Minimum time motion of a mobile robot with two independent, acceleration-driven wheels

This paper deals with the optimal control (time optimal) of a mobile robot moving in an unobstructed planar environment. The mobile robot is equipped with two independent acceleration-driven wheels so that accelerations are bounded. Using the mobile robot´s configuration known through its position and orientation, the problem consists of determining the optimal control that allows the robot to move between two imposed configurations, the start and arrival taking place at zero velocity. Our approach is based on analytically extracting as much information as possible from the Pontryagin´s maximum principle (PMP) before starting a numerical search. The recently reported numerical result, showing that this extremal control which is of “bang-bang” type and only requires four switch times or five sequences, is invalidated. We show a configuration space zone in which no extremal control using five sequences is optimal. We also show that there exist, in a part of this zone, extremal controls requiring seven sequences that are candidates for optimality