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

## TL;DR

This paper introduces a novel multi-robot path planning method combining optimal transport and model predictive control to generate non-overlapping, cost-efficient trajectories in complex environments.

## Contribution

It develops a new approach that integrates optimal transport with MPC for collision-free, optimal multi-robot navigation, addressing path overlaps and dynamic constraints.

## Key findings

- Provides a computational complexity analysis for the proposed method.
- Demonstrates the ability to generate non-overlapping paths efficiently.
- Shows how to incorporate robot dynamics and re-planning into the transport framework.

## 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}.