Multi-agent path-planning in a moving medium via Wasserstein Hamiltonian Flow

TL;DR

This paper introduces a finite-dimensional variational model for multi-agent path planning in moving media, utilizing Wasserstein Hamiltonian flows to optimize agent trajectories towards a target distribution.

Contribution

It develops a novel agent-based formulation using Wasserstein Hamiltonian flows and demonstrates numerical solutions with L-BFGS and shooting methods.

Findings

Effective in dynamic moving media scenarios

Numerical solutions successfully optimize agent paths

Model adaptable to time-dependent environments

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.