Dynamic Differential Flatness of Cable Elasticity of a Cable-driven Parallel Manipulator

Cable manipulator can play a lifting role in the dock stacking, mineral mining, marine fishing and other fields, which has a wide range of applications. However, the cable elasticity itself will affect the accuracy of the cable force control, which in turn affects the positional control accuracy of the end-effector. To solve the problem of control accuracy caused by simplifying the cable to a linear model without considering the cable elasticity, this paper adopts the model of simplifying the cable to a linear spring plus a lightweight connecting rod. The elasticity of the linear spring, i.e., the cable tension is derived through the static equilibrium equation. And a dynamics simulation analysis of the three-cable three-degree-of-freedom parallel manipulator is conducted. The end position and its derivative as the flat output of the system is selected and the linear process of nonlinear control theory is used to prove the differential flatness of the system. Through theoretical analysis and example simulation, the difference of the requested tension force when the cable elasticity is considered or not is compared and analyzed. It is shown that the proposed dynamics analysis of the cable parallel manipulator with cable elasticity has influence on the moment control of the whole manipulator. It is verified that the magnitude of the cable elasticity is ultimately affected by the change of the cable acceleration. And this dynamics analysis can improve the control process caused by the high speed change of the end-effector to analyze the effect of imprecise force control brought by the high speed change of cable elasticity of the cable, It provides a more accurate theoretical basis for establishing a more accurate theoretical model of dynamics