A Class of Quasi-Natural Potentials and Hyper-Stable PID Servo-Loops for Nonlinear Robotic Systems

Abstract

This paper introduces a quasi-natural potential in robot dynamics, which induces a type of sinusoidal position (joint-angle) feedback with saturation in servo-loops. By means of SP-D (Saturated Proportional and Differential) feedback, not only the robot dynamics incorporated with these servo-loops but also the residual error dynamics between the desired and actual joint trajectories satisfy the passivity with respect to the residual input torque and a linear sum of residual velocity and saturated residual position outputs. It is shown by taking advantage of the hyper-stability theory that in the case of set-point control an independent hyper-stable servo-loop constructed from a PI feedback of such a linear sum in addition to the SP-D feedback gives rise to the globally asymptotic stability. It is further shown that in the case of trajectory tracking the passivity of residual robot dynamics with SP-D feedback loops plays a vital role and eventually leads to the adaptability in model-based adaptive control and the learnability in iterative learning.