An Analysis of the Operational Space Control of Robots

Theoretically, the operational space control framework [1] can be regarded to be the most advanced control framework for redundant robots. However, in practice, the control performance of this framework is significantly degraded in the presence of model uncertainties and discretizing effects. Using the singular perturbation theory, this paper shows that the same model uncertainties can create different effects on the task space and joint space control performance. From the analysis, a multi-rate operational space control was proposed to minimize the effects of model uncertainties on the control performance and while maintaining the advantages of the original operational space framework [2]. In this paper, we present a stability analysis of the multi-rate operational space control framework using the Lyapunov's direct method.