Time Optimal Trajectories for a Mobile Robot Under Nonsliding and Radius-of-Turn Constraints

Abstract

The time-optimal path problem for a point mass mobile robot is considered. Given initial and target states, we seek the time optimal path subject to the following constraints: (1) A limitation on its maximal linear acceleration; (2) a speed-dependent nonsliding condition; and (3) a minimal radius of turn. The paper formulates and analyzes the time optimal path problem using standard optimal control formulation with extensive use of the classical Hodograph method. Based on the analysis, the time optimal path consists of five path primitives. Numerical solutions are obtained to support and illustrate the analysis.