Minimal-energy finite-time control of omni-directional mobile robots subject to actuators faults

In this paper, we deal with optimal finite-time trajectory tracking by the omni-directional mobile robots (ODMRs) under: uncertain kinematics and dynamics, the actuator failure, undesirable forces/torques exerted on the mobile platform and unknown friction forces originating from joints directly driven by the actuators. Based on the suitably defined task space non-singular terminal sliding manifold (TSM) and the Lyapunov stability theory, we propose a class of new fault tolerant estimated generalized Jacobian controllers, which seem to be effective in counteracting the unstructured forces/torques. On account of the fact, that the omni-directional mobile robot is a redundant one, a useful criterion function reflecting an energy consumption or \(L_2\) $L_2$ norm of controls - torques, has been utilized in our approach to temporarily optimally track a desired trajectory. The performance of the proposed control law is demonstrated by computer simulations conducted on a four mecanum wheels mobile robot (FMWMR) in conditions of unexpected actuator failure. Additionally, numerical comparisons are also provided with other representative control laws, found in the literature.