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The structure of time-optimal controls for kinematically redundant manipulators with end-effector path constraints

Addresses the problem of the structure of time-optimal control of kinematically redundant manipulators along a prescribed geometric path subject to control constraints. Based on the concept of a regular trajectory derived in Pontryagin et al. (1961) and the extended state space introduced herein it is proved that if the dynamics of a manipulator is defined by n actuators and m path-constrained equations, where m<n, then at most n-m+1 actuators are saturated during the time-optimal movement along a prescribed geometric path given in the work space. Besides, it is shown that these results are also valid for a point-to-point time-optimal control problem.