Kinematically-Constrained Redundant Cable-Driven Parallel Robots: Modeling, Redundancy Analysis, and Stiffness Optimization

This paper develops a general model for kinematically-constrained redundant cable-driven parallel robots (CDPRs), and studies stiffness improving effects and redundancy resolution of such robots aiming stiffness optimization to minimize their undesired perturbations under external disturbances in a desired direction. In the developed model, assuming an axially flexible model for the cables, motion equation is derived. Considering the role of constrained cables in restriction of CDPR's rotational degrees of freedom, the vibration equation of the moving platform is separated from the equation of motion. The resulted vibration equation is a linear dynamic system with a stiffness matrix formed by the cables' tension and the constrained cables' axial stiffness. Based on that, the substantial effects of constrained cables and the potential effects of cables' tension on the stiffness improvement of CDPRs are shown. Accordingly, the cables' tension redundancy problem is formulated. Redundancy resolution is studied considering the directional stiffness of the moving platform as the objective function to maximize. This objective function is derived as a linear function of cables' redundant tensions and the corresponding redundancy problem solved by using a time-efficient method of linear programming. The developed model and the proposed redundancy resolution approach are experimentally tested on an actual warehousing robot to maximize its translational stiffness. Comparison of theoretical and experimental results demonstrates the validity of the proposed optimization approach and the effectiveness of kinematically-constrained actuation method.