Vibrational control of wheeled mobile robots not satisfying ideal velocity constraints: The unicycle case

This paper is concerned with the problem of controlling the unicycle wheeled mobile robot when skidding and slipping effects are taken into account. When the assumption of rolling without slipping is satisfied, wheeled mobile robots with a single platform are known to be flat [3], We first highlight that this is no longer true when those ideal conditions are transgressed, i.e. in the real case. Then, we show that the flatness of the robot may be recovered in the average using vibrational technics. Finally, we concentrate on trajectory tracking and make use of the high frequency approach to build a time-varying control feedback ensuring the convergence of the trajectory tracking error to a limit cycle near the origin.