Shortest Path Set Induced Vertex Ordering and its Application to Distributed Distance Optimal Multi-agent Formation Path Planning
This work addresses distributed path planning for multi-agent systems, offering a novel distributed approach where only centralized methods existed before, though it builds incrementally on prior centralized results.
The study tackled the problem of scheduling distance-optimal paths for multi-agent formation planning on graphs, showing that a vertex ordering induced by the problem enables a more intuitive and faster centralized algorithm, as well as a novel distributed scheduling algorithm, while guaranteeing the same tight convergence time and extending to graphs with non-unit capacities and edge lengths.
For the task of moving a group of indistinguishable agents on a connected graph with unit edge lengths into an arbitrary goal formation, it was previously shown that distance optimal paths can be scheduled to complete with a tight convergence time guarantee, using a fully centralized algorithm. In this study, we show that the problem formulation in fact induces a more fundamental ordering of the vertices on the underlying graph network, which directly leads to a more intuitive scheduling algorithm that assures the same convergence time and runs faster. More importantly, this structure enables a distributed scheduling algorithm once individual paths are assigned to the agents, which was not possible before. The vertex ordering also readily extends to more general graphs - those with non-unit capacities and edge lengths - for which we again guarantee the convergence time until the desired formation is achieved.