A Discrete Method for Time-Optimal Motion Planning of a Class of Mobile Robots

This paper addresses the time-optimal motion planning (TOMP) problem between two configurations for a mobile robot with two independently driven wheels. Different from previous methods, in which one needs to solve a set of differential equations, a discrete method is proposed to solve this problem. The first step is to transform the TOMP problem into a nonlinear programming (NLP) problem by an iterative procedure, in which the sampling period and the control inputs are chosen as variables, and the traveling time is to be minimized. Since it is usually hard to find initial feasible solutions of an NLP problem, a method that combines the concepts of genetic algorithms (GAs) and penalty functions is also proposed. In this manner, the NLP problem can be solved since initial feasible solutions can be generated easily. Simulation results are included to show the validity of the proposed method.