A Mathematical Formalism for the Evaluation of C-Space for Redundant Robots

This paper presents a new general method for obstacle representation in the configuration space (C-space) for redundant robots. The method is based on the analytical deconstruction of the C-space, i.e., the separated evaluation of the C-space portion contributed by the collisions of each link in the kinematic chain. The systematic application of a simple convolution of two functions describing each link and the workspace, respectively, is applied. In order to do that, the transformation of the workspace among reference systems located at one point of each link is needed; in this step a well-known and sound method is used.