Spatial load balancing in non-convex environments using sampling-based motion planners

This paper proposes an algorithm to approximately solve a spatial-load balancing problem for agents, subject to differential constraints, deployed in non-convex environments. A probabilistic roadmap is used to approximate regions via connected sets of vertices, which describe agents' configurations and optimal paths joining them. At each iteration, agents' positions and assigned graph nodes are updated to minimize the cost function. Two graph-node partitions are considered. In the first one, ν̃, all graph vertices are allocated to one agent or another. The second one, ν̃^lower, is a lower approximation that only allocates some of the graph vertices to the agents and has the advantage of requiring less communication than required for ν̃. Algorithm convergence can be guaranteed for ν̃ to a neighborhood of the continuous-space counterpart, and to its solution as sampling dispersion tends to zero. The convergence of the algorithm using ν̃^lower and trade-offs between ν̃^lower and ν̃ are established in simulation for a Euclidean metric case and Dubins' vehicle dynamics.