Collision-free trajectory planning for two robots by giving difference to starting times

A trajectory planning method ensuring collision-free motion and minimum traveling time for two robots is proposed. The robot system under consideration is given specified geometric paths for two robots: then, by using traveled lengths along the paths, a two-dimensional coordination space is constructed for detecting collision. Also the robot dynamics is transformed as a function of the traveled lengths, and is described in the phase plane containing bounds on acceleration and velocity limits derived from a set of constraints on torques and maximally allowable velocities of actuators. Then the main algorithm is provided which simultaneously considers collision avoidance and time optimality on the coordination space and the phase plane, respectively. The proof for optimality of the proposed algorithm is given, and a simulation result is included to show the usefulness of the proposed method