Optimal motions of redundant manipulators with state equality constraints

An approach to the time optimal control of a kinematically redundant manipulator subject to state equality constraints is proposed. The solution is based on an approximation of the prior control set by means of a strictly convex set, with arbitrary accuracy in the Hausdorff sense. This approach produces continuous optimal controls which may be used to provide nominal inputs for online control. Furthermore, the corresponding optimal controls thus obtained retain (in a limit) a bang-bang form if the error of approximation approaches 0. A computer example involving a planar redundant manipulator of three revolute kinematic pairs whose the end-effector moves along a prescribed geometric path, is given