Amer Al Badr
Publications:
Marchuk E. A., Al Badr A., Kalinin Y. V., Maloletov A. V.
CableDriven Parallel Robot: Distribution of Tension Forces, the Problem of Game Theory
2023, Vol. 19, no. 4, pp. 613631
Abstract
This paper highlights the role of game theory in specific control tasks of cabledriven 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 nullspace 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 largesized
cabledriven parallel robot, and the results are shown in examples with numerical simulation.
