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

This paper deals with the tracking control of rigid robot manipulators. By synthesizing the strong robustness of sliding mode control and the good flexibility of PD-NP-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 a bounded nonlinear term of position errors plus an integral action driven by an NP-D controller, where the nonlinear terms are shaped by a continuous bounded nonlinear function of position errors. By using Lyapunov´s direct method, 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-NP-I^NP-D controller has the faster convergence, better flexibility and stronger robustness with respect to initial error; (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-NP-I^NP-D control law, the high-frequency oscillation of the control input vanishes.