Vibration suppression of redundantly controlled cable-driven parallel robots

Cable-driven parallel robots (CDPRs) use flexible cables to connect the end-effector to a fixed base, which is prioritized for large workspace and fast operation speed, but the presence of flexible cables creates a challenge for high-precision control of CDPRs. The mass and elasticity of the cables need to be considered to model the CDPRs in a large workspace more accurately. In this paper, the dynamics of the CDPRs are modeled using the finite element method. In order to more accurately predict the simulation results of the discrete-time model at the actual control frequency, the hierarchical model predictive control (H-MPC) algorithm is proposed with an internal mapping module for mapping control signals and an external prediction module for predictive control. In the control process, we designed a physics-informed neural network (PINN) to predict the state of end-cable elements. Under the same hardware conditions, the H-MPC algorithm effectively reduces the vibration of the end-effector during operation compared to the model predictive control (MPC) algorithm. Our proposed algorithm is validated under various trajectories, and the results show that the H-MPC algorithm can mitigate the vibration condition of the end-effector. We provide new solutions and ideas for the research in high precision control and vibration control of CDPRs. Our H-MPC algorithms are also easier to deploy in industrial controls.