A swarm optimization approach for solving workspace determination of parallel manipulators

Abstract

SUMMARYThis paper presents a novel method to determine the workspace of parallel manipulators using a variant of the Firefly Algorithm, which is one of the emerging techniques in swarm artificial intelligence. The workspace is defined as a set of all the coordinates in the search space that are accessible by the parallel manipulator end effector. The workspace formulation of the parallel manipulator considered in this paper has actuated and passive joint displacements which values are limited by their physical constraints. A special fitness function that discriminates between accessible and inaccessible coordinates is formulated based on the joint limitations. By finding these coordinates using the proposed Firefly Algorithm, the workspace of the manipulator can be constructed. The proposed method is an easy-to-implement alternative solution to the current numerical methods for workspace determination. The method consists of two stages of operation. The first stage maps the workspace to find the initial results with a space filling approach, in which a number of coordinates in the workspace are identified. The second stage refines the results with a boundary detection approach which focuses on the mapping of the boundaries of the workspace. The method is illustrated by its application to determine the 2D, 3D, and 6D workspaces of a Gough--Stewart Platform manipulator. Furthermore, the method is compared with a more rigorous interval analysis method in terms of computational cost and accuracy.