Chattering-free dynamical TBG adaptive sliding mode control of robot arms with dynamic friction for tracking in finite-time

A continuous control system is proposed which guarantees robust tracking in finite time for uncertain robot arms subject to unknown dynamic friction. To achieve this result, several algorithms were combined: a dynamic adaptive sliding mode control; a time base generator (TBG) to yield a time-varying gain, which allows us to obtain finite time convergence; continuous parametrization to compensate for unknown dynamic friction, which in turn yields a continuous friction compensator; and a moving sliding surface, without knowledge of initial conditions, to obtain sliding mode all the time, and hence robustness. Two controllers are derived, the adaptive and the sliding mode version, both with similar closed-loop stability properties. Simulation data of a rigid robot arm is discussed.