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arXiv · 2508.21205

Multi-robot Path Planning and Scheduling via Model Predictive Optimal Transport (MPC-OT)

Usman A. Khan·Mouhacine Benosman·Wenliang Liu·Federico Pecora·Joseph W. Durham
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Abstract

In this paper, we propose a novel methodology for path planning and scheduling for multi-robot navigation that is based on optimal transport theory and model predictive control. We consider a setup where $N$ robots are tasked to navigate to $M$ targets in a common space with obstacles. Mapping robots to targets first and then planning paths can result in overlapping paths that lead to deadlocks. We derive a strategy based on optimal transport that not only provides minimum cost paths from robots to targets but also guarantees non-overlapping trajectories. We achieve this by discretizing the space of interest into $K$ cells and by imposing a ${K\times K}$ cost structure that describes the cost of transitioning from one cell to another. Optimal transport then provides \textit{optimal and non-overlapping} cell transitions for the robots to reach the targets that can be readily deployed without any scheduling considerations. The proposed solution requires $\unicode{x1D4AA}(K^3\log K)$ computations in the worst-case and $\unicode{x1D4AA}(K^2\log K)$ for well-behaved problems. To further accommodate potentially overlapping trajectories (unavoidable in certain situations) as well as robot dynamics, we show that a temporal structure can be integrated into optimal transport with the help of \textit{replans} and \textit{model predictive control}.

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Usman A. Khan, Mouhacine Benosman, Wenliang Liu, Federico Pecora, Joseph W. Durham. 2025-08-28. Multi-robot Path Planning and Scheduling via Model Predictive Optimal Transport (MPC-OT). https://arxiv.org/abs/2508.21205

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