On the topological characterization of robot singularity loci. a catastrophe-theoretic approach

Two-dimensional slices of robot singularity loci contain, in general, cusps. This kind of points are important because their presence indicates the possibility of planning assembly-changing motions that do not meet any singularity. The critical points where the number of cusps changes, as the slice is swept, permit one to decompose a singularity locus into domains where the obtained slices share common topological properties. In this paper, it is shown how Catastrophe Theory provides a solid framework to classify these critical points up to certain types of equivalence giving precise local models to describe them. It is also shown how only three possible types of these critical points exist for generic robots. The presented results are exemplified on a serial 3R robot.