Optimal motion planning for multiple robots having independent goals

This work makes two contributions to geometric motion planning for multiple robots: i) motion plans can be determined that simultaneously optimize an independent performance criterion for each robot; ii) a general spectrum is defined between decoupled and centralized planning. By considering independent performance criteria, we introduce a form of optimality that is consistent with concepts from multi-objective optimization and game theory research. Previous multiple-robot motion planning approaches that consider optimality combine individual criteria into a single criterion. As a result, these methods can fail to find many potentially useful motion plans. We present implemented, multi-robot motion planning algorithms that are derived from the principle of optimality, for three problem classes along the spectrum between centralized and decoupled planning: i) coordination along fixed, independent paths; ii) coordination along independent roadmaps; iii) general, unconstrained motion planning. Several computed examples are presented for all three problem classes that illustrate the concepts and algorithms.

[1]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[2]  J. T. Shwartz,et al.  On the Piano Movers' Problem : III , 1983 .

[3]  J. Schwartz,et al.  On the Piano Movers' Problem: III. Coordinating the Motion of Several Independent Bodies: The Special Case of Circular Bodies Moving Amidst Polygonal Barriers , 1983 .

[4]  椹木 義一,et al.  Theory of multiobjective optimization , 1985 .

[5]  Chee-Keng Yap,et al.  A "Retraction" Method for Planning the Motion of a Disc , 1985, J. Algorithms.

[6]  Tomás Lozano-Pérez,et al.  On multiple moving objects , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[7]  S. Zucker,et al.  Toward Efficient Trajectory Planning: The Path-Velocity Decomposition , 1986 .

[8]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[9]  Kang G. Shin,et al.  A variational dynamic programming approach to robot-path planning with a distance-safety criterion , 1988, IEEE J. Robotics Autom..

[10]  Tomás Lozano-Pérez,et al.  Deadlock-free and collision-free coordination of two robot manipulators , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[11]  A. Barto,et al.  Learning and Sequential Decision Making , 1989 .

[12]  Stephen J. Buckley,et al.  Fast motion planning for multiple moving robots , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[13]  Jean-Claude Latombe,et al.  Numerical potential field techniques for robot path planning , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[14]  Richard S. Sutton,et al.  Planning by Incremental Dynamic Programming , 1991, ML.

[15]  Jean-Claude Latombe,et al.  Robot Motion Planning: A Distributed Representation Approach , 1991, Int. J. Robotics Res..

[16]  Yoshiaki Shirai,et al.  Planning of vision and motion for a mobile robot using a probabilistic model of uncertainty , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[17]  Penny Probert Smith,et al.  Coping with uncertainty in control and planning for a mobile robot , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[18]  M. D. Ardema,et al.  Dynamic game applied to coordination control of two arm robotic system , 1991 .

[19]  Kenneth Basye,et al.  A decision-theoretic approach to planning, perception, and control , 1992, IEEE Expert.

[20]  Kang G. Shin,et al.  Minimum-time collision-free trajectory planning for dual-robot systems , 1992, IEEE Trans. Robotics Autom..

[21]  Jihong Lee,et al.  A minimum-time trajectory planning method for two robots , 1992, IEEE Trans. Robotics Autom..

[22]  Fei-Yue Wang,et al.  A cell mapping method for general optimum trajectory planning of multiple robotic arms , 1994, Robotics Auton. Syst..

[23]  Steven M. LaValle,et al.  A game-theoretic framework for robot motion planning , 1996 .