In this paper, we propose a distributed version of the Hungarian Method to solve the well known assignment problem. In the context of multi-robot applications, all robots cooperatively compute a common assignment that optimizes a given global criterion (e.g. the total distance traveled) within a finite set of local computations and communications over a peer-to-peer network. As a motivating application, we consider a class of multi-robot routing problems with "spatio-temporal" constraints, i.e. spatial targets that require servicing at particular time instants. As a means of demonstrating the theory developed in this paper, the robots cooperatively find online, suboptimal routes by applying an iterative version of the proposed algorithm, in a distributed and dynamic setting. As a concrete experimental test-bed, we provide an interactive "multi-robot orchestral" framework in which a team of robots cooperatively plays a piece of music on a so-called orchestral floor.
NOMENCLATUREIn the following table, we present the nomenclature used in this paper.
Table of NotationV Vertex partitioning of two disjoint sets R (robots) and P (targets) respectively, denoted by V = (R, P ) E i orig Edge set containing the edges between a robot i ∈ R and every target in P w i orig Weight function corresponding to the edge set E i orig G i orig