A Linking Invariant for Truss Robot Motion Planning

In this paper, we introduce a new invariant of C-space components for truss robots: the link-augmented graph. This invariant uses techniques from knot, link, and spatial graph theory to encode the linking information between different closed chains in the robot. For robots with a disconnected free configuration space, this invariant serves as a tool to distinguish robot configurations that lie in different connected components of C-space from each other. This can be used to eliminate goal positions that are unreachable by any collision-free motion, without needing to perform any probabilistic planning. This invariant can also be used to find appropriate assignments of node labels in a specified goal position. We demonstrate the advantages of using this invariant in conjunction with a probabilistic planner, and introduce a variant of RRT-Connect to simultaneously search for all valid goal labelings.