A globally stable SM-PD-INP-D tracking control of robot manipulators

This paper deals with the tracking control of robot manipulators. Synthesizing the strong robustness of the sliding mode control and the good flexibility of PD-I^NP-D control, Proposed is a simple class of robot tracking controller consisting of a linear sliding mode term plus a linear PD feedback plus an integral action driven by an NP-D controller. By using Lyapunov´s direct method and LaSalle´s invariance principle, the simple explicit conditions on the controller gains to ensure global asymptotic stability are provided. The theoretical analysis and simulation results show that: (i) the SM-PD-I^NP-D controller has the faster convergence, better flexibility and stronger robustness with respect to initial errors; (ii) the proposed control laws can not only achieve the asymptotically stable trajectory tracking control but also the tracking errors quickly tend to almost zero without oscillation as time increases; (iii) after the sign function is replaced by saturation function in the SM-PD-I^NP-D control law, the high-frequency oscillation of the control input vanishes.