A dynamic-programming approach to near minimum-time trajectory planning for 2 robots

A numerical trajectory planning method is proposed which ensures collision-free and near time-optimal motions for two robotic manipulators with limited actuator torques and velocities. Constraints on accelerations of the robots that are derived from the limited torques of actuators are transformed to the constraints on the curvatures of the coordination curve in coordination space. A dynamic programming technique is then provided on the discretized coordination space to derive a collision-free and time-optimal trajectory pair for the robots. A numerical example is included.