Structure of minimum-time control law for robotic manipulators with constrained paths

The authors address the problem of the structure of minimum-time control (MTC) of robotic manipulators along a specified geometric path subject to hard control constraints. By using the extended Pontryagin minimum principle (EPMP) and a set of parameterized robot dynamic equations, it is shown that the structure of the minimum-time control law requires that one and only one control torque is always in saturation on every finite time interval along its time-optimal trajectory, while the rest of the torques are adjusted so that the path constraint on the motion is not violated. This is in contrast to the point-to-point minimum-time control law, which requires that at least one of the control torques is always in saturation. Simulation results are presented to verify the structure of the MTC law