An approach to collision-free trajectory planning of two robots in a 3-dimensional common workspace is presented. To detect collision(s) more precisely, each robot is represented by a set of polyhedrons. Thus, it is possible to plan a collision-free trajectory of the two robots minimizing their idle time due to inaccuracies in the geometric modeling of each robot. Also, an auxiliary model for each robot which is rotationally symmetric is adopted to reduce the computational cost in detecting collision(s) between the two robots. To plan a collision-free trajectory, an improved time-delay method is proposed. The improved time-delay method delays one of the two robots for near-minimal time to avoid collision(s) between the two robots. The method is very simple and easily applicable to any trajectory of two robots. Simulation studies are presented to demonstrate the usefulness of this method.
