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

2025-08-28

AI Summary

To address path overlap and deadlock issues arising in multi-robot collaborative navigation toward multiple targets in cluttered environments, this paper proposes a synergistic motion planning framework integrating Optimal Transport (OT) and Model Predictive Control (MPC). Methodologically, OT models spatial resource allocation; non-overlapping initial trajectories are generated via grid-based discretization and spatiotemporal coupling optimization. A receding-horizon MPC then enables real-time re-planning and dynamic scheduling under kinodynamic constraints. Contributions include: (1) the first OT-based conflict-free trajectory generation mechanism that provably avoids deadlock; (2) theoretical computational complexity of O(K³logK) in the worst case and O(K²logK) for well-conditioned instances; and (3) balanced optimality, real-time performance, and adaptability to dynamic environments. Experiments demonstrate significant improvements in system throughput and robustness in densely obstructed scenarios.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Motion and Path Planning
• Multiagent Systems: Multiagent Planning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 ${K imes K}$ cost structure that describes the cost of transitioning from one cell to another. Optimal transport then provides extit{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 $unicode{x1D4AA}(K^3log K)$ computations in the worst-case and $unicode{x1D4AA}(K^2log K)$ 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 extit{replans} and extit{model predictive control}.

Problem

• Multi-robot path planning with obstacle avoidance
• Preventing overlapping trajectories and deadlocks
• Integrating temporal dynamics through model predictive control

Innovation

• Optimal transport theory for non-overlapping robot trajectories
• Discretized space with cost structure for optimal transitions
• Model predictive control integrated with temporal replanning