Near minimum-time geometric paths

Abstract

Robot control algorithms are divided into two stages, namely, trajectory planning and path tracking for path control. 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 planning. There are algorithms available for finding minimum distance path, but even when obstacle avoidance is not an issue, minimum ( Cartesian ) distance is not necessarily equivalent to minimum time. 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 minimize this lower bound.