Torque limited path following by on-line trajectory time scaling

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Abstract
A feedback scheme for path following by trajectory time scaling is presented. The scheme is used in execution of fast trajectories along a geometric path, where the motion is limited by torque constraints. The time scaling is done by using a secondary controller that modifies a nominal trajectory during motion. The nominal, high-performance trajectory typically leads to torques that are at the limits, hence leaving no control authority to compensate for modeling errors and disturbances. By modifying the time scaling of the nominal trajectory when the torques saturate, closed-loop action is possible. A key idea is that a scalar quantity, the path acceleration, is modified, resulting in coordinated adjustment of the individual joint motions. Two algorithms for online trajectory scaling are presented. One is based on online bounds on path acceleration, and one is designed to handle nominal minimum-time trajectories. The functionality of the secondary controller is verified by simulations and experiments.

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