MINIMUM-TIME CONTROL OF RBOTIC MANIPULATORS WITH GEOMETRIC PATH CONSTRAINTS.

Conventionally, robot control algorithms are divided into two stages, namely, path or trajectory planning and path tracking (or path control). This division has been adopted mainly as a means of alleviating difficulties in dealing with complex, coupled manipulator dynamics. Trajectory planning usually determines the timing of manipulator position and velocity without considering its dynamics. Consequently, the simplicity obtained from the division comes at the expense of efficiency in utilizing the robot's capabilities. To remove this inefficiency, at least partially, a solution to the problem of moving a manipulator in minimum time along a specified geometric path subject to input torque/force constraints is considered. The manipulator dynamics are first described using parametric functions that represent geometric path constraints to be honored for collision avoidance as well as task requirements. Second, constraints on input torques/forces are converted to those on the parameters. Third, the minimum-time solution is deduced in algorithm form using phase-plane techniques. Finally, numerical examples are presented to demonstrate the utility of the trajectory planning method developed.