Selection of near-minimum time geometric paths for robotic manipulators

A number of trajectory planning algorithms exist for calculating the joint positions, velocities, and torques which will drive a robotic manipulator along a given geometric path in minimum time. However, the time depends upon the geometric path, so the traversal time of the path should be considered again for geometric planning. There are algorithms available for finding minimum distance paths, but even when obstacle avoidance is not an issue, minimum (Cartesian) distance is not necessarily equivalent to minimum time. In this paper, we have derived a lower bound on the time required to move a manipulator from one point to another, and determined the form of the path which minimizes this lower bound. As numerical examples, we have applied the path solution to the first three joints of the Bendix PACS arm and the Stanford arm. These examples do indeed demonstrate that the derived approximate solutions usually require less time than Cartesian straight-line (minimum-distance) paths and joint-interpolated paths.