Dynamic multi-agent assignment via discrete optimal transport

TL;DR

This paper introduces a novel method for dynamic multi-agent assignment using discrete optimal transport, enabling efficient, cost-effective coordination of heterogeneous agents in changing environments.

Contribution

It reformulates the multi-agent assignment problem as a linear program based on optimal transport, reducing computational costs and improving assignment quality by considering dynamics.

Findings

Cost reduction of up to 50% compared to traditional methods.

Assignment computation can be performed once over the lifetime, saving resources.

Method demonstrated successfully on linear and linearized problems.

Abstract

We propose an optimal solution to a deterministic dynamic assignment problem by leveraging connections to the theory of discrete optimal transport to convert the combinatorial assignment problem into a tractable linear program. We seek to allow a multi-vehicle swarm to accomplish a dynamically changing task, for example tracking a multi-target swarm. Our approach simultaneously determines the optimal assignment and the control of the individual agents. As a result, the assignment policy accounts for the dynamics and capabilities of a heterogeneous set of agents and targets. In contrast to a majority of existing assignment schemes, this approach improves upon distance-based metrics for assignments by considering cost metrics that account for the underlying dynamics manifold. We provide a theoretical justification for the reformulation of this problem, and show that the minimizer of the dynamic assignment problem is equivalent to the minimizer of the associated Monge problem arising in optimal transport. We prove that by accounting for dynamics, we only require computing an assignment once over the operating lifetime --- significantly decreasing computational expense. Furthermore, we show that the cost benefits achieved by our approach increase as the swarm size increases, achieving almost 50\% cost reduction compared with distance-based metrics. We demonstrate our approach through simulation on several linear and linearized problems.