Selection of Near-Minimum Time Geometric Paths for Robotic Manipulators

A number of trajectory or path 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 a numerical example, we have applied the path solution to the first three joints of the Bendix PACS arm, a cylindrical robot. This example does indeed demonstrate that the derived approximate solutions require less time than Cartesian straight-line (minimum-distance) paths and joint-interpolated paths, i.e. those paths for which joint positions qⁱ are given by qⁱ = aⁱ + bⁱ¿.