientation of an autonomous robot is fundamental for its proper and reliable operation. Artificial intelligence algorithms based on which the control is determined, must have the largest possible knowledge of the state in which the controlled object currently is. For many such algorithms, correct localization is essential, as for example in the global path planning problem [5] or the local motion planning problem [6]. Robot localization can be considered from various points of view, the most straightforward of which is the position tracking [7]. In this situation, the initial position and orientation of the robot are known and the only objective is determination of position in particular time instants based for example on robot odometry. Simultaneously, compensation for errors which accumulate in time is required. Another, more difficult, problem is the global localization problem [8], where robot initial pose is not known. The local-

ization process must therefore deduce the initial robot state and then determine the correct position and orientation during its motion. The most difficult of localization problems is the kidnapped robot problem [9], where in addition to the problems introduced by the global localization, the robot state can suddenly change in a way unrelated to robot actions. One may say that the robot has been “kidnapped” during operation and placed in some other unknown place. For execution of the robot localization task, the probabilistic methods are widely applied [10]–[13]. It is due to the fact that all information gathered by robot sensor systems is burdened with some level of error. Minimization of influence of those errors on the localization accuracy can be achieved with probabilistic methods, whose task is to create the representation of probability that describes the robot localization in the best way. Based on the chosen probability function representation, the estimation of position and orientation is carried out. The probabilistic methods are most often based on the recursive Bayesian filter principle, which is the principal tool in the task of estimation of the unknown probability distribution function. This task is made recursively in time using both measurements from sensors and information about actions undertaken by the robot. The task is executed in two basic phases: prediction phase and update (correction) phase. The inherent element of the prediction phase is the robot motion model, by means of which the transformation of the probability function before and after single movement step is described. Most often this model is based on modification of the Gaussian distribution after prediction. In turn, update of position and orientation of the robot is made based on measurements from the robot sensors. By means of the adopted observation model, update of the probability distribution function takes place by minimization of uncertainty caused by errors accumulated in the preceding steps. The best known methods of probabilistic localization are the Kalman filter methods [12], Markov localization [14] and particle filters [15]. They differ mainly in terms of ways of representation of the probability distribution function, and each one of them has certain advantages and drawbacks as compared to others. One of the newest methods based on the probabilistic concept is the Simultaneous Localization and Mapping (SLAM) [16]. This task is difficult because of 73

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the nature of the problem, since the map is required for localization and conversely the information about localization is required to construct the map. A key to efficient localization is also the appropriate model of the robot environment. The most often used solution is the introduction of the map defined adequately to the given problem. The amount of information delivered by robot sensors can directly affect the effectiveness of its localization. Taking into account the presence of noise in sensor signals, uncertainties and limited applicability of sensors themselves, it is beneficial to apply a larger number of different types of sensors. The data fusion is a tool that allows to combine knowledge from various sources to maximize their usefulness [17]. In this way, in the considered cases it is possible to improve the quality of the results, by simultaneously allowing smaller amount or worse quality of the required input data. The aim of the present work is robot global localization on the known environment map, based on the aggregation of sensor data. For the task of localization robot odometry (encoders), inertial sensors and the laser scanner will be used. The proposed localization algorithm will use the Monte Carlo localization method and the hybrid representation of the environment.

E & 6 E E The object of research, on which the developed localization method will be investigated, is the PIAP SCOUT mobile robot [18]. In Fig. 1a the commercial version of the robot is shown. It was designed for quick reconnaissance of places with difficult access, i.e., vehicle chassis, places under seats in means of transportation, narrow rooms and ventilation ducts. The robot is manufactured in various versions, differing mainly in type of equipment installed on-board, which makes it suitable for specialized tasks. The robot locomotion system is hybrid. It consists of tracks and non-steered wheels which operate simultaneously. Two rear wheels are driven independently by DC motors equipped with gear units and encoders, which enable measurement of angular velocity of spin of the driving wheels. The drive from the rear wheels is transmitted to the front wheels via two toothed belts or tracks. a)

b)

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Fig. 2. Kinematic structure of the robot

During investigations the manipulator, camera and auxiliary front tracks were dismantled. The robot has been adapted to realization of experimental research by installing additional frame to mount the necessary equipment (Fig. 1b). On the frame were installed: the laptop computer, the Inertial Measurement Unit and the 2D laser scanner. The kinematic structure of the robot is illustrated in Fig. 2 [19]. The following basic robot components can be distinguished: 0 – mobile platform (robot body with additional frame), 1-4 – wheels, 5-6 – tracks. The mobile platform of the robot is approximately 0.5 m by 0.5 m (length x width), and its mass is about 22 kg. Because the robot is equipped with non-steered wheels, large wheel slips occur during its turning (particularly large during pivot turning). For this reason, in a general case it is not possible to determine robot motion parameters based only on the encoder data. As a result the robot localization is much more difficult. As far as the robot localization is concerned, actual robot state vector has the form:

x =[O x R , O yR , O Ď•0 z ]T ,

(1)

where: OxR, OyR and OĂ‘0z are respectively actual coordinates of the point R of the robot and its heading in the global (stationary) reference system {O}. By analogy, the prediction of the robot state vector can be written as:

xˆ =[O xˆ R , O yˆ R , O ϕˆ 0 z ]T ,

(2)

where elements of this vector are counterparts of the elements of the x vector. In turn, the error of the robot state vector will be denoted as:

~ x = [ O~ x R , O~ yR , O ~ Ď•0 z ]T = x − xˆ , Fig. 1. PIAP SCOUT wheeled mobile robot: a – commercial version [18], b – version adapted to experimental investigations 74

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(3)

where the error of robot position (Euclidean norm) and error of heading will be respectively equal to and , and

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O

~ rR = ( O~ x R )2 +( O~ y R )2 .

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(4)

The space of possible robot states is represented by the collection of particles S of which every i-th particle is described by the state vector: ,

(5)

where: OxRi, OyRi, OĂ‘0zi are respectively possible coordinates of the point R and its heading in the global coordinate system {O} for the i-th particle. In turn, the prediction of the state vector of the i-th particle in the successive step of the algorithm has the form: ,

(6)

where the elements of the vector are the counterparts of the vector xi.

E 1 7 E 3 Robot environment can be [20]: observable where both map and robot in each time instant can be uniquely defined, or partly observable, where neither map nor robot can be uniquely determined in each time instant. Partial non-observability makes localization task more difficult, because significant increase of robot admissible state space is necessary in this case. The environment can be also [20]: deterministic, where result of the actions performed by the robot is certain and completely defined or stochastic, where result of actions performed by the robot is uncertain. For stochastic environments additional probabilistic coefficients have to be introduced. Additionally, robot environment can be [20]: static, where the map of environment does not change during robot operation, or dynamic, where the environment map can change. Dynamic environments are characterized by the presence of moving obstacles, which must be properly recognized and appropriate actions must be undertaken to check their influence on localization. In the present work the environment has hybrid representation in the form of the 2-dimensional static deterministic and fully observable map. It consists of two layers, the first of which is the map of features. In this layer, the walls (obstacles) are represented by segments of known start and end coordinates in the global coordinate system {O}. The second layer has the form of grid occupancy map. The algorithm uses one of the two layers (environment representations) in the way so as to minimize the time of computations. In case of parts of the environment that consist of straight segments, the algorithm uses the map of features, and in case of complex shapes of the environment, the grid occupancy map is used. For the purpose of simulation research, the first layer of the map is created in AutoCAD and then it is converted to the .bmp format in order to obtain the second layer of the map.

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In the case of experimental research, the spatial scanning technique using the 2D laser scanner mounted on the robot is used to obtain the second map layer, and after subsequent conversion of the point cloud into lines, the first layer is obtained.

" E E9 R EO E E 6 E E & The theme of the work is wheeled mobile robot localization using data aggregation from the sensors. To this end, the probabilistic method based on the particle system, that is Monte Carlo localization, will be used. It relies on recursive algorithm which uses the Bayesian theory for posteriori estimation of the distribution. Main features of the Monte Carlo localization are: • capability of using independent sensor data from multiple devices, also burdened with large errors, • : 9 ' & ( ' and map complexity to the computing power of the computer, • the estimate of robot current state is represented by a multimodal probability density function, which enables global localization, • total computation cost of the algorithm is concentrated around places where the largest probability of robot occurrence exists. The Monte Carlo algorithm consists of 3 main phases: • prediction, • update of weights, • resampling. The phases are preceded by the initialization process, which generates M particles on the map and assigns an identical normalized weight to each i-th particle. In the prediction phase, the algorithm predicts the state for each i-th particle from the set S using the motion model. In the subsequent weight update phase, the weight wi is calculated for each i-th particle from the S set. After calculation of weights, the process of their normalization takes place, that is, determination of weights such that the sum of weights of all particles is equal to 1. In the last phase, resampling of the S set takes place. Particles from the S set are drawn with replacement proportionally to the value of the weights (particles with large weights are chosen more often) and put into new S’ set. Analogy to the survival of the fittest is noticeable. Particles with large weights are chosen more frequently so in the map concentrations are created where larger probability of robot position exists. After sampling is completed, the S’ set becomes the S set for the next calculation loop. In this phase, algorithm of reduction of the number of particles based on the Effective Sample Size (ESS) coefficient can be additionally introduced [21]. In the case, when nearly whole population of particles will be close to the unknown robot state x, this coefficient can be used for gradual removal of particles from the remaining region of the map. Process of robot localization was carried out on PIAP premises using the available mobile platform and the following sensors: Articles

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• HOKUYO UTM-30LX 2D laser scanner and environment map, • STM iNEMOv2 sensors module, of which the accelerometer was used, • encoders mounted on the shafts of robot drives. The laser scanner with the environment map has a primary function in the process of determination of weights of the particles in the Monte Carlo localization method by comparing the real readouts from selected laser beams with virtual measurements of each of the particles. The measurements using accelerometer have a corrective function in cases of robot motion with wheel slip. Measurement from encoders is in turn used in the phase of prediction, in the robot motion model. The iterative process of the method takes place in parallel, on two planes: • robot control with sensor data reading and • execution of localization process using the Monte Carlo method. The robot control and sensor data reading plane is responsible for providing information in the form of distance, speed and accelerometer readouts. During experiment the operator moves the robot by tilting the joystick axis. Sensor readouts are made by means of programmatic real-time layers. The amount of particles in the Monte Carlo localization method was experimentally chosen so as to ensure quick and accurate localization in the given environment. One of available resampling algorithms was implemented and a module for optimization of speed of algorithm execution was added.

" ET ET EÂŽE E E The motion model is used for prediction of the state vector for each i-th particle depending on the previous estimated state vector xi and the action an identical for all particles. In the work, for prediction of robot motion speed its odometry and accelerometer were used. From robot odometry, based on known angular speeds of spin of the driven wheels obtained based on the encoder indications, are calculated: robot longitudinal velocity Rvex and angular velocity of turning RĂ“e and the transverse velocity is assumed Rvey = 0, where all those velocities are expressed in the moving coordinate system {R} associated with the robot. Those velocities, on the assumption of zero wheel slip, are determined from the following relationships [19]: ,

, ,

(7) (8)

where: r – geometric radius of wheel (the same for all wheels), W – wheel track (distance between geometric centers of left- and right-hand side wheels). Because of existence of large wheel slips during robot turning, which was pointed out, for instance, in the work [19], those relationships are then burdened with large errors, but thanks to use of the Monte Carlo 76

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localization method, despite those errors localization of the robot is possible with relatively high accuracy. Robot motion velocities can be also determined based on the Raax and Raay accelerations read from accelerometer, based on the following relationships: (9) (10) where t ( ' Ôt is the step time. Similarly as previously, it is assumed that the ground on which the robot moves is horizontal, so & : & * 3

& accelerometer indications is neglected. Additionally, the centripetal (normal) acceleration occurring during robot turning and Coriolis acceleration associated with Earth rotation (which is small) are not taken into account. Next, the robot longitudinal velocity is calculated as a fusion of longitudinal velocities obtained from robot odometry and accelerometer according to the formula: ,

(11)

where the following weights were assumed: Îźe = 0.7, Îźa = 0.3. In turn, robot motion velocities in the global reference system, on the assumption of robot motion on a horizontal ground, can be determined based on the relationship: .

(12)

Based on it, from the robot motion model prediction of the state vector of i-th particle is determined on the basis of the relationship [8]: (13) where xni is declared noise (uncertainty) of motion, which is determined in each iteration for every particle separately. %& 3 Ă–trans Ă–drift, respectively for longitudinal and lateral directions of robot motion. The motion model described above is applied for each i-th particle from the S set.

" E % E-3 ET To each i-th particle from the S set must be assigned appropriate weight wi, proportional to the level of probability that the given measurement is equal to the real value. The particles, from the point of view of which the measurement is close to real values should be given larger weights than those, whose measurements differ significantly.

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To this end, for the laser scanner the sensor model based on the Gauss distribution is used, that is:

particles proportionally to their weights, using the following relationship:

(14)

(17)

where: olaser,k – measurement from the k-th laser scanner beam, k = 0, ..., n, op,k,i – indication “from the point of viewâ€? of the i & ' Ă–02 – experimentally chosen variance describing the sensor noise. In case of the laser scanner, one obtains measurements from n equally spaced beams. Therefore each of the particles also contains n indications. E & 3 Ă–02 is concerned, its small value results in narrow Gauss function, so only the particles of measurements very close to real obtain * *& + 4 * 3 Ă–02, this distribution is wider, so the differences between weights are smaller. After calculation of the weights of all particles, additional normalization of weights is necessary. Without it, the distribution is not the probability distribution. To this end, all weights are divided by the following normalization constant:

where is the eventual prediction of the robot state vector, obtained as a result of data fusion. Next, exchange of the S and S’ sets is performed, and execution of the successive iteration in the next time step. Finally, optimization of the number of particles is done, which allows reduction of time of computation in successive iterations. Because of lack of information on the initial state of the robot (global localization), the Monte Carlo localization requires a large number of particles only at the very beginning of the process. For the task without the problem of the kidnapped robot, keeping large number of particles is less important with time, because the localization problem smoothly transitions to the problem of position tracking. Therefore, it is possible to reduce the number of particles then. To this end, the mechanism reducing the number of particles, when the algorithm discovers that the problem of tracking is more pronounced than the problem of localization, has been introduced. The measuring quantity ESS (Effective Sample Size) was introduced, which informs about the level of closeness of all weights of particles to each other, which is calculated based on the relationship [21]:

(15)

This constant is the sum of all original weights. Finally, weights of particles are given values according to the following formula: (16)

(18)

" E 3 %ET Resampling consists in selection of particles from the S set proportionally to their weights and creation of the new set S’, which will be used in the successive iteration. It is the so called draw with replacement, which means that elements not selected (because of small weight) will be replaced with elements with higher weights. This selection results in keeping in the memory only those places, which are probable from the point of view of localization. After performing the estimation of robot localization, the created S’ set is exchanged with the S set for successive iteration. Next point of iteration is appropriate estimation of robot position based on the cloud of points. To this end, the following two principal methods are used: • maximum weight of the particle and • superposition proportional to weights of particles. %& : ( & 3 & ' & the largest weight is assumed as the position of the robot (the result of the localization). This solution has the disadvantage of “jumpingâ€? behavior in successive steps of the iteration. The second method relies on estimation of position using both weight and position of each particle. Keeping in mind that sum of weights of all particles is equal to one; it is possible to carry out superposition of all coordinates and orientations of

It means that at the time instant, when most of the particles will be concentrated in one place, their number will be reduced. Reduction of the number of particles by the im' ' * ³ ' & ( ( isfaction of the condition: (19) & 8 × (0, 1) is the experimentally chosen index of rate of reduction of the number of particles (0 – very high rate of reduction, 1 – no reduction).

' E 0 E Within the present work multiple investigations in the prepared simulation environment were carried out. On the ideal map (Fig. 3a) created in two variants, by means of lines and in the occupancy map, a series of localization processes was conducted for the simulated robot. In the figure, the map contour is marked red and particular particles – blue. The developed application was also able to show simulated beams of distance readouts from chosen particles in the form of green lines (Fig. 3b). Articles

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of lines necessary for map construction, which is not a problem when using a discrete map of occupation based on a bitmap. It can be also noticed that for small numbers of particles, the level of complexity of the map becomes unimportant. This information is, however, of little use in practical applications, where the common trend is to increase the number of particles. In the following figures, results of simulations of robot localization are shown for various numbers of particles M and various values of variance of sensor Ă–02 as a function of the iteration step. On the basis of the obtained results, it is possible to evaluate the accuracy of robot localization depending on the used number of particles M and the value of Ă–0, which is one of the method settings and has large influence on the results.

a)

b)

Fig. 3. Robot environment map: a –visible particles, b – example of simulated beams

In the simulation research, the following properties were checked: • algorithm speed for various number of particles M (from 2000 to 20 000) and number of lines constructing the map (70 and 140), • algorithm speed for various number of particles M (from 2000 to 20 000) and length of the radius in the case of the bitmap of 1000 x 1000 pixels, • accuracy of localization in the 25-th step of iteration for identical sequence of robot motion (for initial number of particles _­¸6\ \\\ M¸­¸<\ \\\0 • : 3 3 Ă–02 on the localization process. In the simulation, robot position and its error in the map coordinate system, and also all performed simulations of distance measurement were represented in generic units. Additionally, in every trial the initial pose of the robot and its control were the same. In Fig. 4 simulation results were presented where time of simulation T dependency on the number of particles M, for two methods of representation of environment of the robot and for two chosen levels of complexity of those maps, was investigated. The vector map was investigated for the case of 70 and 140 lines, whereas the raster map of the size 1000 x 1000 units for maximum length of the beam equal to respectively 500 and 1000 units. From the obtained results it follows that the time of computation decreases more or less linearly as a function of the number of particles used for robot localization. The time necessary for calculation of the algorithm for the map based on lines can be noticeably smaller. However, geometric complexity of the environment can cause significant increase of the number 78

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Fig. 4. Dependency of time of computation on the number of particles for two levels of complexity of the map

Fig. 5. Position and heading {J|J }U}}}J J~0 = 70

errors for

1 & 3 Ă–0 = 70 convergence of position of the simulated robot with its estimate in the initial steps of the algorithm slightly increased when the number of particles was increased from M = 5000 to M = 10 000 (Figs. 5-6). In turn, in the case of analysis of the problem of & 3 Ă–0 = 200

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Fig. 6. Position and heading 0 = 70

errors for

Fig. 9. Position and heading 0 = 10

Fig. 7. Position and heading 0 = 200

errors for

Fig. 10. Position and heading 0 = 10

Fig. 8. Position and heading 0 = 200

errors for

and identical number of particles (Figs. 7-8), the initial & * * : * * tends to zero. On the other hand, the position error is smaller right from the beginning and ultimately reaches smaller value. 1 & * : & ' ( & Ă–0 = 10 and for M = 20 000 (Fig. 9), the correct localization of the robot was achieved already (' & : '+

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errors for

errors

%& * & 3 Ă–0 resulted in * : 3 * & large number of particles. However, it turned out to be critical for the case in which M ­ 6\ \\\ Ă–0 = 10 (Fig. 10), where the error was large, and in the case of heading, error convergence to zero is not visible. It means that large number of particles in the ( & ( ( & Ă–0 parameter

* : & '

and simultaneously involves risk of failure of the localization task as a whole. The presented results clearly point to experimental character of selection of number of particles M and & ' ( Ă–0 for the given map and used sensors.

( E 183 E 7 % Experimental investigations concerning localization of the PIAP SCOUT robot were carried out in the research environment, whose schematic diagram is shown in Fig. 11. The research platform consists of three main components: • the PIAP SCOUT mobile robot controlled via CAN bus, • the laptop with software running on Ubuntu operating system with Xenomai real-time framework, Articles

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• the system of sensors communicating with the laptop via USB and CAN interfaces.

Fig. 11. Schematic diagram of experimental environment

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ments were used to build a 1000 x 1000 points occupancy map. Next, the layer of the map obtained in this way was linearized using one of the available algorithms, and as a result the second layer of the vector map consisting of 120 lines was obtained. The conducted experimental research involved a series of experiments of localization using the earlier described Monte Carlo method, with aggregation of sensor data taken into account. At first, the experimental standard deviations & 8 Ă–trans ­ \+6 ( Ă–drift ­ \+\Z Ă–0 = 50 m. Next, the proper experimental research was done. During investigations, after measurement of the initial robot pose, the operator using joystick made maneuvers aimed at moving the robot into new location. The task of the algorithm was robot localization during motion and after its completion. After finishing the control process, the final robot pose was measured and also its estimate as a result of localization algorithm operation was determined. During algorithm execution, several quantities were recorded, for instance, values of predicted robot velocities and times required for computation at the given number of particles. In the present work, results of two selected experiments are shown.

183 E

Fig. 12. Robot environment map in the experimental investigations

The first experiment consisted in driving the robot forwards, then making 90 degrees counter-clockwise pivot turn and driving forwards again. In Fig. 13 the desired robot motion is shown in a schematic way. In turn, in Fig. 14 and in Table 1, accuracy of the final robot pose estimation is illustrated, whereas in Fig. 23 selected corresponding steps of the algorithm are shown. As a result of the experiment also the following quantities were recorded: • the number of active particles M involved in the localization process (Fig. 15), • duration of algorithm computation T (Fig. 16) • estimated robot velocities (Fig. 17).

183 E

Fig. 13. Schematic illustration of robot desired movement in the experiment 1 Robot control takes place by means of the control panel, using joystick. Both systems, which are of the robot and of the control panel, were connected using the Wi-Fi network. Experimental investigations of robot localization using the proposed method were performed using the PIAP SCOUT robot described in point 2. Robot environment was the 9 m2 area made out of the part of the room. The robot environment map with the adopted coordinate system is shown in Fig. 12. The map used with the algorithm was created using the space scanning technique. Raw laser measure80

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The second experiment was a natural follow up to the first one and it consisted in robot returning to the starting point from the first experiment. The desired motion of the robot is shown in Fig. 18. The accuracy of the final estimation of the robot pose are illustrated in Fig. 19 and in Table 2, whereas in Fig. 24 are shown selected intermediate steps of the algorithm execution. Similarly as in the previous experiment, the following quantities were recorded during experiment: • number of the active particles M involved in the localization process (Fig. 20), • duration of computations of the algorithm T (Fig. 21), • estimated robot velocities (Fig. 22). As a result of the conducted experiments with a map of little geometric complexity, relatively good accuracy of robot localization was achieved (Tables 1-2).

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Fig. 17. Estimated velocities of robot motion – experiment 1 Fig. 14. Results of robot localization in the experiment 1

Fig. 15. Change of the number of particles – experiment 1

Fig. 18. Schematic illustration of robot desired movement in the experiment 2

Fig. 16. Time of computation for successive steps of the algorithm – experiment 1

Despite larger difficulties in localization in uniform spaces or spaces containing repeating elements, the results of this quality can be considered attractive from the point of view of mobile robotics. At the beginning of each experiment (Figs. 2324), relatively large uncertainty of estimation of position can be observed in the form of scattered distribution of particles all over the map. This dis-

Tab. 1. Accuracy of localization in the final position for the experiment 1

Tab. 2. Accuracy of localization in the final position for the experiment 2

Unit

[m]

Actual pose

O

Estimated pose

O

Estimation error

xR = 2.23

O

xˆ R =2.25

~ x R =–0.02

[m] O

yR = 2.03

O

O

yˆ R =2.09

~ yR =–0.06

[deg]

Unit

Ñ0z = 142.1

Actual pose

O

ϕˆ 0 z =139.4

Estimated pose

O

~ ϕ0 z =+2.7

Error of estimation

O

O

O

[m] xR = 1.14

O

xˆ R =0.91

~ x R =+0.23

[m] O

yR = 0.64

O

O

yˆ R =0.57

~ yR =+0.07

[deg] O

Ñ0z = 44.21

O

O

ϕˆ 0 z =55.85

~ ϕ0 z =–11.64 Articles

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Fig. 19. Results of robot localization in the experiment 2

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for the raster map). One can notice, however, that the mentioned time was significantly different in case of the feature map in comparison to the results of simulation investigations. The explanation is lack of operation of the real-time layer during simulation investigations and absence of the associated latencies (acceleration integration, laser measurements, etc.). The real-time system, in order to achieve high accuracy, operates in the top priority mode with respect to any application in the user space of the Ubuntu system, so its influence on the efficiency is significant. In Figs. 15-16 and Figs. 20-21 it is possible to notice a distinct fall in the required time of computation for the steps where the number of particles was reduced. Linear and angular velocities of the robot exhibit high local variability, because of measurement inaccuracy and instability of robot motion during turning maneuvers (Figs. 17 and 22). Moreover, the drift of error of acceleration integration is also significant. This justifies the supposition that those measurements were burdened with quite significant errors, which, however, was not a problem for robot localization with relatively good accuracy. It was possible due to the fact that the Monte Carlo localization algorithms are robust to this kind of errors, because they themselves operate on the principle of introduction of noise to motion and sensor models.

Fig. 20. Change of the number of particles – experiment 2

tribution underwent consolidation in the successive steps, which resulted in more and more accurate localization. During every experiment, the algorithm gradually reduced the number of particles used for localization depending on the ESS value (Effective Sample Size). Moreover, the results of investigations for selected steps of algorithm operation illustrated in Figs. 23-24 show consistency of estimation of robot pose during robot motion with desired movements presented in Figs. 13 and 18. In the figures also the visualized laser beams drawn from the estimated robot position can be noticed, which are consistent with the environment map. It is the evidence of correctness of the localization process (position tracking) during experiment, and not only after its completion. The time of computations required by the algorithm was dependent proportionally on the number of particles and the level of map complexity (that is, on the number of lines required to its representation for the vector map or the maximum length of the ray 82

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Fig. 21. Time of computation for successive steps of the algorithm – experiment 2

Fig. 22. Estimated velocities of robot motion – experiment 2

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* E # E E& E )

Fig. 23. Selected steps of localization – experiment 1

The proposed algorithm of localization works quickly and effectively on the real mobile robot. The results of localization are satisfactory, and because of speed of algorithm operation its use in real time is possible. Thanks to data aggregation, distance sensors, accelerometers and encoders fulfill their role as components gathering information required for assigning weights to particles and prediction of robot motion. In order to further develop the presented method and increase the accuracy of prediction of robot motion, the following works are planned: • enhancement of fusion of data from the sensors with data from the gyroscope in order to improve accuracy of prediction of robot heading and/or with the global navigation satellite system (GNSS) [22] in case of robot motion in open terrain. • addition of the third spatial dimension of the environment, which will enable localization in the environment of variable surface inclination. # 2/ 91 :1 12 0 The work has been realized as a part of the project entitled “Dynamics modeling of four-wheeled mobile robot and tracking control of its motion with limitation of wheels slipâ€?. The project is financed from the means of National Science Centre of Poland granted on the basis of decision number DEC-2011/03/B/ ST7/02532.

- ./ 0 Piotr Jaroszek* – Industrial Research Institute for Automation and Measurements (PIAP), Warsaw, 02-486, Poland. E-mail: pjaroszek@piap.pl, Maciej Trojnacki – Industrial Research Institute for Automation and Measurements (PIAP), Warsaw, 02-486, Poland. E-mail: mtrojnacki@piap.pl. *Corresponding author Fig. 24. Selected steps of localization – experiment 2 Articles

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1&1 12#10 [1]

Siegwart R., Introduction to Autonomous Mobile Robots, MIT Press, 2004. [2] Cox I. J., Wilfong G. T., ed., Autonomous Robot Vehicles, New York, NY, USA: Springer-Verlag New York, Inc., 1990. DOI: 10.1007/978-1-46138997-2. [3] Fukuda T., Ito S., Oota N., Arai F., Abe Y., Tanaka K., Tanaka Y., „Navigation system based on ceiling landmark recognition for autonomous mobile robot�. In: International Conference on Industrial Electronics, Control, and Instrumentation, 1993. Proceedings of the IECON ’93, vol. 3, 1993, 1466– 1471. DOI: 10.1109/IECON.1993.339287. [4] Hertzberg J., Kirchner F., „Landmark-based autonomous navigation in sewerage pipes�. In: , Proceedings of the First Euromicro Workshop on Advanced Mobile Robot, 1996, 68–73. DOI: 10.1109/EURBOT.1996.551883. [5] Jaroszek P., 0 ( Y+  Y‹ Œ: Y(Global Path Planning), Bachelor of Engineering Thesis, Warsaw University of Technology, Warsaw, 2012. (In Polish) [6] Bartoszek J., Trojnacki M., Bigaj P., „Simulation of semiautonomy mode for ibis mobile robot with analysis of sensor failure tolerance�, Journal of Automation, Mobile Robotics, & Intelligent System., Vol. 5, No. 4, ss. 3–10, 2011. [7] Borenstein J., Navigating Mobile Robots: Systems and Techniques. Wellesley, Mass: A K Peters Ltd, 1996. [8] Yamauchi B., Schultz A., Adams W., „Mobile robot exploration and map-building with continuous localization�. In: 1998 IEEE International Conference on Robotics and Automation. Proceedings, 1998, vol. 4, 3715–3720. DOI: 10.1109/ROBOT.1998.681416. [9] H. M. Choset, Principles of Robot Motion: Theory, Algorithms, and Implementation. MIT Press, 2005. [10] Burgard D., Fox, D. Hennig, i T. Schmidt, „Estimating the Absolute Position of a Mobile Robot Using Position Probability Grids�, 1996. . [11] Cassandra A., Kaelbling L. P., Kurien J., „Acting under uncertainty: discrete Bayesian models for mobile-robot navigation�, w Proceedings of the 1996 IEEE/RSJ International Conference on Intelligent Robots and Systems ’96, IROS 96, 1996, vol. 2, 963–972. [12] Kalman R., „A New Approach to Linear Filtering and Prediction Problems�, Trans. ASME – J. Basic Eng., no. 82 (Series D), 1960, 35–45. [13] Thrun S., „Bayesian Landmark Learning for Mobile Robot Localization�, Machine Learning, vol 33, no. 1, October, 1998, 41–76. [14] Burgard W., Derr A., Fox D., Cremers A., „Integrating global position estimation and position tracking for mobile robots: the dynamic Markov localization approach�. In: 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems,. Proceedings, vol. 2, 730–735. DOI: 10.1109/IROS.1998.727279. 84

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[15] Thrun S., Fox D., Burgard W., Dellaert F., Robust Monte Carlo Localization for Mobile Robots, Artificial Intelligence, vol. 128, no. 1–2, 2001, 99– 141. DOI: 10.1016/S0004-3702(01)00069-8. [16] Bedkowski J., Maslowski A., De Cubber G., „Real time 3D localization and mapping for USAR robotic applicationâ€?, Industrial Robot: An International Journal, vol. 39, no. 5, 2012, 464–474. [17] Mandic D. P., Obradovic D., Kuh A., et al. „Data Fusion for Modern Engineering Applications: An Overviewâ€?. In: Artificial Neural Networks: Formal Models and Their Applications – ICANN 2005, + + ` & + ' ]+ >Q ;+ € Springer Berlin Heidelberg, 2005, 715–721. [18] „PIAP – producer of EOD equipment, EOD robots and surveillance robotsâ€?. [Online]. http://antiterrorism.eu/en/. [19] Trojnacki M., Dynamics modeling of wheeled mobile robots, PIAP Publ. House, Warsaw 2013. [20] Russell S. J., Norvig P., Artificial Intelligence: A odern Approach, Prentice Hall, 2010. [21] Robert C. P., Introducing Monte Carlo Methods with R, 2010 ed., New York: Springer Verlag, 2009. DOI: 10.1007/978-1-4419-1576-4. [22] Perski A., Wieczynski A., Baczynska M., et al., ĂŒ> W";; ' Q+ Badania stacjonarneâ€?, Pomiary Automatyka Robot., vol. 17, no. 4, 2013, 64–77. (In Polish)

Publisher: Industrial Research Institute for Automation and Measurements PIAP

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