Jerk-Limited Time-Optimal Model Predictive Path Following Control of Cable-Driven Parallel Robots

Motion planning and control of cable-driven parallel robots (CDPRs) suffer from difficulties imposed by the flexibility and unilateral property of cables. In contrast to trajectory tracking control which has been extensively studied, path following control of CDPRs has been seldom addressed in existing works. In this letter, we present a real-time model predictive control (MPC) scheme for jerk-limited time-optimal path following control of CDPRs. The proposed MPC scheme solves the control inputs and the timing law of the desired path by simultaneously minimizing the path following error and maximizing the path progress subject to the input and state constraints. To reduce computational complexity, a convex MPC formulation is derived by iteratively linearizing the dynamics and constraints. A high-speed solver for the proposed MPC is developed by leveraging the iterative linear quadratic regulator (iLQR) algorithm and the augmented Lagrangian (AL) method. The feasibility and robustness of the proposed method are validated on a laboratory-developed CDPR through simulations. Experiment results demonstrate that the proposed method outperforms the trajectory scaling method in terms of motion accuracy and motion smoothness.