Contortion and Formation Structures in the Mappings between Robotic Jointspaces and Workspaces

Rooney, J. and Tanev, T. K. (2003). Contortion and Formation Structures in the Mappings between Robotic Jointspaces and Workspaces. Journal of Robotic Systems, 20(7) pp. 341–353.

DOI: https://doi.org/10.1002/rob.10090

Abstract

The concepts of formation in robotic workspace (WS) and contortion in robotic jointspace (JS) are developed, based on the notions of pose and posture, respectively. The approach focuses on the forward and reverse mappings between jointspace and workspace. It utilizes the Cartesian product space JS×WS to interpret these mappings, and, in particular, their singularities as determined by the Jacobians. The singularities are interpreted from the viewpoint of geometric (Clifford) algebra. Initially, systems that have 1D jointspaces and 1D workspaces are discussed before higher-dimensional examples are examined.

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