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DR.A.PURUSHOTHAM* et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 7, Issue No. 2, 305 - 312

Simulation Studies on Dynamic Contact Force Between Mobile Robot Manipulator and Surrounding Environment

environments with human are named humancentered robots [1]. Most of the safety aspects of Mobile manipulators are connected with the mutual interaction between mobile manipulator and the work or surrounding environment. The impulse force generated due to contact is the main mechanical disturbing force that de-stabilizes the overall system. Therefore controlling impulse force in dynamic environment is essential task in mobile robot manipulation system for the safety of robot. Mobile robots have to meet the safety requirements besides the traditional requirements for performance. The mobile manipulator dynamic disturbance depends on its mechanical, electrical and software characteristics. It is known that by means of sensors and feed backs can be cut off some potential anomalies and to be avoided cases of not desired contact or collision. But even the most robust systems are not guaranteed of some unpredictable electrical, sensor or even software errors. That is why the mechanical characteristics of the mobile manipulator systems are the key factor for decreasing dynamic impulse force and increasing the whole safety. In mobile robotic manipulation system, the tasks performed by manipulation system create the impulse forces during the operations. In this paper a simple model of mobile robotic manipulation system developed along with mathematical relations and the influence of the basic mechanical characteristics of manipulator (i.e. stiffness, damping and inertia) is studied in limiting the dynamic impulse force. The safety of the system is realized in terms of reduced impact forces. The choice of mechanical parameters is shown with respect to impact interaction, oscillation damping and contact configuration. The

ABSTRACT: In mobile robotic manipulation system , the tasks performed by manipulation system create the impulse forces during the operations .The impulse force generated due to contact is the main mechanical disturbing force that de-stabilizes the overall system. Therefore controlling impulse force in dynamic environment is essential task in mobile robot manipulation system for the safety of robot. It is also realised that the mechanical characteristics of the mobile manipulator systems are the key factor for decreasing dynamic impulse force and increasing the whole safety. In this paper, a model of a mobile robotic manipulating system is proposed to study the characteristics of dynamic mutual interaction force between the mobile robot Manipulation and the surrounding Environment.

J.ANJANEYULU Assistant Professor of Mechanical Engineering Vasavi College of Engineering, Ibrahimbagh, Hyderabad -500 031, A.P., India Email: anjaneyulu_jalleda@yahoo.co.in

DR.A.PURUSHOTHAM* *Professor of Mechanical Engineering Sreenidhi Institute of Science & Technology (An Autonomous Institution) Hyderabad-501 301, A.P. India Email : apurushotham@rediffmail.com

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Key words: Mobile Manipulation, Surrounding, Stiffness, Damping I.

INTRODUCTION

In the future, robots will take an active role not only in industry, but also in human life. Especially mobile robots are developed for domestic services, waste disposal, earthquake services, military services and entertainment. In all these applications, the interaction between robot and surrounding environment is an important for the success of operations. A few number of scientific publications and scientific congregations and events in recent years form a new scientific area dedicated to the mutual interaction â&#x20AC;&#x153;mobile robots environmentâ&#x20AC;?. Robots that share the space and

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II.

PROBLEM FORMULATION

 k11  The stiffness – K  k 21  k31

k 12

b11  The damping - B  b21  b31

b12

k 22 k32

b22

k13  k 23  k3 

(3)

b13  b23  b33 

(4)

b32

 I 11 I 12 I 13    (5) The inertia - M  I 21 I 22 I 23    I 31 I 32 I 33  Parameters K, B and M are termed as impedance parameters.

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Figure.1 shows the configuration of the mobile manipulator. It resembles three link and three degree freedom articulated robot. The only difference is the base link is mounted on a platform which has the translate degree of freedom in Xdirection. Thus the base link has two degrees of freedom: rotation and translation. The surrounding environment is assumed stationary when the contact of end effector takes places. The mobile platform is treated like a cylindre with height H[m] and diameter D[m]. The joints of the manipulator are presented like cylindres with length l1, l2, l3 [m] and diameters d[m].

For the mobile articulated manipulation shown in Figure.1, various terms in equation (1) can be written as  Fx  The contact force - Fcont   Fy  (2)  Fz 

simulation studies are carried out using Matlabsimulink software. The paper is organized as follows: The problem formulation for the model of mobile robot system is done in chapter-II. ChapterIII gives the simulation results of the model. Finally conclusions are drawn in chapter IV.

Fig.1: Configuration of mobile manipulating system

The basics of the control approach of the dynamic mutual interaction between the mobile robot manipulation system and the surrounding environment are founded by Neville Hogan in 1985[2]. This approach is called impedance control. The dynamic force of the manipulator end effector interaction with the surrounding environment can be presented by the equality:

 x The position of end effector at the time t- X   y   z  (6) .  x.  The velocity of end effector at the time t - V   y  . z   (7)

The position of end effector at the time t=t 0--- x0  X 0   y 0  (8)  z 0  t 0

Fcont  K [ X 0  X ]  B[V0  V ]  MV / t (1)

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It is important to produce manipulators possessing naturally low impedance in order to achieve natural safety in the mutual interaction “robotsurrounding”. But, most of the up to date robot manipulators designed so far possess high effective impedance. [3]. The manipulation system impedance must be specified to certain suitable levels in order to increase the safety level. This can be achieved by means of specifying separately the components of the mechanical impedance: (i) inertia, (ii) damping and (iii) stiffness.

I q 22  [(0.25m2  m3 )l22  m3l2l3 cos 3  0.25m3l32 ] I q 23  [(0.25m3l32  0.5m3l2l3 cos 3

I q32  [(0.25m3l32  0.5m3l2l3 cos 3 I q33  [(0.25m3l32  J 11 J   J 21  J 31

J 12 J 22

J 13  J 23  J 33 

(12)

J 32 Where J 11   sin 1 [l 2 cos 2  l3 cos( 2   3 )] J 12   cos1 [l 2 sin  2  l3 sin( 2   3 )] J 13  l3 cos1 sin( 2   3 )]

J 21  cos1 [l 2 cos 2  l3 cos( 2   3 )] J 22   sin 1 [l 2 sin  2  l3 sin( 2   3 )] J 23  l3 sin 1 sin( 2   3 )]

J 31  0

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If the end effector effective inertia is reduced then the shock impulse force is also reduced because it is dependent mainly on the inertia and on the velocity variation. The effective inertia can be actively modulated by means of feed backs and then it is dependent on the characteristics of the close loop control system. A series of restrictions exist here such as driving forces and torque’s range, sensor delays, stability problems and others. Another inertia modulation approach is the passive approach that requires kinematics redundancy in the manipulation system. The redundant number of degrees of mobility allows manipulator configuration variation at the same positioning of the end effector [4]. The configuration variation yields new inertia Mq in the system which is given by

I q11  (0.25m2  m3 )l22 cos2  2  m3l2l3 cos 2 cos( 2  3 )  0.25m3l32 cos2 ( 2  3 )

The velocity of end effector at the time t=t 0 , .  x.  (9) V0   y  . z   t 0

M  J T M q J 1

(10)

Where J is the Jacobean of the system. For the configuration of shown in figure.1, the Inertia and Jacobian can be calculated respectively as:  I q11 0 0    M q   0 I q 22 I q 23  (11)  0 I q 32 I q 3   

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J 32  l 2 cos 2  l3 cos( 2   3 )] J 33  l3 cos( 2   3 )]

q  [ 1 ,  2 ,  3 ]T Where q is joint angles of manipulator and (l1,l2,l3) lengths of the arms of the manipulator. The low inertia reduces the impulse force but after collision in the phase of contact for the reduction of the contact force major role act the compliance qualities of the manipulator. Compliance is defined for the increase of the safety level at contact in the mechanical structure. Two basic approaches are known – active and passive for the stiffness modulation to secure levels. The active approach is based on the use of sensors and position and force feed backs by means of which a desired parametric proportion is balanced. It guarantees a wide range of stiffness variation, but it does not ensure high level of safety due to a low resolution or noise of the sensors, long calculation time and instability in the servo system. The passive approach is realised by means of the physical compliance of the robot limbs and/or additional compliance mechanisms [5]. This approach is independent of the servo systems, but the range of the impedance parameter variation is limited. Passive approach is more convenient.

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K  J T K q J 1

(13)

B  JK q J T

(14)

Thus, equation (1) presented by means of matrixes of stiffness, damping and inertia in joint coordinates is shown below:

Fcont  J T K q J 1[ X 0  X ]  J T Bq J 1[V0  V ]  J T M q J 1 (20) [ X ] and [V ] is evaluated from the platform . position and velocity X b  T X  and  X  The  b initial impact of end effector with the surrounding is depends up on the velocity of the platform. The position and velocity transfer from platform to end effector can be evaluated as:

X b  T X 

;

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 k1 0 0  K q   0 k 2 0  (15)  0 0 k 3  b1 0 0  B   0 b2 0  (16)  0 0 b3  The compliance matrix B is the inverse of the stiffness matrix. By means of the three limbs manipulator, it is possible to modulate a maximal stiffness along the tangent to the trajectory of motion.For realisation of passive compliance in the robot joints controllable compliant mechanism is used. In each joint except an actuator for position control is added an additional actuator for stiffness variation of a passive compliant element. Thus, joint position and stiffness are controlled independently. Such a model can be seen in [8](Ogata T., T.Komiya and Sh.Sugano, 2005). The introduction of compliance increases the level of safety in the contact realisation, but increases the possibilities for oscillation in the contact as well. Damping is modulated by means of using two basic approaches-active and passive in order to overtake this problem. The active approach uses sensors and a position and a force feed back, by means of which an additional damping force of the drives is maintained proportional to velocity and directed against it [4](Kang S.,2001).

electro-magnetic brakes proportional to the joint angular velocity.

The configuration variation, as with the inertia, defines transformations among the stiffness matrixes and the compliance matrix in joint and absolute co-ordinates as follows:

Fq  Bq q .

(17)

q  [1 , 2 ,  3 ]T

(18)

X b

.  X   J [V ] (21) b

Where x  b .  y   x.b  .     b  and  X    y b  (22)  zb   b  .     zb    1

And T 4x4 is the transformation matrix relates end effector and platform coordinates. T11  cos1 cos( 2   3 ) T12   cos1 sin( 2   3 ) T13  sin 1 T14  cos1 [l 2 cos 2  l3 cos( 2   3 )] T211  sin 1 cos( 2   3 ) T22   sin 1 sin( 2   3 ) T23   cos1 T24  sin 1 [l 2 cos 2  l3 cos( 2   3 )]

(19) Fq  [Fq1 , Fq 2, Fq3 ]T The passive approach is realised by additional damping mechanisms [8]. The damping effect is created by control of the electric current in the

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T32  cos( 2   3 ) T33  0 T34  l1  l 2 sin  2  l 3 sin( 2   3 ) T41  0 T42  0 T43  0 T44  1

III. SIMULATION STUDIES

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The dynamic force due to the robot- environment interaction is evaluated while changing mechanical characteristics – inertia, damping and stiffness. Simulations are made using Mat Lab Simulink software. The mobile base is treated like a cylindre with height H= 0.6m and diameter D= 0.3m. The joints of the manipulator are taken like cylindres with length l1=0.4,and l2=0.4, l3=0.2 [m] and diameters d=0.08m. Studies are examinated with solid (m1=5.429 kg, m2=5.429 kg, m3=1.853kg) and hollow (m1=0.677kg, m2=0.677kg, m3=0.387kg) bodies. An evaluation of dynamic interaction between mobile robot manipulator and the surrounding is made, evaluating contact force, when the endefector realizises collision with the fixed solid barrier, shown in figure1. The dynamic shock force between the endefector and the barrier is simulated at a horizontal motion of the mobile robot with speed V=0.2m/s.

When the arm configuration is changed, the effective inertia, stiffness and resulting force are changed too. When using configuration Fig. 2 (a) the impulse force is reaching up up to 160 N which is shown in Fig.2(b)., and in configuration Fig.3 (a) case , it reaches up to 110 N(see the Fig.3(b)). The average contact force for the manipulator configuration shown in Fig. 2 (a) is about 116 N, and that of configuration shown in Fig.3 (a) is about 68N. If the manipulator is more compliant , the contact stiffness force decreased to k1=k2=k3=100 Nm/rad. With same conditions of figures 2(a) and 3(a), the variation of contact forces are simulated as shown in figures 4 (a) and (b). In the case low arm stiffness, the contact forces are decreased to 25N and 14N. It is understood that the insertion of compliance doesn't decrease the impulse force but contact force reduce partially.

T31  sin( 2   3 )

Fig. 2(a): Manipulator Configuration-1

(i) The simulations with solid bodies

In this section, the contact forces are evaluated by considering the links of manipulator as a solid bodies , the stiffness of joints as k1=k2=k3= 500 Nm/rad , and damping of joints as b1=b2=b1 =1 Nms/rad. Figure 2(a) and (b) shows respectively the variation of the contact force on collision between the end effector and the barrier when q  [1  0 0 ,  2  90 0 ,  3  0 0 ]T and q  [1  90 0 ,  2  90 0 ,  3  90 0 ]T .

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Fig. 2(b):Simulation of contact force with high arm stiffness for the configuration Shown Fig.2(a)

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(ii) The simulations with hollow bodies: A reduction of the inertia can be achieved by creation of mobile robot manipulator with light arm. In this section, the contact forces are evaluated by considering the links of manipulator as a hollow bodies , the stiffness of joints as k1=k2=k3= 100 Nm/rad , and damping of joints as b1=b2=b1 =1 Nms/rad. The figure 5(a) and 5(b) shows respectively the variation of the contact force with hallow bodies with q  [1  0 0 ,  2  90 0 ,  3  0 0 ]T and q  [1  90 0 , 2  90 0 , 3  90 0 ]T .It conclude that when the arms is with low inertia the impuls force decreases to 40 N. The low inertia allows faster attenuation of impact oscillations. The simulations are made with joint’s damping b1=b2=b3=1 and 0 [Nms/rad]. Figures 6(a) and 6(b) show the change of contact force: (a) with damping b1=b2=b3=1 Nms/rad and (b) without damping b1=b2=b3=0 Nms/rad. It is observed from these figures that the low stiffness creates contact oscillations, therefore it's necessary a joint damping. The simulation studies gives an understanding that the mechanical characteristics are the key factor for decreasing dynamic contact forces and thus increasing the whole safety during the interaction “mobile robot-surrounding”. It can also understand that during a collision between robot arm and the surrounding, the impulse force is greatly influenced by the speed of motion of base and the effective arm inertia. By a kinematics redundancy and choosing an appropriate configuration the effective inertia can be reduced till lower level. During an unexpected collision. it is impossible to guarantee the necessary arm configuration. Therefore the low arm inertia is recommended for impact conditions. The simulation studies on interaction between mobile manipulator robot and surrounding suggests that the system has to be with light bodies’ links and motors. In case of need of more powerful and heavier motors, they can be placed on the base using cables and other light transmissions as base parameters not much influences the dynamic contact force. The stiffness and damping of the manipulation system must be increased to certain levels in order to decrease the level of contact force.

Fig. 3(a): Manipulator Configuration-2

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Fig.3(b):Simulation of contact force with high arm stiffness for the configuration Shown Fig.3(a)

Fig.4(a) :Simulation of contact force with low arm stiffness for the configuration Shown Fig.2(a)

Fig. 4(b) :Simulation of contact force with low arm stiffness for the configuration Shown Fig.3(a)

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IV. CONCLUSIONS

Fig. 5(b) :Simulation of contact force with low arm stiffness for the configuration Shown Fig.3(a)

Fig.5(a) :Simulation of contact force with low arm stiffness for the configuration Shown Fig.2(a)

A simple model of Mobile manipulating system is proposed to study the dynamic mutual interaction between the mobile robot Manipulation system and the surrounding Environment. The mathematical relations developed using two basic approaches known as active and passive impedance modulations. The model proposes redundancy so that the additional inertia come into system and reduces the dynamic contact forces thus creates a natural security in the interaction of robot and environment. It is possible to use devices with controlled passive joint compliance for achieving requirements of performance. The introduction of compliance decreases the level of impulse force but during an impact or immediately change of speed, the compliant arm is tended to oscillations. The presence of damping in joints decreases these oscillations. V.

ACKNOWLEDGMENT

The author thanks Dr. P. Narasimha Reddy, Executive Director of Sreenidhi Institute of Science and Technology (An Autonomous Institution) Hyderabad, A.P.India-501301 for his encouragement and suggestions in carrying out this research work.

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REFERENCES

Fig. 6(a) :Simulation of contact force with low arm stiffness and Zero arm damping for the configuration Shown Fig.2(a)

Fig. 6(b) :Simulation of contact force with low arm stiffness and zero damping for the configuration Shown Fig.3(a)

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[1]. ZINN M., O.KHATIB, B.ROTH, J.K.SALISBURY (2004), A NEW ACTUATION APPROACH FOR HUMAN FRIENDLY ROBOT DESIGN, THE INT. JOURNAL OF ROBOTICS RESEARCH, VOL.23,NO 4-5, PP.379-398.

[2]. Hogan N. (1985) Impedance Control: An Approach to Manipulation: Part II â&#x20AC;&#x201C; Implementation, Trans. of the ASME:Journ. of Dyn. Syst., Meas. and Contr. Vol.107, pp.8-16. [3]. Kostadinov K., G. Boiadjiev (2002) Development of Impedance Control Method for Mechatronic Systems, in W. Schiehlen &M. Valasek , Proceedings of NATO ASI Virtual Nonlinear Multibody Systems, Prague, Vol.1, June 23- July 3, 2002, pp.101-106. [4]. Kang S., K.Komorya, K.Yokoi, T.Koutoku, K.Tanie (2001). Reduced Inertial Effect in Damping-based Posture Control of Mobile

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[8].Ogata T., T.Komiya and Sh.Sugano (2005), Interactive evolution of human-robot communication in real world, Journal of Intelligent robots and systems, Vol.34, pp.1438-1443.

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