Polynomial-Time Algorithms for Multi-Agent Minimal-Capacity Planning

TL;DR

This paper presents polynomial-time algorithms for assigning targets to multi-agent teams operating under resource constraints in stochastic environments, ensuring minimal resource capacity for infinite visitation tasks.

Contribution

It introduces a novel polynomial-time algorithm that reduces the minimal-capacity planning problem to a graph-theoretical problem, enabling scalable solutions for large multi-agent systems.

Findings

Algorithm solves target assignment with minimal resource capacity in polynomial time.

Applicable to large-scale scenarios with hundreds of agents and locations.

Demonstrated scalability in underwater vehicle monitoring tasks.

Abstract

We study the problem of minimizing the resource capacity of autonomous agents cooperating to achieve a shared task. More specifically, we consider high-level planning for a team of homogeneous agents that operate under resource constraints in stochastic environments and share a common goal: given a set of target locations, ensure that each location will be visited infinitely often by some agent almost surely. We formalize the dynamics of agents by consumption Markov decision processes. In a consumption Markov decision process, the agent has a resource of limited capacity. Each action of the agent may consume some amount of the resource. To avoid exhaustion, the agent can replenish its resource to full capacity in designated reload states. The resource capacity restricts the capabilities of the agent. The objective is to assign target locations to agents, and each agent is only responsible for visiting the assigned subset of target locations repeatedly. Moreover, the assignment must ensure that the agents can carry out their tasks with minimal resource capacity. We reduce the problem of finding target assignments for a team of agents with the lowest possible capacity to an equivalent graph-theoretical problem. We develop an algorithm that solves this graph problem in time that is \emph{polynomial} in the number of agents, target locations, and size of the consumption Markov decision process. We demonstrate the applicability and scalability of the algorithm in a scenario where hundreds of unmanned underwater vehicles monitor hundreds of locations in environments with stochastic ocean currents.