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Frontiers of Mechanical Engineering

Front Mech Eng    2012, Vol. 7 Issue (2) : 219-230     https://doi.org/10.1007/s11465-012-0320-9
RESEARCH ARTICLE |
A total torque index for dynamic performance evaluation of a radial symmetric six-legged robot
Kejia LI1(), Xilun DING1, Marco CECCARELL2
1. Robotics Institute, School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100191, China; 2. Laboratory of Robotics and Mechatronics, University of Cassino, 03043 Cassino, Italy
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Abstract

This article focuses on the dynamic index and performance of a radial symmetric six-legged robot. At first the structure of the robot is described in brief and its inverse kinematics is presented. Then the dynamic model is formulated as based on the Lagrange equations. A novel index of total torque is proposed by considering the posture of the supporting legs. The new index can be used to optimize the leg’s structure and operation for consuming minimum power and avoiding unstable postures of the robot. A characterization of the proposed six-legged robot is obtained by a parametric analysis of robot performance through simulation using the presented dynamic model. Main influences are outlined as well as the usefulness of the proposed performance index.

Keywords six-legged robots      dynamic modeling      performance index     
Corresponding Authors: LI Kejia,Email:likejia5@gmail.com   
Issue Date: 05 June 2012
 Cite this article:   
Kejia LI,Xilun DING,Marco CECCARELL. A total torque index for dynamic performance evaluation of a radial symmetric six-legged robot[J]. Front Mech Eng, 2012, 7(2): 219-230.
 URL:  
http://journal.hep.com.cn/fme/EN/10.1007/s11465-012-0320-9
http://journal.hep.com.cn/fme/EN/Y2012/V7/I2/219
Fig.1  The radial symmetric six-legged robot
Fig.2  Different gaits of the radial symmetric six-legged robot.
(a) Insect gait; (b) mammal gait; (c) mixed gait
Fig.3  Two groups of possible solutions for a leg
Fig.4  The posture of supporting leg 1.
(a) Stable posture; (b) unstable posture
LD1LD2LD3LD4LD5LD6
L2/mm300270100200150230
L3/mm300330500400450370
Tab.1  Six examples of leg design
Fig.5  The joint torques during motion of leg 1.
(a) The torque of hip pitching joint; (b) the torque of knee joint
Fig.6  The value of index and for six design examples.
(a) Index ; (b) index
Case 1Case 2Case 3Case 4Case 5
L2/mm300270240330360
L3/mm300330360270240
Tab.2  Different lengths of and
Case 1Case 2Case 3Case 4Case 5
m2/kg21.81.62.22.4
m3/kg2.52.72.92.32.1
Tab.3  Different groups of m and m /kg
10% change of L2 and L310% change of m2 and m310% change of step length10% change of joint angles
τ12 change20%0.43%2.2%4.3%
τ13 change40%Neglect10%Neglect
Tab.4  The effect of different parameters to the joint torques of supporting legs
Fig.7  Results of simulation for different length of leg.
(a) Torque of hip pitching joint; (b) torque of knee joint
Fig.8  Results of simulation for different mass distribution of leg.
(a) Torque of hip pitching joint; (b) torque of knee joint
Fig.9  Results of simulation for different step length.
(a) Torque of hip pitching joint; (b) torque of knee joint
Fig.10  Results of simulation for different posture of supporting legs.
(a) Torque of hip pitching joint; (b) torque of knee joint
Fig.11  The robot walks in four different poses.
(a) Pose 1; (b) pose 2; (c) pose3; (d) pose 4
Smax/mTtot of one stepTtot of per meterTime spent per meter/s
Pose 10.2693.4359.237.7
Pose 20.21270.6333.029.4
Pose 30.1541.727813.3
Pose 4000
Tab.5  Results form numerical simulation for total torque and time spent in four different poses
Fig.12  The robot walks by four different step lengths.
(a) ; (b) ; (c) ; (d)
Step length/mTtot of one stepTtot of per meterTime spent per meter
S10.2693.4359.237.7
S20.13107.8829.2315.4
S30.087111.91286.223
S40.043115.8269346.5
Tab.6  Results form numerical simulation for total torque and time spent in the same pose
1 Chen W J, Yao S H, Low K H. Modular formulation for dynamics of multi-legged robots. In: Proceedings of the 8th International Conference on Advanced Robotics , 1997, 279–284
2 Barreto J P, Trigo A, Menezes P, Dias J, Almeida A T. FBD—The free bodydiagram method. Kinematic and dynamic modeling of a six leg robot. International Workshop on Advanced Motion Control , 1998, 423–428
3 Yiu Y K, Cheng H, Xiong Z H, Liu G F, Li Z X. On the dynamics of parallel manipulators. In: proceedings of IEEE International Conference on Robotics and Automation , 2001, 4: 3766–3771
4 Ding X L, Li K J, Xu K. Dynamics analysis of six-legged robot with elastic joints using screw theory. Journal of Central South University (Science and Technology) , 2011, 42: 589–595
5 Silva M F, Tenreiro Machado J A. Kinematic and dynamic performance analysis of artificial legged systems. Robotica , 2008, 26(1): 19–39
doi: 10.1017/S0263574707003554
6 Bowling A. Mobility and dynamic performance of legged robots. In: proceedings of the IEEE International Conference on Robotics and Automation , 2005, 4100–4107
7 Bowling A. Dynamic performance, mobility, and agility of multilegged robots. Journal of Dynamic Systems, Measurement, and Control , 2006, 128(4): 765–777
doi: 10.1115/1.2229252
8 Erden M S, Leblebicioglu K. Torque distribution in a six-legged robot. IEEE Transactions on Robotics , 2007, 23(1): 179–186
doi: 10.1109/TRO.2006.886276
9 Low K H, Bai S P. Terrain-evaluation-based motion planning for legged locomotion on irregular terrain. Advanced Robotics , 2003, 17(8): 761–778
doi: 10.1163/156855303322395190
10 Bai S P, Low K H, Zielinska T. Quadruped free gait generation for straight‐line and circular trajectories. Advanced Robotics , 1998, 13(5): 513–538
doi: 10.1163/156855399X01774
11 Carbone. G., Shrot A., Ceccarelli M., Operation strategy for a low-cost easy-operation Cassino Hexapod. Applied Bionics and Biomechanics , 2008, 4(4): 149–156
12 Carbone. G., Suciu M, Ceccarelli M, Pisla D. Design and simulation of cassino hexapode walking machine. International Journal of Mechanics and Control , 2009, 10(2): 27–34
13 Rodriguez N, Eduardo N. A New Design for Cassino hexapod Robot. In: Proceedings of the ASME 10th Biennial Conference on Engineering Systems Design and Analysis (ESDA2010) , 2010, 3: 1–6
14 Zielinska T, Heng J. Development of a walking machine: mechanical design and control problems. Mechatronics , 2002, 12(5): 737–754
doi: 10.1016/S0957-4158(01)00017-4
15 Wang Z Y, Ding X L, Rovetta A. Analysis of typical locomotion of a symmetric hexapod robot. Robotica , 2010, 28(6): 893–907
doi: 10.1017/S0263574709990725
16 Wang Z Y, Ding X L, Rovetta A, Giusti A. Mobility analysis of the typical gait of a radial symmetrical six-legged robot. Mechatronics , 2011, 21(7): 1133–1146
doi: 10.1016/j.mechatronics.2011.05.009
17 Chen X D, Sun Y, Jia W C. Motion Planning and Control of Multilegged Walking Robots. Wuhan: Huazhong University of Science and Technology Press , 2006 (in Chinese)
18 Roberson R E. Dynamics of Multibody Systems. New York: Springer-Verlag, 1988, 475
19 Agarwal A, Gautam P, Roy S. Dynamic modeling and optimal foot force distribution of quadruped walking robot. Trends in Intelligent Robotics, Communications in Computer and Information Science , 2010, 103: 146–153
doi: 10.1007/978-3-642-15810-0_19
20 Gardner J F. Efficient computation of force distributions for walking machines on rough terrain. Robotica , 1992, 10(05): 427–433
doi: 10.1017/S0263574700010638
21 Zhou D B, Low K H, Zielinska T. An efficient foot‐force distribution algorithm for quadruped walking robots. Robotica , 2000, 18(4): 403–413
doi: 10.1017/S0263574799001824
22 Yamamoto Y, Yun X P. Effect of the dynamic interaction on coordinated control of mobile manipulators. International Conference on Robotics and Automation , 1996, 12: 816–824
23 White G, Bhatt R, Tang C, Krovi V. Experimental evaluation of dynamic redundancy resolution in a nonholonomic wheeled mobile manipulator. IEEE/ASME Transactions on Mechatronics , 2009, 14(3): 349–357
doi: 10.1109/TMECH.2008.2008802
24 Eslamy M, Moosavian S. Dynamics and cooperative object manipulation control of suspended mobile manipulators. Journal of Intelligent and Robotic Systems: Theory and Applications , 2010, 60(2): 181–199
doi: 10.1007/s10846-010-9413-z
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