Global Position Tracking of Robot Manipulators via SM-NPID-like Controllers with Two Nonlinear Integral Actions

This paper deals with the tracking control of robot manipulators with uncertain payload. Proposed is a set of novel SM-NPID-like tracking controllers consisting of a linear combination of the linear sliding mode control, proportional control mode, derivative control mode, nonlinear control mode shaped by a nonlinear function of position errors, and two nonlinear integral control modes driven by a nonlinear function of position errors and its derivative, respectively. 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 proposed controllers have the faster convergence, better flexibility and stronger robustness with respect to initial errors and uncertain payload; 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.