Quasi-Natural Potential and Saturated-Position Feedback

Abstract

Abstract A class of quasi-natural potentials is introduced, which brings in the concept of saturated-position feedback and renders the pair of an SP-D (saturated proportional and differential) output signal and the torque input passive. Then hyperstability theory suggests a negative feedback connection of such a non-linear passive block with a linear positive real block, which enables the overall system to be globally asymptotically stable for set point regulation. This consideration is extensively applied to non-linear robot dynamics under holonomic constraint or coordination control of multiple arms.