Minimum time closed-loop tracking of a specified path by robot

The minimum-time trajectory of a robot following a specified path involves alternate intervals of acceleration and deceleration along the path. Perturbation control is used to design a feedback scheme which takes this characteristic, as well as control saturation, into account. The feedback mechanization involves updating the control, the switching times, and the final time based on the available measurements of deviation of the robot from its nominal path. It requires precomputation of control gains along the nominal path, and much computation is avoided in real time. Controller design is simply the tuning of certain weights in the performance index. The method is illustrated by commanding a two-link rigid robot to track a straight line. Extensions of the control scheme to improve robustness to tip-mass change are also discussed