Modeling and Control of Mobile Robots with More than Two Independent Steering Wheels not Satisfying Ideal Geometrical and Kinematical Constraints

Abstract

We consider in this paper, wheeled mobile robots equipped with more than two independent steering wheels. These wheels must be coordinated at each instant to guarantee the existence of an Instantaneous Center of Rotation. These coordination conditons can be viewed as geometrical constraints on the wheels orientations. Moreover, due to various effects such as deformability or flexibility of the wheels, the ideal kinematical constraints (corresponding to pure rolling and non slipping conditions) are never strictly satisfied. We propose a singular perturbation approach to study the robustness of linearizing dynamic state feedback laws, obtained in the ideal case to solve trajectory tracking problems, versus the dynamical effect induced by the violation of these position and velocity constraints.