Robust tracking of uncertain robotic manipulators using high order nonlinear feedback

For rigid robots controlled by PD controllers, this paper is concerned with the robust tracking problem in the presence of lumped uncertainties and bounded torque disturbance. Assuming that the effect of uncertainties is upper bounded by a quadratic function of tracking error, we propose a nonlinear control scheme, which explicitly accounts for the absolute uncertainty bound, to improve the transient tracking performance of PD controlled robots. This scheme is composed of switching (or nonswitching) nonlinear feedback with gains proportional to polynomial of tracking error, which can also be made adaptive to avoid high gain transient. The proposed scheme guarantees that the tracking error is globally and uniformly bounded (and converges to a residual set if no switching) with improved transient and convergence speed and internal signals are globally and uniformly bounded. Simulations of a planar two-link rigid robot are given to illustrate the effectiveness of the nonlinear control schemes in tracking transient and accuracy.