Near-minimum time feedback controller for manipulators using on-line time scaling of trajectories

A near-minimum time feedback controller for robotic manipulators with bounded input torques is developed. Since the bang-bang input torque obtained from the time-optimal control theory leaves little or no room for the extra torque of the feedback control action, it is difficult to combine a minimum time open-loop controller with an additional feedback controller. A simple solution to this problem has been to solve the minimum time problem using arbitrarily reduced torque bounds so that a torque head room is created for the feed back control action. Such a scheme, however wastes considerable input torque potential and gives significantly larger execution time of the trajectory than the theoretical minimum time calculated from the time-optimal control theory. A stable feedback controller is developed in this paper which applies a time scaling method to move a manipulator in near-minimum time sing the allowable input torques efficiently. This new feedback controller algorithm adapts to an uncertain environment and automatically adjusts the desired speed along a specified path to be as fast as possible while avoiding the velocity saturation condition. Numerical examples of the near-minimum time feedback controller are provided using a two-link SCARA manipulator.