Multi-agent path-planning in a moving medium via Wasserstein Hamiltonian Flow
Abstract
We present a finite dimensional variational model for multi-agent path-planning in which a group of agents traverses from initial positions to a target distribution in a moving medium. The model is derived using the agent-based formulation of the Wasserstein Hamiltonian flows that transport between probability distributions while optimizing a running cost. The objective is the mismatch between their final positions and the target distribution. The constraints are a system of Hamiltonian equations that provide the trajectories of the agents. The free variables on which the optimization is defined form a finite vector of the initial velocities for the agents. The model is solved numerically by the L-BFGS method in conjunction with a shooting strategy. Several simulation examples, including a time-dependent moving medium, are presented to illustrate the performance of the model.
Keywords
Cite
@article{arxiv.2602.17885,
title = {Multi-agent path-planning in a moving medium via Wasserstein Hamiltonian Flow},
author = {Christina Frederick and Haomin Zhou},
journal= {arXiv preprint arXiv:2602.17885},
year = {2026}
}