Dynamic modeling and noncollocated control of a flexible planar cable-driven manipulator

This paper investigates the dynamic modeling and passivity-based control of a planar cable-actuated system. This system is modeled using a lumped-mass method that explicitly considers the change in cable stiffness and winch inertia that occurs when the cables are wound around their respective winches. In order to simplify the modeling process, each cable ismodeled individually and then constrained to the other cables. Exploiting the fact that the payload is much more massive than the cables allows the definition of a modified output called the μ-tip rate. Coupling the μ-tip rate with a modified input realizes the definition of a passive input-output map. The two degrees of freedom of the system are controlled by four winches. This overactuation is simplified by employing a set of load-sharing parameters that effectively reduce four inputs to two. The performance and robustness of the controllers are evaluated in the simulation.