Dynamic Multiagent Assignment Via Discrete Optimal Transport

We propose an optimal solution to a dynamic assignment problem to assign a group of moving agents to another group of moving targets. Our approach leverages connections to the theory of discrete optimal transport to convert the problem into a tractable linear program. We simultaneously solve for the optimal assignment and the control of the individual agents. As a result, we can account for dynamics and capabilities of a heterogeneous set of agents and targets. In contrast to existing assignment schemes, this approach considers cost metrics informed by the underlying agent dynamics and capabilities rather than just distance. We show that the minimizer of the dynamic assignment problem is equivalent to the minimizer of the associated Monge problem from optimal transport. We prove that the resulting approach only requires a single assignment computation over the operating lifetime, rather than periodic reassignment. Furthermore, we demonstrate cost benefits that increase as the network size increases, achieving almost 50% cost reduction compared with distance-based metrics. We demonstrate our approach through simulation on several multiagent and multitarget tracking problems.