Passivity-Based Pose Regulation and Jacobian-Based Force Distribution of a Cable-Driven Parallel Robot

Abstract

This paper investigates the set-point pose regulation of a six degree-of-freedom cable-driven parallel robot (CDPR) from a passivity perspective. The proposed control method makes use of the existence of a passive input-output mapping from a modified control input in task space to the velocity and angular velocity of the payload. A pose regulation control law that does not require an attitude parameterization and instead directly uses the direction cosine matrix is presented and shown to achieve asymptotic closed-loop stability. An additional contribution of this work is the development of a novel Jacobian-based force distribution method to account for the redundantly-actuated nature of CDPRs. An optimal linear programming formulation of this method is shown to match the performance of existing approaches in the literature. A numerical CDPR example is presented to illustrate the implementation of the proposed pose regulation control law and force distribution method.