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Generating optimal dynamic motions for closed-chain robotic systems. (English) Zbl 1071.70004

Summary: In a previous work [T. Chettibi et al., ibid. 23, No. 4, 703–715 (2004; Zbl 1060.70016)] we proposed an efficient method to plan optimal motions for serial manipulators and we asserted that this technique could be extended to handle more complex robotic systems. In this paper, we will show the effectiveness of this method in solving the Optimal Free Motion Planning Problem (OFMPP) for Closed-Chain Robots (CCR) and coordination of multiple robotic mechanisms. These are typical examples of holonomic mechanical systems known to be complex but of a large utility. But the fact that these systems are usually redundantly actuated, induces additional complexity in computing their dynamics and generating optimal motions.

MSC:

70E60 Robot dynamics and control of rigid bodies

Citations:

Zbl 1060.70016
Full Text: DOI

References:

[1] Angeles, J., Fundamentals of Robotic Mechanical Systems. Theory, Methods, and Algorithms (1997), Springer · Zbl 0865.70001
[2] Ascher, U. M.; Petzold, L. R., Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations (1998), SIAM · Zbl 0908.65055
[3] Betts, J. T., Survey of numerical methods for trajectory optimization, J. Guidance Control Dynamics, 21, 2, 193-207 (1998) · Zbl 1158.49303
[4] Bicchi, A.; Pallottino, L.; Bray, M.; Perdomi, P., Randomized parallel Simulation of constrained multibody systems for VR/Haptic applications, (Proc. IEEE Int. Conf. on Rob. & Aut., Korea (2001))
[5] Bien, Z.; Lee, J., A minimum time trajectory planning method for two robots, IEEE Trans. Robotics and Automation, 8, 3 (1992)
[6] Bryson, A. E., Dynamic Optimization (1999), Addison-Wesley-Longman
[7] Chettibi, T.; Lehtihet, H. E.; Haddad, M.; Hanchi, S., Minimum cost trajectory planning for industrial robots, Eur. J. Mech. A, 703-715 (2004) · Zbl 1060.70016
[8] Chettibi, T.; Haddad, M.; Rebai, S.; Hentout, A., A Stochastic off line planner of optimal dynamic motions for robotic manipulators, (1st Inter. Conf. on Informatics in Control, Automation and Robotics, Portugal (2004))
[9] Chen, Y., Structure of the time-optimal control law for multiple arms handling a common object along specified paths, IEEE Trans. Automat. Control, 37, 10 (1992) · Zbl 0770.93070
[10] Cheng, H.; Liu, G. F.; Yiu, Y. K.; Xiong, Z. H.; Li, Z. X., Advantages and dynamics of parallel Manipulators with redundant Actuation, (IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (2001)), 171-176
[11] Cortés J., 2003. Motion planning algorithms for general closed-chain mechanisms, Ph.D. thesis, Institut National Polytechnique de Toulouse, France; Cortés J., 2003. Motion planning algorithms for general closed-chain mechanisms, Ph.D. thesis, Institut National Polytechnique de Toulouse, France
[12] Djurovic, M. D.; Vukobratovic, M. K., A contribution to dynamic modelling of cooperative manipulation, Mech. Mach. Theory, 25, 4, 407-415 (1990)
[13] Dombre, E.; Khalil, W., Modélisation, Identification et Commande des Robots (1999), Hermes · Zbl 0931.70001
[14] Garg, P. D.; Kumar, M., Optimization techniques applied to multiple manipulators for path planning and torque minimization, Engrg. Appl. Artificial Intelligence, 15, 241-252 (2002)
[15] Hull, D. G., Conversion of optimal control problems into parameter optimization problems, J. Guidance Control Dynamics, 20, 1, 57-62 (1997) · Zbl 0912.90256
[16] Kahn, M. E.; Roth, B., The near minimum time control of open loop articulated kinematic chains, ASME J. Dyn. Sys. Meas. & Cont., 11, 164-172 (1971)
[17] Kavraki, L.; Latombe, J. C., Randomized preprocessing of configuration space for fast path planning, (Proc. IEEE Int. Conf. on Rob. & Aut., San Diego (1994)), 2138-2139
[18] Kim, C. Y.; Yoon, Y. S., Task space dynamic analysis for multi-arm robot using isotropic velocity and acceleration radii, Robotica, 15, 319-329 (1997)
[19] Latombe, J. C., Motion planning: a journey of robots, molecules, digital actors, and other artifacts, Int. J. Robotics Res., 18, 11, 1119-1128 (1999)
[20] Latombe, J. C., Robot Motion Planning (1991), Kluwer Academic
[21] LaValle, S. M.; Yakey, J. H.; Kavraki, L. E., A probabilistic Roadmap Approach for systems with Closed kinematic chains, (IEEE Int. Conf. on Rob. & Aut (1999))
[22] Luh, J. Y.S.; Zheng, Y., Computation of input generalized forces for robots with closed kinematic chain mechanisms, IEEE J. Rob. & Aut., RA-1, 2, 95-103 (1985)
[23] Mao, Z.; Hsia, T. C., Obstacle avoidance inverse kinematics solution of redundant robots by neural networks, Robotica, 15, 3-10 (1997)
[24] Murray, J. J.; Lovell, G. H., Dynamic modelling of closed-chain robotic manipulators and implications for trajectory control, (IEEE Int. Conf. on Rob. & Aut. (1989)), 522-528
[25] Nakamura, Y.; Ghodoussi, Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators, (IEEE Trans. Rob. & Aut. (1989)), 951-956
[26] Nearchou, A. C.; Aspragathos, N. A., A genetic path planning for redundant articulated robots, Robotica, 15, 213-224 (1997)
[27] Overmars, M.H., 1992. A random Approach to motion planning, Technical report RUU-CS-92-32, Utrecht University; Overmars, M.H., 1992. A random Approach to motion planning, Technical report RUU-CS-92-32, Utrecht University
[28] Schneider, S. A.; Cannon, R., Object Impedance control for cooperative manipulation: theory and Experimental results, IEEE Trans. Rob. & Aut., 8, 3, 383-394 (1993)
[29] Shin, K. G.; Zheng, Q., Minimum time trajectory planning for dual robot systems, (Proc. 28th IEEE Conf. on Decision and Control (1989))
[30] Steinbach, M.C., 1995. Fast recursive SQP methods for large scale optimal control problem. Ph.D. thesis, Universität Heidelberg; Steinbach, M.C., 1995. Fast recursive SQP methods for large scale optimal control problem. Ph.D. thesis, Universität Heidelberg · Zbl 0826.49026
[31] Stryk, O. V.; Bulirsch, R., Direct and indirect methods for trajectory optimization, Ann. Oper. Res., 37, 357-373 (1993) · Zbl 0784.49023
[32] Stryk, O. V., Numerical solution of optimal control problems by direct collocation, (Optimal Control Theory and Numerical Methods, Int. Ser. Numer. Math., vol. 111 (1993)), 129-143 · Zbl 0790.49024
[33] Trinkle, J. C.; Milgram, R. J., Complete path planning for closed kinematic chains with spherical joints, Int. J. Rob. Research, 773-789 (2002)
[34] Xie, H.; Bryson, I. J.; Shadpey, F.; Patel, R. V., A robust control scheme for dual arm redundant manipulators: experimental results, (Proc. IEEE Int. Conf. Rob. Aut. (1999)), 2507-2512
[35] Yoshikawa, T.; Zheng, X.-Z., Coordinated dynamic hybrid position/force control for multiple robot manipulator handling one constrained object, Int. J. Rob. Research, 12, 3, 219-230 (1993)
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