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

This paper is concerned with the problem of trajectory tracking of a unicycle wheeled mobile robot when small skidding and slipping effects are taken into account. For this purpose, bye propose a dynamic modelisation based on a singular perturbation approach and referenced to the trajectory to be tracked We highlight the necessity for the reference trajectory, to satisfy the dynamics of the skidding effects and propose a first time-varying stabilising control law. It is based on the linear quadratic theory and, under some conditions on the reference trajectory, it makes the error vector locally asymptotically converge to Zero. When the assumption of rolling without slipping is satisfied, wheeled mobile robots are known to be pat. We prove that this is no longer true when those conditions are transgressed We then show that the flatness of the robot may be recovered in the average by using vibrational techniques. We finally make use of the high-frequency approach to build a second time varying stabilising control law that ensures the global convergence of the trajectory tracking error to a limit cycle near the origin.