JAMRIS 2015 Vol 9 No 1

VOLUME 9

N째 1

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 (Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Japan)

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The reference version of the journal is e-version.

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 (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) Laszlo T. Kóczy (Szechenyi Istvan University, Gyor and Budapest University of Technology and Economics, Hungary) 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) 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° 1, 2015 DOI: 10.14313/JAMRIS_1-2015

CONTENTS 3

41

Editorial

DOI: 10.14313/JAMRIS_1-2015/6

5

Chemical Scanner for Mobile Robot Navigation

DOI: 10.14313/JAMRIS_1-2015/1 12

Perceptual Colour Correlogram and Perceptionbased Statistical Features of Colour Texture

DOI: 10.14313/JAMRIS_1-2015/2 18

RGB-D Sensors in Social Robotics ! " # % &

DOI: 10.14313/JAMRIS_1-2015/3 28

Semantic Place Labeling Method ' ( # ) * # + ,-

DOI: 10.14313/JAMRIS_1-2015/4 34

Architecture of an Autonomous Robot at the IT Level ( #'

# # (

! ( #

! ( &.

DOI: 10.14313/JAMRIS_1-2015/5

2

Intuitive User Interfaces for Mobile Manipulation Tasks / -' 0 0

Articles

53

Robot Grasp Synthesis Under Object Pose Uncertainty

(

DOI: 10.14313/JAMRIS_1-2015/7 62

Leg’s Tip-Ground Contact Detection Based on Drive Currents in a Real Walking Robot ! )

DOI: 10.14313/JAMRIS_1-2015/8 68

The Role of Compliant Elements in Two-Legged Robot’s Foot Model ! ( 1-

! #

( -#

DOI: 10.14313/JAMRIS_1-2015/9 77

Planning the Waypoint-Following Task for a Unicycle-Like Robot in Cluttered Environments # 0 ! !2 !

DOI: 10.14313/JAMRIS_1-2015/10

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N° 1

2015

Editorial

Robotics is about intelligent connection of perception to action. Perception is the result of observation, i.e. sensing or technically speaking a measurement that leads to the comprehension of the robot’s surroundings or their state. Perception of the environment is of paramount importance to the functioning of robots, especially in semistructured and unstructured dynamic environments. It is the foundation on which robot actions are based, starting from obstacle detection for the purpose of navigation and ending with object recognition for the purpose of understanding the ontological context in which those actions are to be performed. This issue of Journal of Automation, Mobile Robotics and Intelligent Systems collects papers devoted to different aspects of robot perception. This collection is composed of 10 papers. They deal with: • diverse sensors providing perceptual data, • methods of sensoric data processing leading to object and scene recognition, • utilization of ontologies in the process of deriving meaning from the observed data, • methods of sensoric data processing for the purpose of robot control, • use of the results of perception in control of robots.

8 -. 9 . . ; -'

. . '

< tory and visual), going through methods of processing the obtained data and ending with understanding its semantics, so that it can be used for decision making or control. The next two papers are devoted to perception employed in grasping used both in telemanipulated and autonomous robots. Subsequent two papers deal with proprioception employed for walking machine control. The last paper assumes that the perception of the environment in the form of a map is already available to the robot and focuses on motion planning in environments containing obstacles. The following text provides a concise insight into the contents of each of those papers.

The paper entitled Chemical Scanner for Mobile Robot Navigation, authored by Piotr Batog and Andrzej

- - 2 2 8

# 2 . . detects odour gradient, which in turn can be used for mobile robot navigation. The sensor exhibits increased sen

; - -

- 8 2

' >. # presented comprehensibly and compared with the simulation results based on theoretical considerations.

The paper entitled Perceptual Colour Correlogram and Perception-based Statistical Features of Colour Texture,

by Konrad Bojar, introduces the perceptual colour correlogram, generalizing the concept of the spatial grey-level dependency matrix to the case of colour textures. The paper extends Haralikâ&#x20AC;&#x2122;s features extracted from a grey-level

# - .. # > - 8

- # 2 ? .- . . . - - differences are used. The proposed approach enhances robot capabilities of recognising objects in real cluttered ; # 2 >. # - 8 .

2 An analysis of two open source libraries, namely Microsoft Kinect SDK and OpenNI coupled with NiTE, is conducted in the paper entitled RGB-D Sensors in Social Robotics, - ' ! " # % &

2 -

# . - '

@ .

orientation, as well as the stability of the tracking process. Those parameters are important from the point of view of utilising those libraries to design perception subsystems for social robots.

- C ' ( # ) * # + ,-

. . titled Semantic Place Labeling Method discuss the utilisation of a Sick laser scanner and a Kinect RGB-D sensor in object recognition. Dempster-Shafer theory was employed to infer the type of the encountered room based on its 2 ? > #. '

. ' '

8 2 - -

the robot is able to deduce the type of the room it is currently located in. Thus, a semantic localisation is performed.

The paper establishes a direct link between percepts and higher-level ontological concepts what enables the deduction of the purpose of the room, thus classifying it.

The paper: Architecture for an Autonomous Robot at the IT Level, - ' ( #'

# # ( F

! ( &. ! ( # . ' '- ings and their contents. The instances of that ontology are utilised by a robot control system structured as a Service Oriented Architecture. Execution of a service requires the elaboration of a plan composed of elementary actions 8

# . .

2 .

-

.

Articles

3

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 8,

N° 1

2014

executed as expected, otherwise an exception has to be handled, usually requiring an update of the state of the en; # #

# . .

2 . . .. ' ; 8

a simulation environment.

Igor Zubrycki and Grzegorz Granosik authored the paper Intuitive User Interfaces for Mobile Manipulation Tasks, in which they present the development of a human-machine interface to gesture-based control of grippers attached to telemanipulators. The paper focuses on the perception of the human hand motions which are subsequently translated into gripper motion commands. To perceive the hand gestures the sensor glove, Kinect and Leap Motion sensors have been used. As some of the grippers have a different kinematic structure than that of a human hand the mapping of the motion of the latter into that of the former is not a straightforward task.

Wojciech Szynkiewicz in his paper entitled Robot Grasp Synthesis Under Object Pose Uncertainty discusses the . ' # . ' . ' .. > # ' -. J- -

8 -

the number of shape parameters. The parameters of those superquadrics have to be obtained from the perception subsystem. Then a grasp appropriate for that object can be planned. The position and orientation of the grasped object can be estimated by cameras, however even then some uncertainty as to its pose remains, thus this fact has to be taken into account in the planning process. Dynamic simulation taking into account pose uncertainty, object shape modelling by superquadrics and three measures of grasp quality have been used in grasp synthesis for a ma .- J- .. +8

..

- 2 ! )

. .

Legâ&#x20AC;&#x2122;s Tip-Ground Contact Detection Based on Drive Currents in a Real Walking Robot considers the problem of contact detection between the ground surface and the walking robot leg tip. In this case a proprioceptive input is formed by the measurement of total current drawn by the servomotors of each leg.

Detection of leg contact with the ground is essential for proper control of walking. The proposed control method ; 8 9+ # 2 . . #. # '

gait patterns and diverse parameters of motion.

The paper The Role of Compliant Elements in Two-Legged Robotâ&#x20AC;&#x2122;s Foot Model, authored by Magdalena Sylwia 1-

! #

( -#

;

8 - . # #. and springs mounted in each foot of a biped on its postural stability. The proper choice of the parameters of these passive elements improves the postural stability and as a result reduces the need for the compensatory swaying of ' Q ' 2 '

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8

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#' ' J- 2 #. mentation of the ZMP based control method requires a proprioceptive input from force sensors located in the feet of the biped. This is an example showing how adequate design of a mechanism can aid proprioception in devising appropriate control of the bipedâ&#x20AC;&#x2122;s gait. # 0 ! !2 !

. .

Planning the Waypoint-Following Task for a Unicycle-Like Robot in Cluttered Environments investigate the problem of motion planning in cluttered environments. A - . # ' ' -' 2 ? * # - 8 . goal in a cluttered environment, which is represented as a two-dimensional occupancy grid. This map is obtained by perceiving the real environment. The obtained path is then supplemented with robot orientations in the selected .

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# - ; ' 2 . . # . # ' ; 8 ' #- >. # 2 All of the enumerated topics are at the forefront of the currently ongoing research into robot perception. Each of the papers gives a valuable insight into a particular problem, providing its formulation and deriving a solution. This selection of papers reveals the wide scope and diversity of contemporary research conducted on robot perception.

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+ BCD ) D B ) D E CF C G +

/ CH G # C H CD A C B H I ) D B 6 J B H Submitted: 4th November 2014; accepted 10th December 2014;

Konrad Bojar DOI: 10.14313/JAMRIS_1-2015/2 Abstract: In this paper a novel definition and understanding of colour correlogram has been proposed. The proposed colour correlogram generalizes the spatial graylevel dependency matrix (SGLDM) to the case of colour textures. This generalization is based on perceptual colour difference measure expressed in the language of the CIELab colour space components. Application of the colour difference instead of arbitrary colour indices or colour components themselves allows to avoid colour-shuffling palletization and introduction of multidimensional objects, respectively; the proposed perceptual colour correlogram is a single 2D matrix. At the same time, a simple relation of the proposed colour correlogram to the spatial graylevel dependency matrix for graylevel textures is retained.

Based on this relation it will be shown that there exists a vector of statistical features built from the perceptual colour correlogram which can be used to describe textures in perceptual terms. These statistical features and their abovementioned perceptual interpretation generalize Haralick concepts derived for the SGLDM. Keywords: perceptual colour correlogram, perceptual texture features, colour texture classification

$ Colour images acquired in the visible range of electromagnetic spectrum are the cheapest and at the same time the most reliable source of measurements for numerous branches of robotics, including environment perception, mapping, simultaneous localization and mapping, intelligent object manipulation, etc. The ratio of quality and accuracy of measurement data to price of the detector is for digital cameras significantly higher compared to the same ratio for ultrasonic sensors and laser scanners of equivalent spatial range and scanning resolution. In fact, actual price of solutions incorporating visual cameras in the system is substantial effort needed to design and engineer suitable measurement image analysis methods and algorithms. This refers especially to the task of detection, segmentation, and classification of objects of interest. In order to enhance efficacy and efficiency of algorithms it is often decided to employ more than one sensor. In most cases, the second sensor is another visible range camera forming a stereo pair with the first one, or a laser scanner allowing generation of 12

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RGB-D images. However, supplementing visible range cameras with auxiliary sensors does not eliminate difficulties to discern textures on flat surfaces, mostly in the far field area of the scene.

The above reasoning leads to the conclusion that texture analysis in an arbitrary region of interest (ROI) is still a problem with no satisfactory and universal solution. In practice the ROI may happen to be very irregular â&#x20AC;&#x201C; topologically not connected, and of non-smooth boundary. Irregularity of the ROI is a substantial problem for methods based on global transformations [4], such as Fourier or wavelet transformation, or on resolution pyramids. For irregular ROIs far better results are obtained by local (pixelbased [4]) methods. Such methods do not require the ROI to be very regular, as far as it does not contain significantly many holes of size comparable to the size of pixel neighborhood system used in calculations.

Such methods are often based on statistical texture features where during calculation process of statistics the ROIs boundary, and in particular â&#x20AC;&#x201C; shape of this boundary, do not yield any significant contribution to the final feature value. Most commonly used texture features satisfying this condition are based on histogram [11] or on more general concept of SGLDM [5], or on colour correlogram [6], colour cooccurrence matrix [1], and local binary patterns [9]. This class of features is implementation-friendly due to its parallelization potential and no necessity of exhaustive floating-point computations.

In this paper we propose a novel form of colour correlogram and new statistical features of construction similar to SGLDM-based features. The proposed colour correlogram and its derived features retain perceptual interpretation of the SGLDM and its derived features [5], respectively. This property distinguishes our concept of correlogram from other correlograms known in literature.

Organization of the subsequent is as follows. Section 2 contains a brief overview of existing correlograms, in both grayscale and colour. In Section 2.1 the SGLDM and Haralick features as a basis or our definitions are described. In Section 2.2 I outline colour correlogram definitions and point out their flaws. In Section 3 I propose perceptual colour correlogram and introduce its several statistical features with elaboration of their perceptual interpretation. In Section 4 I discuss results of simple numerical experiments revealing typical perceptual colour correlogram form and typical texture feature values. Section 5 contains summary and conclusions.

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! 6. #">0% ) & ) & * , 45$ $ * % .

Spatial GrayLevel Dependency Matrix (SGLDM) defined in Haralickâ&#x20AC;&#x2122;s paper [5] is a common base for all basic concepts and objects discussed in this paper.

Texture features calculated from this matrix are still successfully applied for texture analysis and classification [3, 12]. Currently known generalizations of the SGLDM to the colour domain comprise colour correlogram [6] and colour cooccurrence matrix [1]. Colour correlogram relies on palletization (indexing) process of colours and calculation of the SGLDM of the resultant texture, and colour cooccurrence matrix is in fact a set of SGLDMs, one per every colour channel pair.

All abovementioned concepts are introduced in this section.

! 6. #">0% @ &$ N A 9 " & 6 5 Let be a subset of two dimensional integer latbe the set of graylevels, tice , let be a texture. We assume that the inteand let is endowed with the maximum metric . ger lattice In order to be more specific, the metric is a func, , and tion which for arbitrary is defined by

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By means of the above PDFs, for every texture H and distance value d the following scalar texture features can be introduced [2,4]: 1. Energy (second angular moment) (7) is convex, hence more conThe function centrated PDF yields higher energy value. When the SGLDM entries concentrate around given intensities, it follows that the texture is uniform. Therefore, energy is a global measure of texture uniformity.

2. Contrast (inertia) (8) Contrast measures local texture non-uniformity because the weighting factor promotes far-fromdiagonal regions of the SGLDM. Large values of such entries mean that locally there are many pixels pairs

8

2 .. for example, when there are numerous sharp edges.

Hence, off-diagonal SGLDMs yield higher values of and contrast measures local texture non-uniformity.

3. Correlation (9)

(1) denote cardinality of an arbitrary set .

Let The above notation allows us to introduce the SGLDM by means of the following formula (2)

and are means and are standard where deviations of the respective marginal distributions , . For SGLDM defined by (2) those distributions are equal, hence this feature is another measure of uniformity of .

4. Inverse difference moment (local uniformity) (10)

where is a free parameter. We will not consider directional dependency of texture, hence orientation parameter present in a more general version of the is diSGLDM is omitted. It is straightforward that agonal and this diagonal is simply the histogram of the texture . Therefore SGLDM should be considered as a generalization of histogram. Moreover, from the is symmetdefinition (2) it follows that the matrix ric. It the subsequent text we will omit the superscript as far as it is clear which particular value of is being concerned or when value of is arbitrary. induces a two-dimenEach and every matrix sional probability density function (PDF) by the following normalization: (3)

In order to simplify further considerations, let us introduce the following marginal distributions of the PDF : ,

(4) (5) (6)

Opposed to contrast , we conclude that inverse difference moment measures local texture uniformity because the weighting factor promotes near-diago (0Â&#x2021;"! #.

8 -

far-from-diagonal regions. This happens when many pixels have neighbours of similar intensity. Hence, nearly-diagonal SGLDMs yield higher values of , and inverse difference moment measures local texture uniformity.

5. Entropy (11) is concave, hence more The function yields higher entropy uniform, or constant, PDF value. This means that the more is the SGLDM spread . This hapalong its diagonal, the higher value of pens when many pixels have neighbors of much different intensity. Therefore, the texture is disordered,

8

# # 0 '' . . known in statistical mechanics.

In Haralickâ&#x20AC;&#x2122;s work [5] fourteen texture features have been introduced, while above we have cited only five. Our choice of five features from the full set of fourteen is dictated by the fact that only five of them Articles

13

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can be easily transferred to the colour domain while retaining their analogous perceptual motivation. The remaining nine features can also be transferred to the colour domain, however their meaning is yet unknown. Finding good perceptual motivation for those transferred features is left for future papers.

! ! ) & ) & * ,O ) & ) % $5O # $ $ & A 9 ) & 6 5 Let

be the RGB colour cube and let be any palette (has right inverse in the be a colour texture. category of sets), and let Â&#x192;

8 - # by the following formula:

(12)

' ; 8

# given by (2). However, the SGLDM and the colour correlogram differ substantially, and those differences # # ; 8

. Although the palette range 8

( tion 2 on the set level, it misses numerous additional structures which accompanied the set of graylevels.

Namely, has no natural ordering, hence every permutation of induces a palette carrying equivalent information content, and there is no natural way to distinguish any such permutation. Also, has no natu . 8

' - - 2 sequence, there is no metric on . Additionally, has no natural linear structure allowing scaling, adding, and subtracting colours. In other words, there is no natural way to assess perceptual colour difference , and actual relation of colours between and is not perceptually connected with actual reand for any . lation of colours and In consequence, the above shortcomings of the palette range do not allow to introduce not only features (7)â&#x20AC;&#x201C;(11), but any features involving arithmetic operations on elements of . Although there is no . '

8 -

; - colour correlogram, metrics on a set of all colour cor # <^_U ' - - 8 2 # rics allow employing colour correlograms (12) for Content-Based Image Retrieval (CBIR) tasks [7, 10]. be Now, let be the HSV colour cone and let , which means that every element of is an not further than from some element of (close-touniform quantization). Opposed to previous situation where had no structure, here inherits metric (and therefore also topology) and linear structure from the HSV colour space. Naturally, any colour texture consists now of three independent components, namely 2 0 ; 8 #- + #. nent colour cooccurrence matrix by the following formula [1,13]:

where 14

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(13) . Basically, every colour cooccur-

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rence matrix component is an SGLDM (2) and has properties identical to those of the SGLDM, and therefore we have six independent SGLDMs. Hence, for every such component texture features (7)â&#x20AC;&#x201C;(11) can be computed. In total 30 features can be obtained canin this way. However, mixed components not be given perceptual meaning. Still, those features can be successfully applied to classification of textures [1].

- 0 9$ $ $ 6. $ & + 3 $ 9 . + 3 & ) & ) & * , # $ $ & A When considering application of the above generalizations of the SGLDM to robot perception one immediately encounters conceptual problems because either there are no understandable features, like in the case of colour correlogram, or such features have no clear perceptual interpretation comparable to (7)â&#x20AC;&#x201C; (11) for grayscale textures. This motivates us to de8 . . - - # . ;

-

8 2 8 . #.

proper colour space in which all colour components are easily interpretable in perceptual terms. It is most convenient to use the CIELab colour space [8] which is tailored for this task. The next step is to choose a . . 8

-' of which will serve as actual colour range for textures. A good starting point is to observe that all desired mathematical properties of are assured when we choose to be an -net in . In order to quantize the colour space uniformly in perceptual terms we assume that has metric structure induced by any perceptual colour difference function from the range of â&#x20AC;&#x2122;s described in [8]. Additionally, we assume that the coordinate-wise projection of which the set onto its component forms a set is metrically uniform. This property assures that the and the set of graylevels is comanalogy between plete. be a colour texture and let  Let be any perceptual colour difference function. We by 8 . . - - # means of the following formula:

(14) where is a free parameter. It is straightforward is zero except for the line and this line that is simply the histogram of the texture component . Therefore the perceptual colour correlogram should be considered as a generalization of component of colour texture histogram. It the subsequent text we will omit the superscript as far as it is clear which particular value of is being concerned or when value of is arbitrary.

The perceptual colour correlogram is also connected to the SGLDM by a simple relation. Namely, when the texture is actually gray, which means that , the perceptual colour correlogram are related by (14) of and the SGLDM (2) of the the following formula:

Journal of Automation, Mobile Robotics & Intelligent Systems

,

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(15)

because we assumed previously that the set is metis a non-negative metric. It is rically uniform and easily seen that the perceptual colour correlogram has all the desired properties and none of the drawbacks pointed out in Section 2.2: itâ&#x20AC;&#x2122;s both dimensions have natural order, topology, linear structure, and metric structure consistent with human perception of colours. / . - ; 8

the following PDFs induced by the PPC:

,

(16)

.

(17)

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The more is the PPC is spread along its depen. This happens dent dimension, the higher value of when many pixels have neighbors of many different colours. Such colour textures are highly disordered. * ' ; 8 8 ;

- of the perceptual colour correlogram and we have proved that these features have perceptual interpretation.

1 & 9 ; , $ & 453 $, ; & ) & 5 The features (18)â&#x20AC;&#x201C;(22) introduced above clearly generalize Haralickâ&#x20AC;&#x2122;s features (7)â&#x20AC;&#x201C;(11). Hence, it is expected that they should have strong discriminative power for colour textures. In order to check whether this statement is actually true, we have used MITâ&#x20AC;&#x2122;s vismod texture database [14]. Two examples of these textures are shown in the figure below.

The second equality in the above equation states equals the marginthat the marginal distribution for the SGLDM. al distribution Now, we are ready to define statistical features of the perceptual colour correlogram: 1. Energy (second angular moment) (18) yields higher energy value.

Concentrated PDF

- 8 > and values, it can be shown that the texture is uniform.

Therefore, energy is a global measure of colour texture uniformity.

2. Contrast (inertia) (19) Contrast measures local texture non-uniformity because the weighting factor promotes the region of is large. Large values of such enthe PPC for which tries mean that locally there are many pixels pairs of

8

- 2 3. Correlation (20)

where and are means and are standard de, viations of the respective marginal distributions , where the latter marginal distribution is defined . By its definition, correlain the same manner as tion measures constancy of .

4. Inverse difference moment (local uniformity) (21) Opposed to contrast , we conclude that inverse difference moment measures local colour texture uniformity.

5. Entropy (22)

Fig. 1. The top image shows colour texture of beans,

: :" ; : : : : % : !: 4

: Articles

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Journal of Automation, Mobile Robotics & Intelligent Systems

Both images have been acquired in the similar lightning conditions and using the same exposure . # 2 Â&#x152; - ' # 9^_Â 512.

Acquired texture resolution implies that each texture consists of 262,144 pixels and contains numerous characteristic microstructure cells. Therefore, description of such a texture in statistical terms is reasonable.

For textures shown in Fig. 1 the SGLDMs were calculated, and conversion to grayscale has been and components of texachieved by dropping tures after transforming it to the CIELab colour space.

Exemplary SGLDM surface plot and PPC surface plot is shown in the figure below.

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non-uniform. This follows directly from the very definition of : when it means that a not trained observer easily sees significant colour difference.

For both texture classes shown in Fig. 1, Haralickâ&#x20AC;&#x2122;s features (7)â&#x20AC;&#x201C;(11) and proposed features (18)-(22) were calculated. Values of these features are assembled in the table below.

Feature

Coffee texture in Fig. 1

Beans texture in Fig. 1

4.2Ă&#x2014;10â&#x20AC;&#x201C;4

5.2Ă&#x2014;10â&#x20AC;&#x201C;4

6.0Ă&#x2014;10â&#x20AC;&#x201C;4

8.2Ă&#x2014;10â&#x20AC;&#x201C;4

5.0Ă&#x2014;102

5.1Ă&#x2014;102

7.5Ă&#x2014;102

6.7Ă&#x2014;102

8.8Ă&#x2014;10â&#x20AC;&#x201C;6

8.6Ă&#x2014;10â&#x20AC;&#x201C;6

â&#x20AC;&#x201C;4.3Ă&#x2014;10â&#x20AC;&#x201C;6

9.1Ă&#x2014;10â&#x20AC;&#x201C;6

6.2Ă&#x2014;10â&#x20AC;&#x201C;2

6.9Ă&#x2014;10â&#x20AC;&#x201C;2

1.0Ă&#x2014;10â&#x20AC;&#x201C;1

1.5Ă&#x2014;10â&#x20AC;&#x201C;1

3.8

3.8

4.0

3.9

Tab. 1. List of mean values of Haralick features and proposed features for textures shown in Fig. 1

Fig. 2. The top plot contains the SGLDM of the L* component of the upper texture depicted in Fig. 1. The lower plot contains the PPC of the upper texture depicted in Fig. 1 During calculation of the above PPC, simplest . ' 8

- # - used. Hence, the colour difference was simply Euclidean distance in the CIELab colour space. For both SGLDM and PPC the free distance parameter was set to 30 pixels. This value is larger than typical microstructure cell size (here â&#x20AC;&#x201C; grain size), hence summa

.

8

of the SGLDM and the PPC was running over several microstructure cells. / ' ; 8 -

;

' dimension while there is no sigis skew along its

8

(0Â&#x2021;"! (0Â&#x2021;"!

almost rotationally symmetric. Such phenomenon was observed for all investigated textures of approximately symmetric histogram of intensity, and the reason for this is explained by the relation (15) of both matrices. which The PPC attains a broad maximum at means that the investigated texture is perceptually 16

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Values shown in the above table prove that the proposed features can discriminate textures shown in Fig. 1. It must be noted that differences among colour features (18)â&#x20AC;&#x201C;(22) for both texture classes are larger than differences among respective grayscale features (7)â&#x20AC;&#x201C;(11). This can be explained by the fact that the investigated texture classes are more distinct when colour components are retained than when those components are disregarded; it has been observed that the beans texture is more uniform mainly in its component, while its colour components are very similar to these of coffee texture.

Hereby we have shown an example of natural colour textures for which the proposed features (18)â&#x20AC;&#x201C; (22) express discriminatory capabilities not worse Haralick features (7)â&#x20AC;&#x201C;(11). More extensive test for larger set of colour texture classes will be performed in future. Also, in coming research it will be investigated whether the proposed features (18)â&#x20AC;&#x201C;(22) allow to discern textures which cannot be separated by Haralickâ&#x20AC;&#x2122;s features (7)â&#x20AC;&#x201C;(11).

8 # ,, In this paper we introduced a novel type of colour correlogram, the perceptual colour correlogram, generalizing concept of the spatial graylevel dependency matrix (SGLDM) to the case of colour textures. For construction of the perceptual colour correlogram measure describing perceptual colour we used the difference. Therefore it became possible to interpret the introduced colour correlogram in perceptual terms. The PDF induced by the perceptual colour correlogram was used to define five statistical features generalizing Haralick features of the SGLDM. These

Journal of Automation, Mobile Robotics & Intelligent Systems

features can be used for colour texture classification or statistical modelling.

It is planned to investigate the introduced statistical features more thoroughly in order to gain deeper understanding of their relations to Haralick features.

This understanding should prove useful to define further perceptual colour correlogram features. Also, extensive numerical experiments should be conducted to test actual discriminative power of the introduced statistical features. Moreover, it seems that the proposed features can be easily generalized to account for texture orientation parameter (horizontal, vertical, and two diagonals) present in the generalized SGLDM. In future works the proposed features will be compared to state-of-the-art features, like Gabor-filter features present in MPEG-7 texture descriptor.

) ;<=>40"4%4;6# This work was supported by â&#x20AC;&#x153;Autonomy in rescue and exploration robotsâ&#x20AC;?, RobREx, realized for The National Centre for Research and Development, grant number PBS1/A3/8/2012.

?6@< Konrad Bojar â&#x20AC;&#x201C; Laboratory of Autonomous Defense Systems, Industrial Research Institute for Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486 Warsaw, Poland.

E-mail: kbojar@piap.pl, www: http://www.piap.pl.

4A4 4;)4# §]^{ ; X2 2 Â&#x17D;0

- matrix for colour images: application to colour texture classificationâ&#x20AC;?, Image Analysis & Stereology, vol. 23, 2004, 63â&#x20AC;&#x201C;72. DOI: 10.5566/ias.v23. p63-72. §]_{ %2 0 - %2 Â&#x17D; #. ; - # > measures for maximum likelihood texture classificationâ&#x20AC;?, IEEE Transaction on Systems, Man and Cybernetics, vol. 21, no. 1, 1991, 252â&#x20AC;&#x201C;261. DOI: 10.1109/21.101156. §]`{ 2 Â&#x2C6;

!2 Â&#x17D; #. ; ations of dynamic textures by means of the SGLDM with application to solar EIT imagesâ&#x20AC;?, Machine Graphics & Vision, 2008, vol. 17, no. 3, 219â&#x20AC;&#x201C;247. §]~{ " > 2 * Â&#x2C6;2 2 Â&#x17D;/# > - niques â&#x20AC;&#x201C; Surveyâ&#x20AC;?, 3rd International Conference on Advanced Computing & Communication Technologies, Rohtak, April 6â&#x20AC;&#x201C;7, 2013.

DOI 10.1109/ACCT.2013.49. §]9{ * Â&#x152;2 ( #- # 2 "

/2 Â&#x17D; >tural features for image classificationâ&#x20AC;?, IEEE Transactions on Systems, Man and Cybernetics, vol. 3, no. 6, 1973, 610â&#x20AC;&#x201C;621. DOI: 10.1109/ TSMC.1973.4309314. §]|{ *- %2 2 Â&#x17D;(.

- / >

Applicationsâ&#x20AC;?, International Journal of Computer Vision, vol. 35, no. 3, 1999, 245â&#x20AC;&#x201C;268. DOI: 10.1023/A:1008108327226.

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§] { (2

!2 0 '' - !2 Â&#x17D; . - colour descriptor based on spatial distribution: A top-down approachâ&#x20AC;?, Image and Vision Computing, vol. 28, 2010, 1309â&#x20AC;&#x201C;1326. DOI: 10.1016/j.imavis.2010.01.012. §]}{ ! !2 Â&#x17D; /[Â&#x2021; +' - ference formulasâ&#x20AC;?, Colour Research and Application, vol. 25, 2000, no. 1, 49â&#x20AC;&#x201C;55. DOI: 10.1002/ (SICI)1520-6378(200002)25:1<49::AIDCOL7>3.0.CO;2-4. §]Â&#x20AC;{ Â&#x2C6; Â&#x2021;2 Â&#x2021;-#

2 # (2 Â&#x17D;(- ; LBP based texture descriptors for image classificationâ&#x20AC;?, Expert Systems with Applications, Vol. 39, 2013, 3634â&#x20AC;&#x201C;3641. DOI: 10.1016/ j.eswa.2011.09.054.

[10] S. Shim, T. Choi, â&#x20AC;&#x153;Image indexing by modified colour cooccurrence matrixâ&#x20AC;?. In: Acoustics, Speech, and Signal Processing. Proceedings * April 6â&#x20AC;&#x201C;10, 2003, vol. 3, IIIâ&#x20AC;&#x201C;577.

DOI: 10.1109/ICASSP.2003.1199540.

[11] Swain M., Ballard D., â&#x20AC;&#x153;Colour indexingâ&#x20AC;?, International Journal of Computer Vision, vol. 7, no. 1, 1991, 11â&#x20AC;&#x201C;32. DOI: 10.1007/BF00130487.

[12] Raheja J., Ajay B., Chaudhary, â&#x20AC;&#x153;Real time fabric defect detection system on an A. embedded DSP platformâ&#x20AC;?, Optik-International Journal for Light and Electron Optics, 2013, vol. 124, no. 21, 5280â&#x20AC;&#x201C;5284.

DOI: 10.1016/j.ijleo.2013.03.038.

[13] Vadivel A., Sural S., Majumdar A., â&#x20AC;&#x153;An integrated colour and intensity cooccurrence matrixâ&#x20AC;?, Pattern Recognition Letters, 2007, vol. 28, 974â&#x20AC;&#x201C;983.

DOI: 10.1016/j.patrec.2007.01.004.

[14] http://vismod.media.mit.edu/pub/VisTex/ VisTex.tar.gz, MIT Texture Database, accessed on 13 Dec. 2014.

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Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N° 1

2015

> EgH 6 /" B G ) C 0

7CH G 0 j )B H

C CD =CDk E Submitted: 15th October 2014; accepted 11th January 2015

. / DOI: 10.14313/JAMRIS_1-2015/8 Abstract: To ensure an effective walking over uneven terrain for multilegged walking robots, there is necessary to detect the contact between the legâ&#x20AC;&#x2122;s tips and the ground. It is essential to determine the moment when we should end the swing phase of the leg. This paper presents a method of detecting contact with the ground based on total current drawn by the servomotors of each robotâ&#x20AC;&#x2122;s legs.

The method was developed using a 4-legs supported gait on 5-legged walking robot â&#x20AC;&#x201C; PentOpiliones. This detection method has been tested and positively verified on a real robot. Also there has been tested the limitation of above method using a gait with different robot postures and different speeds.

Keywords: 5-legged walking robot, walking on uneven terrain, 4-legs supported gait, ground contact detection, servomotor current, load estimation

1. Introduction To allow the robot to move over an uneven terrain it is necessary to detect the moment when the leg is landing on the ground [11]. This detection can be realized in many ways, using different sensors, typically located at the legâ&#x20AC;&#x2122;s tips: â&#x20AC;&#x201D; mechanical switches â&#x20AC;&#x201C; the simplest sensors, which under the load are mechanically switched, close the circuit and signalize the collision. They return a binary signal; are easy to use but often sensitive to mechanical damage. They are used for example in many hexapod robots [6] â&#x20AC;&#x201D; strain gauges â&#x20AC;&#x201C; depending on the number of sensors, they allow to measure forces and torques along many directions [5]. They perform an accurate measurement, but usually are larger and more expensive than mechanical switches. â&#x20AC;&#x201D; sensors that measure mechanical deformation â&#x20AC;&#x201C; while placing the leg, its tip is deformed, what can be measured for example with a potentiometric displacement sensor. It is particularly suitable for solutions where the leg tip must be elastic for example to absorb the impacts. â&#x20AC;&#x201D; proximity sensors â&#x20AC;&#x201C; depending on the ground properties in robotâ&#x20AC;&#x2122;s environment, there can be used a capacitive proximity sensors, inductive or reflective infrared light sensors. They detect the proximity between the ground and legâ&#x20AC;&#x2122;s tip, 62

however, they require that the ground must have some specific properties, for which the sensor is sensitive.

Another method to detect the leg contact with the ground can be realized base on measurement of supply current drawn by the servomotors in each of the robotâ&#x20AC;&#x2122;s legs. Such a possibility was decided to consider in this paper. The remainder of the paper is structured as follows: section 2 describes the outline of the robot construction, section 3 presents the 4-legs supported gait used during this research, while section 4 provides a detail description of legs current measurements. The algorithm of ground detection is described in section 5 and in section 6 it is verified during the gait on uneven terrain. Section 7 shows the efficiency of ground detection in gait with various parameters. The paper is concluded in section 8 with a short film presented the results of a developed gait with a ground detection.

2. Robot Platform Used in the Research As a platform for research a 5-legged walking robot â&#x20AC;&#x201C; PentOpiliones was used [9]. It is a robot with five legs and a radial symmetry (Fig. 1a). The legs are positioned at 72 degrees to each other, similarly like in other 5-legged robots [2]. This solution allows moving legs in each direction with the same simplicity [4].

The construction is driven by a standard servomotors, like these used in remote control models, and have a torque of 1.0 Nm. Legs have a classical kinematics scheme with three degrees of freedom and insect-like structure [3]. The two main segments of a leg (femur and tibia) have length of 150 and 250 mm, respectively. The legs in robot were indicated with a consecutive number from 1 to 5 (Fig. 1b).

3. Gait used in the research During the research, there was used a 4-legs supported gait. The goal was to develop a method of the effective detecting the contact between the legâ&#x20AC;&#x2122;s tips and the ground during the landing phase of the leg.

This is necessary to provide the gait on an uneven terrain where the level of the ground is uncertain.

In 4-legs supported gait at any time exactly one leg is moved, while the others support the robot. It consists for each of the legs from following phases: â&#x20AC;˘ Swing phase â&#x20AC;&#x201C; on flat terrain it lasts exactly 20% of time (1/5 gait cycle) and is divided into: â&#x20AC;&#x201D; leg rises up â&#x20AC;&#x201C; the legâ&#x20AC;&#x2122;s tip is constantly raised up to desired level, â&#x20AC;&#x201D; leg floats to the front â&#x20AC;&#x201C; the legâ&#x20AC;&#x2122;s tip is constantly

Journal of Automation, Mobile Robotics & Intelligent Systems

carried along the half-circle trajectory to the front (in direction of movement), â&#x20AC;&#x201D; leg lands â&#x20AC;&#x201C; legâ&#x20AC;&#x2122;s tip is constantly lowered until the contact with the ground is detected (if the robot is walking on uneven terrain we donâ&#x20AC;&#x2122;t know on which level is the ground), â&#x20AC;&#x201D; legâ&#x20AC;&#x2122;s correction, trunk carried â&#x20AC;&#x201C; there can be a delay in the ground detection and legâ&#x20AC;&#x2122;s tip can override the real level of the ground.

In this situation it is necessary to move the legâ&#x20AC;&#x2122;s tip back to the position where the ground contact was really detected. It is necessary to align the load among all legs.

Additionally in this phase, the trunk is constantly transferred to the front relative to the ground, with a distance of 1/5 step length.

This ensure the moving of the robot and is realized by moving the legâ&#x20AC;&#x2122;s tips constantly to the back with a distance of 1/5 step length. â&#x20AC;˘ stance phase â&#x20AC;&#x201C; the leg end is on the ground and supports the weight of the robot. During this phase, all other legs are consecutively performing a swing phase.

The above phases for any two legs lying side by side are shifted with 144 degrees in phase to each other. This means that after the swing phase of any leg, the leg on the opposite side of the robot starts the swing phase (they moves in the following order: leg number 1, 3, 5, 2, 4, 1â&#x20AC;Ś. The 4-legs supported gait can be realized without detecting the ground contact

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Fig. 2. Leg trajectory in 4-legs supported gait

only on a flat terrain, because only then we can exactly determine when the leg should ends its swing phase without using any additional sensors.

During the research there was used a 4-legs supported gait with a legs trajectory shown in Figure 2 and with the following specification [10]: â&#x20AC;˘ step length: 80 mm, â&#x20AC;˘ maximal height of legs lift up: 200 mm below the trunk, â&#x20AC;˘ average height of trunk above the ground: 255 mm, â&#x20AC;˘ maximal height of legs put down: 315 mm below the trunk, â&#x20AC;˘ duration of one step: 3.5 sec, â&#x20AC;˘ distance between the leg neutral support point and the robotâ&#x20AC;&#x2122;s center: 260 mm.

The analysis of the legs load was performed 50 times per second, what is sufficient due to the dynamics of the robot.

1 % 9 . ) ) , the Robotâ&#x20AC;&#x2122;s Legs

Fig. 1. PentOpiliones â&#x20AC;&#x201C; 5-legged walking robot used for a research

In PentOpiliones robot simple servomotors without the possibility of current measurement are used.

Nevertheless, in electronic circuit was considered the possibility to measure a total current drawn by each of five robot legs. These five currents signals drawn by each of the leg are the only information used during this research to determine the load of the legs. We proved that this is sufficient information to detect the moment when the leg has a contact with the ground and to allow walking on uneven terrain.

The supply current drawn by all three servomotors in each leg is measured basis on voltage drop on a shunt resistor with a resistance of 10 mOhm (Fig. 3).

This voltage is amplified 50 times and shifted to the ground level by the INA168 amplifier [8]. Next the signal is converted by a 12-bit analog to digital converter in a main robot microcontroller: STM32F407 [7]. The above measurement method allows the measure up to 3 Amps with an absolute error smaller than 30 mA. As confirmed by further tests, this accuracy is sufficient enough.

The electronic circuit in servomotor is a switching regulator and it controls the motor with a frequency of 1000 Hz, so it draws a pulse current. To allow the Articles

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analyzed in a real time in the robot control application to verify the quality of all tested filters.

5. Analysis of Legs Load

Fig. 3. Part of an electronic schematic which measure the supply current in one of the legs

estimation of leg load base on drawn current it is necessary to average it. Therefore, the microcontroller samples the current at a frequency of 50 kHz and averages it with the digital FIR filter:

(1)

where: P – value of averaged current, z[i] – measuring sample delayed by i measurements relative to the most recent.

According to the above formula (1), the filter works on the last 2000 samples (40 ms of time) and as was validated by the practical tests this filter behaved the best among several tested filter. The results of filtering was wirelessly sent to the computer and

The first test was executed to familiarize oneself with a correlation between the value of measured current in each of the legs and a legs load. There was used a 4-legs supported gait on a flat terrain, but legs were not stopped when they touched the ground, and they were farther moved down, up to the end of their working space. That means that during the leg landing in a swing phase, the leg was lowered so low, that after the collision with the ground there was a big overload on its servomotors. It can be observed in the Fig. 4 of legs current consumption. In the presented case the robot was moving in the direction of the leg number 1.

The supply current consumed by each of the legs during the landing phase varies considerably among them. This is because the legs are not always arranged ideally symmetrically (in regular pentagon) and at various moments, some of the legs are more loaded.

After analyzing the data we decided that it is worth to add an additional parameter to easier determine the moment of leg tip contact with the ground. Let’s call this parameter as an overload current in putting the i-th leg (Ki): (2) where: Ik – current consumed by the k-th leg.

The overload current is defined as a weighted arithmetic sum of supply current consumed by consecutive legs. It is due to the fact that in the leg which has a ground contact, the load will increase the most

Fig. 4. Legs consumed current during the walk without ground detection 64

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Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N째 1

2015

after this contact (weight 5). Simultaneously in two nearest legs the load will decrease (weight -2) and in two legs on the opposite side the load will also increase (weight 1). The above coefficients were determine experimentally. Such defined parameter of an overload current is appropriate to determine the moment when the leg had a contact with the ground and it was shown in Fig. 5 during the situation of landing leg number 3 from the Fig. 4.

Based on increase of the overload current, there is a possibility to detect a leg contact with the ground.

After some tests, to resist the detection to the external disruptions, it was decided that the ground contact will be approved if the instantaneous overload current exceeds the average overload current more than the offset of 375 mA (Fig. 5). An average overload current is averaged by a digital low pass filter with a time constant of 250 ms.

: U $9$ $ 0 2 & 3 % . 9 " 0 $

Fig. 5. Chart with an overload current of the leg number 3 during the swing phase. This is enlarged chart fragment indicated in Fig. 4 with a black frame

To expand the 4-legs supported gait on a flat terrain to a gait on an uneven terrain it is necessary to detect the moment of leg contact with the ground to ends the landing phase of the leg [1].

In the previous section, after ground contact detection, the leg landing phase was not stopped. This was because we wanted only to observe the behavior of the overload current. In this section, the algorithm will stop the leg landing phase immediately when the ground contact is detected.

Above method based on overload current is sufficient for ground detection. It was verified in practice on an uneven terrain. Recorded measurements of cur-

Fig. 6. Legs consumed current during the walk on uneven terrain with ground detection Articles

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Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

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Fig. 7. Enlarged fragment from the Fig. 6 (landing phase of the leg number 1)

rents are illustrated in Fig. 6. There are 3 steps performed consecutively with the leg number 1, 3 and 5.

For each of these steps, there is also marked a calculated overload current.

We can see that unlike the Fig. 4, in Fig. 6 leg landing phase is much shorter. It lasts only to the moment when a leg contact with a ground is detected.

The above algorithm has an assumption that the leg end hit on the ground during its landing phase. Otherwise, the leg will be lowered until the end of its working space, and will stop over the ground (in case of very deep holes in the ground).

In Fig. 6 we can also see the constantly growing current for some of the legs (leg 2 and 4 from 3.0 to 4.5 second or leg 1, 2 and 4 from 6.5 to 7.9 second). It is caused by a poor quality of servomotors. The control error in servomotor regulator is slowly increasing, while the servomotor does not react by some friction on the gear and this cause the increasing of the current. Nevertheless, the above situations do not have an influence to the ground detecting, because landing the leg on the ground cause more significant changes in measured currents.

Two fragments from Fig. 6 (which shows the landing phase of the leg number 1 and 3) were enlarged and are shown in Fig. 7 and Fig. 8. The overload current in this figures was scaled to increase the clarity.

In Fig. 7 and Fig. 8 we can clearly see the current consumed by each of the leg and the overload current during the practical test on uneven terrain. The landing phase of the leg is always ending, when the ground is detected. We can also observe that during the ground contact there is not any significant increase in current of leg which was putting down. Therefore, it was necessary to introduce and calculate an overload current, which allows to determine the moment of ground con66

Articles

Fig. 8. Enlarged fragment from the Figure 6 (landing phase of the leg number 3)

Fig. 9. Different poses used in robot gait tact more precisely.

As practical tests have shown, the moment of ground detection determine on above method, existed almost exactly on the moment of a real support of the leg. There was only a slight delay from ground contact to detect it by algorithm. Nevertheless, the change in a legâ&#x20AC;&#x2122;s tip position during this delay was very small and comparable to the backlash which is a result of used servomotors quality. Therefore, this delay could be neglected and there is no necessary to correct the legâ&#x20AC;&#x2122;s tip position after ground detection.

W * 9 33&$ $&$ 9 . 0 2 & 3 Method The developed method works effectively with the gait specified in section 3. It was a gait with a neutral robot poses, like Pose I in Fig. 9, and was relatively slow (3.5 second for 1 step). In further tests, the speed of gait was increased to determine the limitation of this method. The results are shown in Figure 10. With the faster speed there was more false detection of the ground. The time of one step was decreasing each 0.25 second from a 3.5 second, and for each try robots made 50 steps while there was counting the number

Journal of Automation, Mobile Robotics & Intelligent Systems

VOLUME 9,

N° 1

2015

4A4 4;)4#

Fig. 10. Limitation of the ground detection according to the different poses and speed

of false ground detection.

The method of ground detection was also tested for a different poses: with a right angle in the last joint and with highly raised trunk (Pose II and Pose III in Fig. 9). These poses are less optimal in terms of motion range and stability, nevertheless it was expected that it may be better in contact detection. As shown by the tests (Fig. 10), the efficiency of ground detection is similar to each other. The maximal speed of a robot for proper ground detection is about 2.25 second per step and the robot pose does not have a big influent to it.

X ) & $ The measurement of the total current drawn by each of the legs provides a small amount of data. Despite this, it was proved in practice that it is sufficient for proper ground detection and to provide the gait on uneven terrain.

The developed method was shown on video1.

It works successfully in 4-legs supported gait with a speed not faster than 2.25 second per step. During the higher speed, the algorithm begins to return some false ground detections. There were also tests to expand the above method to a 3-legs supported gait.

Nevertheless it is more complicated task and this attempt was not successful.

The described method of ground detection has a big potential, especially in a small walking robots.

In these robots often there is not enough space to mount a special contact sensor in the legs or limited funds does not allow to buy this sensors. This method could be also used as a redundant method to detect the ground in more sophisticated robots.

;<64# A supplemental video is available at: http://lrm. cie.put.poznan.pl/JAMRISgaitMW.wmv

?6@<

â&#x20AC;&#x201C; Poznan University of Technology, Institute of Control and Information Engineering, ul. ` |Â +Â&#x20AC;|9

e-mail: wasik.m@gmail.com, www: http://www.cie.put.poznan.pl/.

§]^{ "2 2 Strategia adaptacyjnego * " ! 3  % nie (Robot motion adaptive strategy of walking on uneven ground), Warsaw Univ. of Tech.

-'2 * - ' # ' 2 2 C. Zielinski, Warsaw 2010, 625â&#x20AC;&#x201C;634. (in Polish) §]_{ 2 Â&#x152;2 # 2 '- (2 -

â&#x20AC;&#x153;The Study on Optimal Gait for Five-Legged Robot with Reinforcement Learningâ&#x20AC;?. In: Proc. Int. Conf. on Intelligent Robotics and Applications ICIRA, 2009, 1170â&#x20AC;&#x201C;1175, DOI: 10.1007/978-3642-10817-4_114. §]`{ Â?2 "- 2 (2 Â&#x2030;- %2 Â&#x2021; - Â&#x17D; . 0

#

* > .

Robotâ&#x20AC;?. In: Proceedings of the IEEE International Conference on Robotics & , New Zealand, December 2009, 1851â&#x20AC;&#x201C;1855, DOI: 10.1109/ICCA.2009.5410582. §]~{ 2 / - 2 - - 2 -' 2 Â&#x17D;Y#ni-directional Gait of Limb Mechanism Robot Hanging from Grid-like Structureâ&#x20AC;?. In: Proceedings of the 2006 IEEE/RSJ International & ! ) * , October 2006, 1733â&#x20AC;&#x201C;1737. DOI: 10.1109/ IROS.2006.282133. §]9{ 02+(2 # *2 %2 ( %2 Â&#x2030; Â&#x17D;" ; .# 6-axis Force/Moment Sensor for Humanoid Robotâ&#x20AC;&#x2122;s Footâ&#x20AC;?, IEEE Sensors, October, 2007, 217â&#x20AC;&#x201C; 220, DOI: 10.1109/ICSENS.2007.4388375. §]|{ 2 !

- !2 Â&#x152;2 2 ! -# ?2 (

â&#x20AC;&#x153;Walking Hexapod Robot in Disaster Recovery: Developing Algorithm for Terrain Negotiation and Navigationâ&#x20AC;?, New Advanced Technologies, Aleksandar Lazinica (Ed.), ISBN: 978-953-307067-4, InTech, 2010. DOI: 10.5772/9437. §] { ( !

( !`_?~ 9>> ( !32F407xx, Doc ID 022152 Rev 3, http://www. st.com/. 2012. §]}{ > / -# /Â&#x2C6; ^`} /Â&#x2C6; ^|} * +(

Measurement CURRENT SHUNT MONITOR, http://www.ti.com/, 2005. ]Â&#x20AC;{ !2 ) Â&#x17D;

. & F ' ) Â&#x2020; <" > -

of 5-legged walking robot). In: Innowacyjne % " % * *

3 Â % (Innovative solutions in the field of automation, robotics and measurement), Series: PIAP Monographies, Warsaw, 2013. (in Polish) ]^Â { !2 ) !2

2 ( . Â&#x17D;Â&#x192; conventional 5-legged robot for agile locomotionâ&#x20AC;?. In: Nature-Inspired Mobile Robots. Proceedings of the 16th International Conference on

* ! ^ ! ) * 33 Technologies for Mobile Machines, 2013, 335â&#x20AC;&#x201C; 342, DOI: 10.1142/9789814525534_0043.

[11] T. Zielinska, 6 " 3 % 3 q % %

% * !

(Walking nachines: fundamentals, design, control and biological patterns), Warsaw, PWN 2003. (in Polish).

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