Tracking Control of Cable-driven Parallel Robots Considering Cable Sag Effects

Abstract

Parabolic equation is utilized to represent the curve of a long span cable. The relationship among cable force, cable end displacement and cable length variation is derived by using parabolic equation. Dynamics model of cable-driven robots is established on the basis of cable mechanical equation, which shows that the resultant cable force acting on the end-effector is directly related to cable length and end-effector pose. A linear expansion of the mechanical equation is carried out to facilitate introducing the mechanical model into the control design, then the relationship between the cable force increment acting on end-effector and the cable length variation and the end-effector displacement is obtained. The cable force on end-effector can be expressed as the addition of its desired value and a corresponding increment resulting from the error of cable length and the error of end-effector pose. In the control design, a feedback controller is first designed for the cable force by using Lyapunov method. Then, by utilizing the above-mentioned incremental relationship, a nonlinear controller based on the end-effector pose feedback is constructed, in which the cable length adjustment quantity serves as the controller for output control. It is essentially a nonlinear PD controller with compensation terms. Controller parameters can be adjusted automatically along with the variation of system state. Numerical examples validate the control algorithm.