Adaptive Optimal Stochastic Trajectory Planning and Control (AOSTPC) for Robots

Abstract

In optimal control of robots, the standard procedure is to determine first off-line an optimal open-loop control, using some nominal or estimated values of the model parameters, and to correct then the resulting increasing deviation of the actual trajectory or the actual performance of the system from the prescribed trajectory, from the prescribed values of performance, resp., by on-line measurement and control actions. However, on-line measurement and control actions are in general very expensive and time consuming. By adaptive optimal stochastic trajectory planning and control (AOSTPC) i.e., by incorporating into the control design the available a priori and sample information about the unknown model parameters using stochastic optimization methods, the mean absolute deviation between the actual and prescribed trajectroy can be reduced cosiderably. Hence, robust optimal controls are obtained. The corresponding feedforward and feedback (PD-) controls are derived by means of stochastic optimzation methods and by using stability requirements. Morever, analytical estimates are given for the reduction of the tracking error, hence, for the reduction of the on-line correction expenses by (AOSTPC).