Quasi-time-optimal motion planning of mobile platforms in the presence of obstacles

This paper addresses a problem of optimal motion planning of mobile platforms amidst obstacles, considering the mobile platform dynamics. Due to nonholonomic constraints, actuator constraints, and state constraints by obstacle avoidance, the planning problem of mobile platform with two independently driven wheels is a complicated one. In this study, a dynamical model for the mobile platform is presented, including nonholonomic kinematic constraints. The idea of a path parameter is introduced to simplify the planning problem by considering the dynamics and nonholonomic constraints. Using the path parameter, the optimal motion planning problem is divided into two sub-problems: 1) time-optimization of trajectory along specified path, and 2) search for optimal path. Then two methods are proposed the solve the problems using the path parameter and parametrization by B-spline function. Finally, quasi-time-optimal solution for the original problem are planned by combining the two methods. Numerical examples show effectiveness of the motion planner