Screw dynamics modeling of parallel robots and its hyperbolic convergence law sliding mode control strategy

Abstract

This study introduces a method to establish the dynamic model of a parallel robot using screw theory and the d’Alembert-Lagrange equation. Based on this model, a robust sliding mode control strategy utilizing hyperbolic convergence laws is proposed. The d’Alembert-Lagrange equation and screw theory are employed to construct a concise dynamic equation for the parallel robot, making it more suitable for control applications. Additionally, a formula for directly calculating the inertial wrench is presented. To achieve precise control, a sliding mode control strategy with double hyperbolic convergence law is implemented to ensure chattering-free performance. A novel double hyperbolic convergence law disturbance observer is designed to estimate unmodeled dynamics and uncertain disturbances, enhancing the system’s robustness. The control strategy is validated through numerical simulations, demonstrating significant improvements in chattering-free performance, tracking accuracy, and tracking speed.