| description abstract | Abstract. This study addresses the challenge of controlling an under-constrained, suspended four-cable-driven parallel mechanism (CDPM). The inherent geometrico-static problem introduces complex inverse kinematics and forces a trade-off between computational efficiency and control precision. To improve trajectory tracking accuracy, a novel fully closed-loop, real-time control strategy is proposed. First, for the configuration in which cables are attached to the four vertices of a rigid square moving platform, numerical iterative simulations were carried out in matlab r2021a. These simulations solved the inverse kinematics and revealed a functional relationship coupling the moving platform's translational and rotational motions. Next, a motion controller for the CDPM was designed and optimized. To avoid the high computational cost of numerical iterative methods—which is prohibitive for real-time closed-loop control—and to prevent pseudo-drag in the cables, the derived coupling function was innovatively applied as an empirical model. By integrating a 6-degree-of-freedom motion tracking system and tension sensors, a double closed-loop proportional–integral–differential (PID) control was successfully implemented. Experimental results show that the proposed control strategy achieves significantly higher stability, accuracy, and real-time performance compared with open-loop control. The average end-effector trajectory tracking error decreased from 2.2312 mm to 0.3465 mm, representing an 84.5% improvement in positioning accuracy. Moreover, the Fréchet distance, a measure of trajectory similarity, improved from 3.0952 to 0.9287, indicating a 70.0% performance enhancement. This research demonstrates that empirical model-based double closed-loop PID control offers an effective solution for the real-time control of complex CDPMs. It provides critical technical support for deploying CDPMs in high-precision industrial applications. | |
