A Taylor-Based Continuation Method for the Determination and Classification of Robot Singularities

Abstract

Robot design in contexts such as computer-assisted medical interventions remains challenging. Compact, dexterous mechanisms with particular mobilities are needed, the synthesis of which requires a systematic evaluation of workspace and singular positions. The evaluation of singular positions and their classification are still difficult to perform in a systematic manner. In this paper, an automated method is presented and evaluated on a complex planar mechanism. A higher-order continuation method is used to provide continuous and accurate representation of singular locii. Classification is then performed by testing all the existing singularity types through a direct evaluation. Only the mechanism loop-closure equations are required thanks to automatic differentiation and the Diamanlab software developed for use of continuation. The evaluation of the method shows promising results.