Robust Stabilization of Wheeled Mobile Robots Moving on Uncertain Uneven Surface

A solution is presented to the robust control problem of wheeled mobile robots moving on an uneven surface that is not exactly known. Quadratic surface with unknown but bounded coefficients is utilized to locally approximate the uneven surface. The design procedure is based on the transverse function method, integrator backstepping, and Lyapunov redesign technique. After exploring the left-invariance property of the kinematic subsystem of the wheeled mobile robots with respect to the standard group operation of the Lie group SE(2) we use transverse function to derive smooth "virtual" control laws which render the error subsystem exponentially stable. Then, the integrator backstepping technique is applied to the nominal dynamic system due to the smoothness of the "virtual" control laws. Finally, a Lyapunov redesign component is constructed to handle the gravity disturbance caused by the surface. Driven by the proposed control laws, the wheeled mobile robot has the ability to adapt to varying uneven surface condition. Some simulations are provided to validate the effectiveness of the algorithm