An Optimization Approach to the Determination of the Boundaries of Manipulator Workspaces

Abstract

An optimization approach to computing the boundaries of the workspaces of planar manipulators is presented. This numerical method consists of finding a suitable radiating point in the output coordinate space and then determining the points of intersection of a representative pencil of rays, emanating from the radiating point, with the boundary of the accessible set. This is done by application of a novel constrained optimization approach that has the considerable advantage that it may easily be automated. The method is illustrated by its application to two planar mechanisms, namely a planar Stewart platform and a planar redundantly controlled serial manipulator. In addition to the exterior boundaries of the workspace, interior curves that represent configurations at which controllability and mobility may be limited, are also mapped. The optimization methodology, implemented here for the planar case, may readily be extended to spatial Stewart platforms. [S1050-0472(00)00304-4]