Distributed-Infrastructure Multi-Robot Routing using a Helmholtz-Hodge Decomposition

Abstract

Using graphs and simplicial complexes as models for an environment containing a large number of agents, we provide distributed algorithms based on the Helmholtz-Hodge decomposition that, given desired flow rates on edges or across faces, produce incompressible approximations to the specified flows. These flows are then "lifted" to produce hybrid controllers for the agents, and a related algorithm is described that computes continuous streamfunctions over the environment, also in a distributed way.