Cable-Driven Parallel Robot: Distribution of Tension Forces, the Problem of Game Theory

This paper highlights the role of game theory in specific control tasks of cable-driven parallel robots. One of the challenges in the modeling of cable systems is the structural nonlinearity of cables, rather long cables can only be pulled but not pushed. Therefore, the vector of forces in configuration space must consist of only nonnegative components. Technically, the problem of distribution of tension forces can be turned into the problem of nonnegative least squares. Nevertheless, in the current work the game interpretation of the problem of distribution of tension forces is given. According to the proposed approach, the cables become actors and two examples of cooperative games are shown, linear production game and voting game. For the linear production game the resources are the forces in configuration space and the product is the wrench vector in the operational space of a robot. For the voting game the actors can form coalitions to reach the most effective composition of the vector of forces in configuration space. The problem of distribution of forces in the cable system of a robot is divided into two problems: that of preloading and that of counteraction. The problem of preloading is set as a problem of null-space of the Jacobian matrix. The problem of counteraction is set as a problem of cooperative game. Then the sets of optimal solutions obtained are approximated with a fuzzy control surface for the problem of preloading, and game solutions are ready to use as is for the problem of counteraction. The methods have been applied to solve problems of large-sized cable-driven parallel robot, and the results are shown in examples with numerical simulation.