Modeling and control of wheeled mobile robots not satisfying ideal velocity constraints: the unicycle case

We are concerned with the stabilization about a reference trajectory of a wheeled mobile robot when skidding and slipping effects are taken into account. For this purpose we propose a dynamical modeling 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. We also propose a time-varying stabilizing control, based on the linear quadratic theory, ensuring the asymptotic convergence of the unicycle wheeled mobile robot about the reference trajectory, according to some conditions on the reference trajectory (accelerations should be sufficiently small)