Coordinating the motions of multiple robots with specified trajectories

Coordinating the motions of multiple robots operating in a shared workspace without collisions is an important capability. We address the task of coordinating the motions of multiple robots when their trajectories (defined by both the path and velocity along the path) are specified. This problem of collision-free trajectory coordination arises in welding and painting workcells in the automotive industry. We identify sufficient and necessary conditions for collision-free coordination of the robots when only the robot start times can be varied, and define corresponding optimization problems. We develop mixed integer programming formulations of these problems to automatically generate minimum time solutions. This method is applicable to both mobile robots and articulated arms, and places no restrictions on the number of degrees of freedom of the robots. The primary advantage of this method is its ability to coordinate the motions of several robots, with as many as 20 robots being considered. We show that, even when the robot trajectories are specified, minimum time coordination of multiple robots is NP-hard.

[1]  Micha Sharir,et al.  Motion Planning in the Presence of Moving Obstacles , 1985, FOCS.

[2]  E. J.,et al.  ON THE COMPLEXITY OF MOTION PLANNING FOR MULTIPLE INDEPENDENT OBJECTS ; PSPACE HARDNESS OF THE " WAREHOUSEMAN ' S PROBLEM " . * * ) , 2022 .

[3]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[4]  Dinesh Manocha,et al.  Fast distance queries with rectangular swept sphere volumes , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

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

[6]  Steven M. LaValle,et al.  Optimal motion planning for multiple robots having independent goals , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[7]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[8]  Eugene L. Lawler,et al.  Chapter 9 Sequencing and scheduling: Algorithms and complexity , 1993, Logistics of Production and Inventory.

[9]  Thierry Siméon,et al.  Multiple Path Coordination for Mobile Robots: A Geometric Algorithm , 1999, IJCAI.

[10]  Myung Jin Chung,et al.  Collision avoidance of two general robot manipulators by minimum delay time , 1994, IEEE Trans. Syst. Man Cybern..

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

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

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

[14]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[15]  Sartaj Sahni,et al.  Complexity of Scheduling Shops with No Wait in Process , 1979, Math. Oper. Res..

[16]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

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