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Optimal trajectory tracking control of omni-directional mobile robots

In the present work, a new task space nonsingular terminal sliding mode (TSM) manifold defined by non-linear integral equation of the first order with respect to the task tracking error and a kind of computed torque method are introduced to control four mecanum wheeled mobile robot (FMWMR). On account of the full rank of the Jacobian matrix of the omni-directional holonomic mechanism, the proposed control scheme is shown to be globally finite-time stable despite uncertain dynamic equations and (globally) unbounded disturbances acting on the FMWMR. Moreover, the proposed control law provides (locally) optimal solution. The numerical simulations carried out for a youBot platform with four mecanum wheels illustrate both the performance of the proposed control scheme and simultaneously its minimizing property for some practically useful objective function.