Multi-robot mixing using braids

This paper presents a method for automatically achieving multi-robot mixing in the sense that the robots follow predefined paths in a somewhat loose sense while ensuring that their actual movements are rich enough. In particular, we focus on the mixing problem, where the robots have to interweave their movements, for example to ensure sufficiently rich pairwise interactions or to cover an area along the path. By formally specifying mixing levels through strings over the Braid Group, the resulting hybrid system can execute a geometric interpretation of these strings, where the level of mixing is dictated by the string length. The feasibility of the proposed approach is illustrated on a particular class of multi-robot systems that cooperatively have to achieve the desired mixing levels.