Optimal Path Planning of Suspended Cable Robot by Polynomial Interpolation of Four Degree and Triangular Optimizer Algorithm

Abstract

The purpose of this article is finding the optimal path with minimum effort to move the end-effector of the three cable spatial robot in work space. For this work, first, kinematic and dynamic modeling is done of the three cable spatial robot. Then simulation and results extraction are done by both direct and indirect methods. Based on of indirect solution method is the calculus of variations. Optimality necessary condition is given in order to minimize the torque between the two points and is extracted using the pontryagin minimum principle. This optimality condition is formed a boundary value problem of two-point, which can be solved using numerical algorithms. Direct method is created by combining a metaheuristic optimization method, a polynomial interpolation and the robot equations. This article is used the metaheuristic method of triangular optimizer algorithm and the polynomial interpolation of four degree. This new combination created with the polynomial of four degree, instead of using the intermediate values of the path as design variables, specified constants of polynomial puts the design variable in order to path optimization. The indirect method gives the exact response, but extraction of optimality condition its, is the difficult in terms of calculations mathematical. While the direct method gives the approximate response without algebraic calculations. Finally, two examples are done with direct method and indirect method. The results comparisons are show the appropriate efficiency of the suggested direct method