Finite‐time control of mobile manipulators subject to unknown/unstructured external disturbances
M. Galicki
Abstract
Abstract A robust finite‐time control law is proposed for mobile manipulators with uncertain both kinematic and dynamic equations. Moreover, the following external disturbances are allowed to act on the system: unstructured forces exerted on the end‐effector, slip reaction forces affecting the platform wheels, unknown friction forces coming from joints directly driven by the actuators and undesirable unstructured forces caused by singular configurations. In order to cope with both parametric uncertainties and unknown/unstructured external disturbances, we first transform the original control problem whose non‐holonomic constraints are violated into a steering one in an extended space of generalized coordinates with extended non‐holonomic constraints of the Pfaffian form and then introduce a task space non‐singular terminal sliding manifold. Based on the Lyapunov stability theory, a new class of estimated extended transposed Jacobian control laws is derived which both effectively counteract the external forces and significantly reduce the slipping phenomena. A second order sliding technique is involved in our control law to eliminate undesirable chattering effect. An illustrative example of a mobile manipulator control demonstrates the advantages of the approach. Moreover, numerical comparisons with other representative controllers well‐known in the literature are also given.