Dynamic Modeling and Adaptive Control of a Single Degree-of-Freedom Flexible Cable-Driven Parallel Robot

Abstract

This paper investigates the dynamic modeling and adaptive control of a single degree-of-freedom flexible cable-driven parallel robot (CDPR). A Rayleigh–Ritz cable model is developed that takes into account the changes in cable mass and stiffness due to its winding and unwinding around the actuating winch, with the changes distributed throughout the cables. The model uses a set of state-dependent basis functions for discretizing cables of varying length. A novel energy-based model simplification is proposed to further facilitate reduction in the computational load when performing numerical simulations involving the Rayleigh–Ritz model. For control purposes, the massive payload assumption is used to decouple the rigid and elastic dynamics of the system, and a modified input torque and modified output payload rate are used to develop a passive input–output map for the naturally noncollocated system. A passivity-based adaptive control law is derived to dynamically adapt to changes in cable properties and payload inertia, and different forms of the adaptive control law regressor are proposed. It is shown through numerical simulations that the adaptive controller is robust to changes in payload mass and cable properties, and the selection of the regressor form has a significant impact on the performance of the controller.