Jerk-Limited Online Trajectory Scaling for Cable-Driven Parallel Robots

Abstract

Motion planning of cable-driven parallel robots (CDPRs) suffers from difficulties imposed by the flexibility and unilateral property of cables. Existing methods either rely on specific motion primitives or employ complex numerical search or optimization processes, which cannot be applied to real-time applications with arbitrary path constraints. Aiming to narrow this research gap, this paper proposes a look-ahead online scaling approach to generate feasible trajectories of CDPRs subject to cable velocity, acceleration, jerk and tension constraints. Firstly, based on a desired path, the constraint equations are converted into the equivalent bounds on the path states by a look-ahead bounds estimation module. Then the timing law is online scaled by three cascaded controllers to fulfill the estimated bounds. Finally, the scaled timing law and the desired path are combined to form the final trajectory. Comparative studies on a laboratory-developed CDPR prototype demonstrate that the proposed approach outperforms state-of-the-art methods in terms of solution quality and computation time. Note to Practitioners–This paper was motivated by the problem of generating feasible trajectories of cable-driven parallel robots (CDPRs) subject to cable velocity, acceleration, jerk and tension constraints. Existing approaches either rely on specific motion primitives or employ complex numerical search or optimization processes, which cannot be applied to real-time applications with arbitrary path constraints. This paper proposes a look-ahead online scaling approach to generate feasible trajectories of CDPRs subject to these constraints. The approach uses a look-ahead bounds estimation module to determine the constraint bounds on the path states and preserve the stability of the approach. And a cascaded trajectory scaling algorithm is designed to steer the constrained path states to track a reference signal. A theoretical proof of the convergence of the scaling algorithm is provided. Through comparative studies, we show that the approach outperforms state-of-the-art methods in terms of solution quality and computation time. Experiments on a real robot prototype indicate that our method effectively improves motion accuracy and alleviates robot vibrations by considering the jerk constraints.