Trajectory tracking control of a mobile manipulator with an external force compensation

This paper considers the problem of the accurate task space finite-time control susceptible to both undesirable disturbance forces exerted on the end-effector and unknown friction forces coming from joints directly driven by the actuators as well as unstructured forces resulting from the kinematic singularities appearing on the mechanism trajectory. We obtain a class of estimated extended transposed Jacobian controllers which seem to successfully counteract the external disturbance forces on the basis of a suitably defined task-space non-singular terminal sliding manifold (TSM) and the Lyapunov stability theory. Moreover, in order to overcome (or to minimise) the undesirable chattering effects, the proposed robust control law involves the second-order sliding technique. The numerical simulations (closely related to an experiment) ran for a mobile manipulator consisting of a non-holononic platform of (2;0) type and a holonomic manipulator of two revolute kinematic pairs show the performance of the proposed controllers and make a comparison with other well-known control schemes.