Boundary equations of configuration obstacles for manipulators

A method is described for obtaining the boundary equations of configuration obstacles for stick-figure manipulators in three-dimensional environments. Polyhedral obstacles are represented as a collection of planar triangular patches, and the intersection conditions between a line segment and a triangular patch are used to derive boundary equations. It is shown that the boundary equation for the nth joint variable can be solved explicitly in terms of the 0th, 1st, . . ., (n-1)th joint variables. The expressions can be used to compute configuration obstacles or to analyze the geometry of contacts between manipulators and obstacles