Abstract
The article discusses the application of optimization algorithms to solve the problem of determining the workspace of robots. The development of a numerical method for approximating the set of solutions of a system of nonlinear inequalities that describe the restrictions on the geometric parameters of a robot based on the concept of non-uniform coverings is considered. An approach is proposed that allows you to reduce the number of boxes and numbers describing each of the boxes. Reducing the number of boxes is achieved by combining the boundary boxes of the covering set and the area between them along one of the axes. The dimensions along the other axes are equal for all boxes, which allows them to be described by one number. The transition to the integer space is described. Thus, converting non-uniform covering sets to a partially ordered set of integers reduces computational complexity. An algorithm for converting boxes of a covering set is presented. The approach has been tested for a 3-RPS robot.
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