An SLF approach to trajectory tracking control of input-restricted robot manipulators

Abstract

In this paper, the problem of trajectory tracking of robot manipulators that have input restrictions is addressed. The model adopted for the input nonlinearity is the hard saturation function. An unconstrained nonlinear trajectory tracking controller is introduced, which guarantees trajectory tracking even in the presence of input nonlinearities in the robot manipulator. This approach differs from many other studies, where controllers are limited by the use of smooth saturation functions. In this research, the closed-loop system is analyzed using a strict Lyapunov function (SLF) that allows concluding global uniform asymptotic stability for unperturbed robot manipulators, as well as input-to-state stability (ISS) and global uniform ultimate boundedness (GUUB) of the error signals for the perturbed case. In fact, this paper provides for the first time an SLF-based solution to the problem of designing a trajectory tracking controller for hard-saturation input constrained robot manipulators. Experimental results on a three-degree-of-freedom robot manipulator support the main theoretical findings given in this paper. A comparison with respect to other controllers based on smooth saturation functions is presented. Better tracking accuracy is obtained with the proposed controller.