Robust Tracking Control of Wheeled Mobile Robots Not Satisfying Nonholonomic Constraints

This paper focuses on the trajectory tracking problem of wheeled mobile robots not satisfying the ideal "rolling without slipping" constraints. Robust control laws are proposed to deal with the slipping of the wheels. The design procedure consists of three main steps. A bounded transverse function is firstly constructed, by which a smooth embedded submanifold is defined, and the nominal kinematic model of the wheeled mobile robots is augmented. Then the left-invariance property of the nominal kinematic model is explored with respect to standard group operation of the Lie group SE(2) and the nominal error system is derived. Consequently, smooth exponential control laws are designed for the nominal error system, thus the nominal tracking error model is rendered practically stable. Finally, an additional control component is constructed to robustify the nominal tracking control laws. Simulations are provided to demonstrate the effectiveness of the robust control laws