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In this paper, we propose a method of planning collision-free trajectory for two manipulators along specified joint paths. The joint path of each manipulator is represented by a path parameter and two path parameters generate a two-dimensional space which contains the collision region of two manipulators. In order to connect the path parameter with time, a time scale factor is introduced. In a three-dimensionl space constituted by the two-dimensional space of the path parameters and the time scale factor, minimum time trajectories for two manipulators are searched under joint torque constraints and collision-free condition by dynamic programming. There are two advantages in this method. One is that deadlock does not occur in the search because the collision region is obtained beforehand. And the other is that the proposed method considers manipulator dynamics, therefore, not only collision avoidance but also minimization of traveling time is carried out at the same time.

Collision-Free Trajectory Planning for Two Manipulators. The Case of Using Virtual Coordination Space.