A numerical continuation approach using monodromy to solve the forward kinematics of cable-driven parallel robots with sagging cables.

Designing and analyzing large cable-driven parallel robots (CDPRs) for precision tasks can be challenging, as the position kinematics are governed by kineto-statics and cable sag equations. Our aim is to find all equilibria for a given set of unstrained cable lengths using numerical continuation techniques. The Irvine sagging cable model contains both non-algebraic and multi-valued functions. The former removes the guarantee of finiteness on the number of isolated solutions, making homotopy start system construction less clear. The latter introduces branch cuts, which could lead to failures during path tracking. We reformulate the Irvine model to eliminate multi-valued functions and propose a heuristic numerical continuation method based on monodromy, removing the reliance on a start system. We demonstrate this method on an eight-cable spatial CDPR, resulting in a well-constrained non-algebraic system with 31 equations. The method is applied to four examples from literature that were previously solved in bounded regions. Our method computes the previously reported solutions along with new solutions outside those bounds much faster, showing that this numerical method enhances existing approaches for comprehensively analyzing CDPR kineto-statics. • We introduce a numerical continuation method for solving the kinetostatics of CDPRs. • The Irvine sagging cable model is reformulated to eliminate multi-valued functions. • We propose a new heuristic monodromy algorithm to solve non-algebraic systems. • We solve an eight-cable spatial CDPR, a well-constrained system with 31 equations. • The new approach finds solutions more quickly than previously published methods. [ABSTRACT FROM AUTHOR]