Near-optimal motion planning for nonholonomic systems using time-axis transformation and gradient method

In this paper, an optimal motion planning scheme using time-axis transformation and gradient method is proposed for nonholonomic systems. The motion planning of nonholonomic systems can be formulated as a nonlinear optimal control problem. However, the optimal control problem is too difficult to solve due to peculiar difficulty in the control of the nonholonomic systems. To alleviate the difficulty, we first convert the optimal control problem to a bidirectional, fixed-domain optimal control problem by using quasi-time variable. Then, a numerical algorithm which is based on the gradient method is developed for the optimal control problem and its convergence property with respect to final state error is proved. The optimal motion planning scheme is also applied to a 2-link planar free-joint manipulator. The simulation results show the effectiveness of the proposed optimal motion planning scheme.