Investigation of Quasi-Optimal Motion of a Mobile Robot: the Maximum Principle Based Approach*

Abstract

This paper concerns the quasi time-optimal motion in a simplified model of a mobile robot with constraints imposed on the state variables. As it is known, in this kind of problems involving the so-called unicycle type of dynamics, the classical assumptions of regularity with respect to the state constraints are not fulfilled. This fact greatly complicates the analysis of such control problems through the use of Pontryagin’s maximum principle. Moreover, the difficulties are also due to the presence of a singular control mode which is related to the angular velocity. The paper proposes a certain regularization approach in order to overcome the obstacles above and to develop a tool for the subsequent numerical implementation.