Minimum-time motions of manipulators with obstacles by successive searches for minimum-overload trajectories

We present a practical method for finding obstacle free minimum-time motions for manipulators subject to the bounds of velocity-dependent actuator forces. The optimal motion planning problem is converted into a finite dimensional nonlinear programming by means of parameter optimizations with quintic B-splines. We introduce the concept of the minimum-overload trajectories in which the motion time is specified to be faster than the motors can handle, and the actuator overloads are minimized during the motion. By successive searches for the minimum-overload trajectories, the minimum-time motions are determined for a spatial 6-link manipulator without simplifying any of the kinematic, dynamic or geometric properties of the manipulator or the obstacles. In the resultant minimum-time motions, almost all of the joint actuators are close to saturation during the motions.