Topological characterization of safe coordinated vehicle motions

The paper characterizes the homotopy properties and the global topology of the space of positions of vehicles which are constrained to travel without intersecting on a network of paths. The space is determined by the number of vehicles and the network. Paths in the space correspond to simultaneous non-intersecting motions of all vehicles. We therefore focus on computing the homotopy type of the space, and show how to do so in the general case. Understanding the homotopy type of the space is the central issue in controlling the vehicles, as it gives a complete description of the distinct ways that vehicles may move safely on the network. We exhibit graphs, products of graphs, and amalgamations of products of graphs that are homotopy equivalent to the full configuration space, and are far simpler than might be expected. The results indicate how a control system for such a network of vehicles (such as a fleet of automatically guided vehicles guided by wires buried in a factory floor) may be implemented