Actuators redundancy resolution scheme with computational time reduction purpose for parallel cable robots with considering the rupture limits of the cables

Cable parallel robots usually require at least one additional actuator force in addition to degrees of freedom to keep the cables in all directions in the workspace, which solves an optimization problem to determine the cable tensile force. In this paper, a convex optimization problem is formulated on a parallel cable robot using optimization conditions through the Karush-Kuhn-Tucker theory and the analytical-iteration method to achieve a minimum force vector of actuators that has less computational time and volume. Where the lower and upper limits of the optimization variables are applied, respectively, to ensure that the cables remain in tension and take into account the saturation limit of the actuators or the rupture limit of the cables (whichever is less), and equal constraints that the relationship between actuator force and force are expressed in the moving platform, defined by the force of the actuators as the sum of the basic solution and the homogeneous solution, -located in the null space of the transpose of Jacobin matrix. Comparison of the results of analytical-iterative solution presented in this paper with numerical algorithms of MATLAB software optimization shows that this method is much faster than these algorithms to converge to the optimal response.