On the Problem of Tension Forces Distribution in Cable System of Cable-Driven Parallel Robot

Abstract

The paper proposes a method for controlling tension forces in statically indeterminable cable-driven systems based on the non-negative least squares method with control of singular or near-singular solutions and a complete search of all possible cable configurations. For cable-driven parallel robots the problem of controlling the cable tension forces is critical, because in the absence of control the cable tension forces are distributed unevenly, which leads to reduced robustness of the system, increased energy consumption and increased deterioration. And in special cases of cable system configuration the tension forces become so great that they lead to cable breaks. At the same time, correction of cable tension force distribution should not lead to significant deviations from the specified position of the mobile platform or, formulating the problem in terms of forces, to violation of kinetostatic equations. Thus, the problem of controlling the tension forces in the cable parallel robot system is solved as a problem of optimizing the tension forces of the cables according to the criteria of minimizing the norm of their vector in the configuration space and minimizing the norm of incoherence of the vector of forces and moments in the operational space of the robot. The developed algorithm is based on the solution of underdetermined systems of linear algebraic equations with finding the minimum least squares norms and subsequent zeroing of negative components of the solution vector. The paper considers examples of the solution of the set problem for the lower cable group of a construction 3D printer based on a cable-driven robot and for a 12-cable system