A Regularization Approach to Analyze the Time-Optimal Motion of a Mobile Robot under State Constraints using Pontryagin’s Maximum Principle

Abstract

This work concerns the investigation of time-optimal control problem for a simplified mobile robot model subject to state constraints. In this type of problems, which involve the so-called unicycle dynamics, the well-established regularity conditions with respect to the state constraints are not fulfilled. This fact greatly complicates the analysis of the control problem bearing in mind the use of the maximum principle. Moreover, the difficulty is also due to the presence of a singular control mode with respect to the angular velocity. Herein, a regularization approach is proposed in order to overcome these obstacles. A certain tool for the numerical implementation is developed. The numerical analysis is provided for a sample problem.