Regular perturbations to the motion of a three-wheeled mobile robot with the front-wheel drive under restricted state variables

The time-optimal motion of a three-wheeled mobile robot with the front-wheel drive in the presence of a state constraint given by the unit circle is investigated. The poor property of this problem consists in the lack of regularity of the dynamics w.r.t. the state constraint. Therefore, a certain regularization technique is developed in order to overcome the phenomenon of non-regularity. We propose a construction of an approximating sequence of regular ε-problems. It follows that a regular w.r.t. the state constraint problem is numerically solvable in the framework of the indirect approach, that is, by using the maximum principle, due to the continuity of the measure-multiplier which is ensured under the regularity condition. This fact justifies the necessity for the perturbation analysis undertaken in this article.