A discrete trajectory planner for robotic arms with six degrees of freedom

A discrete trajectory planner is described which has been shown to be capable of planning optimal trajectories for a six-degree-of-freedom robot with minimum time/energy objective functions and realistic constraints on the joint velocities, joint torques, joint jerks, and hand velocity. It is also flexible enough to handle other objective functions and constraints, provided they can be satisfactorily discretized. An alternative formulation of the discrete trajectory planner is also provided for the efficient generation of optimal trajectories when equal time intervals are required. Once an optimal trajectory is planned offline with the discrete trajectory planner, the open-loop solution can be fed to the online feedback controller for trajectory tracking. Computation time taken by the discrete trajectory planner is acceptable for offline planning purposes. Numerical examples are presented for the Stanford manipulator using all six degrees of freedom