Distributed policies for equitable partitioning: Theory and applications

Abstract—The most widely applied resource allocation strat-egy is to balance, or equalize, the total workload assigned to each resource. In mobile multi-agent systems, this principle directly leads to equitable partitioning policies in which (i) the workspace is divided into subregions of equal measure, (ii) each agent is assigned to a unique subregion, and (iii) each agent is responsible for service requests originating within its own subregion. In this paper, we design distributed and adaptive policies that allow a team of agents to achieve a convex and equitable partition of a convex workspace. Our approach is related to the classic Lloyd algorithm, and exploits the unique features of Power Diagrams. We discuss possible applications to routing of vehicles in stochastic and dynamic environments, and to wireless networks. Simulation results are presented and discussed. I

Distributed and Adaptive Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment

In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival, location and on-site service are stochastic; the objective is to minimize the expected system time (wait plus service) of the demands. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized a-priori task assignment and are not robust against changes in the environment, e.g. changes in load conditions; therefore, they are of limited applicability in scenarios involving ad-hoc networks of autonomous vehicles operating in a time-varying environment. First, we present a new class of policies for the 1-DTRP problem that: (i) are provably optimal both in light- and heavy-load condition, and (ii) are adaptive, in particular, they are robust against changes in load conditions. Second, we show that partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules in its own region, are optimal in heavy-load conditions. Finally, by combining the new class of algorithms for the 1-DTRP with suitable partitioning policies, we design distributed algorithms for the m-DTRP problem that (i) are spatially distributed, scalable to large networks, and adaptive to network changes, (ii) are within a constant-factor of optimal in heavy-load conditions and stabilize the system in any load condition. Simulation results are presented and discussed.Comment: Paper to be submitted to IEEE Transactions on Automatic Contro