An Approximation Theory of Optimal Control for Trainable Manipulators

A theoretical procedure is developed for comparing the performance of arbitrarily selected admissible controls among themselves and with the optimal solution of a nonlinear optimal control problem. A recursive algorithm is proposed for sequential improvement of the control law which converges to the optimal. It is based on the monotonicity between the changes of the Hamiltonian and the value functions proposed by Rekasius, and may provide a procedure for selecting effective controls for nonlinear systems. The approach has been applied to the approximately optimal control of a trainable manipulator with seven degrees of freedom, where the controller is used for motion coordination and optimal execution of object-handling tasks.