Direct Geometrico-static Problem of Underactuated Cable-Driven Parallel Robots with 3 Cables: Convergence Analysis

This paper investigates the convergence properties of the Newton method when applied to the direct geometrico-static problem of underactuated cable-driven parallel robots with three cables. The analysis, grounded in the Kantorovich theorem, provides a systematic method to compute the maximum admissible error on cable length measurements that guarantees the problem to converge to a unique solution using the Newton method. Furthermore, the accuracy of the estimated pose is quantified. Simulation results are provided for a representative robot throughout its reachable workspace. The outcomes of this study may support the development of more reliable pose estimation methods for underactuated cable-driven parallel robots.