Single landmark feedback-based time optimal navigation for a differential drive robot

Abstract

In this paper, we propose a feedback-based control approach to execute the time optimal motion trajectories for a differential drive robot. These trajectories are composed of straight lines and rotations in place. We show that the evolution of the position of a single landmark over time, in a local reference frame, makes it possible to track a prescribed time-optimal robot’s trajectory, based on feedback of the landmark’s position. We also show that the closed-loop system is an exponentially stable one with a nonvanishing perturbation, and that globally uniformly ultimately boundedness of the tracking errors can be achieved. The two main results of this work are: 1) Our approach leverages visual servo control type of methods with tools from optimal control for executing time-optimal trajectories in the state space based on feedback information. 2) The approach is able to work with the minimum number of landmarks–only one–this represents a necessary and sufficientcondition for landmark-based navigation. Experiments in a physical robot, a nonholonomic differential drive system equipped with an omnidirectional laser sensor, are shown, which validate the proposed theoretical modelling.