Efficient wrench-closure and interference-free conditions verification for cable-driven parallel robot trajectories using a ray-based method

Abstract

This letter introduces a novel approach to verify the feasibility of curved trajectories under both the interference-free (IFC) and wrench-closure (WCC) conditions for spatial cable-driven parallel robots (CDPRs). Existing ray-based methods can only be used either for translation or single degree-of-freedom (DoF) motion, limiting its use to verify the motion of practical trajectories. In this work, the trajectory representation proposed allows the IFC and WFC for the entire trajectory to be verified by simply solving a set of univariate polynomial equations. The translation motion is expressed as polynomial time parametric functions and the orientation motion is defined using a spherical linear interpolation (SLERP) in the quaternion representation for a desired start and end orientation. It is then shown that for the proposed trajectory representation, the IFC and WFC can be verified by solving a set of univariate polynomial equations. Moreover, the exact degree of the resulting polynomial equations are derived for a 6-DoF spatial CDPR. Simulation on a range of different trajectory forms, from linear, quadratic and cubic paths to higher degree functions, show the effectiveness of the method. Finally, comparison with the well-accepted point-wise method shows that the proposed method is more efficient, accurate and ensures the solution continuity.