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 deviation of the effective trajectory or performance of the system from the prescribed trajectory, from the prescribed performance values, resp., by on-line measurement and control actions. However, on-line measurement and control actions are expensive in general and very time-consuming, moreover, they are suitable only for rather small deviations. By adaptive optimal stochastic trajectory planning and control (AOSTPC), i.e., incorporating sequentially the available a priori and measurement information about the unknown model parameters into the optimal control design process by using stochastic optimization methods, the (conditional) mean absolute deviation between the actual and prescribed trajectory, performance, resp., can be reduced considerably, hence, more robust controls are obtained. The corresponding feedforward and feedback (PD-)controls are derived by means of sequential stochastic optimization and by using stability requirements. In addition, methods for the numerical computation of the controls in real-time are presented. Moreover, analytical estimates are given for the reduction of the tracking error, hence, for the reduction of the on-line measurement and correction expenses by applying (AOSTPC).