Feasible minimum distance feedback-based-navigation for a differential drive robot in an environment with obstacles

Consider a differential drive robot (DDR) equipped with an omnidirectional sensor that provides the distances from the robot to corners and walls in a simply connected polygonal environment. Furthermore, the robot does not know a global geometric representation of the world and does not know its position in a global reference frame either. This paper addresses the problem of executing the DDR motion with closed-loop controllers to make the center of the robot travel the smallest distance in the environment to attain a goal configuration modeled as a landmark. As a result, the principal contribution of this article is a closed-loop optimal navigation strategy that does not require the availability of a global geometric map. A formal analysis on the optimality of the task is provided and experiments in a physical DDR are also given. These experiments show the practical viability of the proposed theoretical modeling.