Modelling and Control of Wheeled Mobile Robots not Satisfying ldeal Velocity Constraints: The Unicycle Case

摘要

This paper is concerned with the problem of tra- jectory tracking of a unicycle wheeled mobile robot when small skidding and slipping effects are taken into account. For this purpose, we propose a dynamic modelisation based on a singular pertur- bation approach and referenced to the trajectory to be tracked. We highlight the necessily for the reference irajectory to satish ihe 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 assump- tion of rolling withoul slipping is satisfied wheeled mobile robols are known to be flat. 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 glo- bal convergence of the trajectory tracking error to a limit cycle near the origin.