Non-iterative optimization algorithm for cable tension distribution of a class of n + 2 cable-driven redundant parallel robots based on computational geometry

For the multi-solution problem of tension distribution optimization in a class of n + 2 cable-driven redundant parallel robots (n-Dof), iterative optimization or geometric methods are typically used to solve this problem. The iterative optimization method fails to meet the real-time requirements due to the influence of factors such as the initial point and the number of cables. This paper proposes a novel non-iterative search algorithm based on the geometric features of the tension feasible region (TFR). This algorithm can optimize the tension optimal solution (TOS) in real time through geometric search, overcoming the limitations of traditional iterative search algorithms. The algorithm solves the TOS in two steps. Firstly, based on the analysis of the geometric features of the TFR, the TFR is searched through the proposed translation and rotation calculation rules. Secondly, the TOS is solved through the geometric feature points of the TFR. Specifically, this paper improves the traditional solution method of 1-Norm TOS, and analyzes the vertical geometric conditions for obtaining the min/max 2-Norm TOS, as well as the TOS calculation formulas of the centroid and weighted barycenter. Finally, numerical simulations and prototype experiments are conducted for two multi-degree-of-freedom coupled motion examples, and analyzes the experimental time consumption of the algorithm in each control cycle. Both numerical simulations and prototype experiments show that the proposed algorithm in this paper can quickly obtain the TOS and fully meet the requirements of real-time control.