A class of globally stable SM-NPID-like tracking controllers for robotic manipulators

This paper deals with the tracking control of robot manipulators. Proposed is a class of new SM-NPID-like tracking controllers consisting of a linear combination of the linear sliding mode control, proportional control, derivative control, nonlinear control shaped by a nonlinear function of position errors, linear integral control driven by differential feedback, and nonlinear integral control driven by a nonlinear function of position errors. 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 with the asymptotically stable integrator have the faster convergence, better flexibility and stronger robustness with respect to initial errors and uncertain payload; ii) the proposed control laws not only can achieve the asymptotically stable trajectory tracking control but also can make the tracking errors quickly tend to almost zero without oscillation as time increases.