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

arXiv: https://arxiv.org/abs/2508.21205 · HTML: https://mlsanity.com/paper/2508.21205/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Builds on (most cited first, 9 of 9)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Target Assignment and Path Finding for Teams of Agents](https://mlsanity.com/paper/1612.05693/) (2016)
- [Accelerating Motion Planning via Optimal Transport](https://mlsanity.com/paper/2309.15970/) (2023)
- [Multi-Agent Path Finding in Continuous Spaces with Projected Diffusion Models](https://mlsanity.com/paper/2412.17993/) (2024)
- [Improved Anonymous Multi-Agent Path Finding Algorithm](https://mlsanity.com/paper/2312.10572/) (2023)
- [DeepFleet: Multi-Agent Foundation Models for Mobile Robots](https://mlsanity.com/paper/2508.08574/) (2025)
- [Dynamic multi-agent assignment via discrete optimal transport](https://mlsanity.com/paper/1910.10748/) (2019)
- [Optimal mass transport and kernel density estimation for state-dependent networked dynamic systems](https://mlsanity.com/paper/1809.07496/) (2018)
- [Continuum Swarm Tracking Control: A Geometric Perspective in Wasserstein Space](https://mlsanity.com/paper/2303.15638/) (2023)

## Abstract (arXiv)

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× K cost structure that describes the cost of transitioning from one cell to another. Optimal transport then provides textitoptimal 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 unicodex1D4AA(K3log K) computations in the worst-case and unicodex1D4AA(K2log 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 textitreplans and textitmodel predictive control.