Optimization based on motion planning of nonholonomic nonlinear systems using global adaptive dynamic programming

In this paper, an iteration algorithm of global adaptive dynamic programming (ADP) is developed to tackle the optimization motion planning problem of nonholonomic nonlinear systems. The motion planning optimal control problem of nonholonomic systems can be redesign as dynamic problem which is to search a control input for making the system from an initial state to a terminal state, when the terminal state constraints are specified and the performance criteria is related to the control energy. The proposed algorithm is to find a feasible control input satisfying nonholonomic constraints and the necessary optimality conditions. First, this paper converts the motion planning problem into the problem of finding the solution of Hamilton-Jaccobi-Bellman - (HJB) equation. The scheme contains of redesigning the problem of solving the HJB as an optimization problem, which is solved via the proposed method. This method can reduce huge computation and solve non-intergrable problems caused by nonholonomic constraints. And, the control strategy is globally stabilizing for the nonholonomic nonlinear systems. Based on the current ADP theory, an online learning policy is devised to implement the novel iteration algorithm. Finally, the novel algorithm of ADP is applied to wheeled mobile robot. The numerical simulation results can clearly validate the effectiveness of the proposed algorithm.