CHORD: Closed-Loop Hierarchical Motion Planning for Multi-Robot Systems via Diffusion Transformers and Density-Informed DMPC

Abstract

Large-scale multi-robot trajectory planning faces significant challenges in computational efficiency, scalability, trajectory quality, and safety, especially in complex, obstacle-dense environments. To address this, we propose CHORD, a hierarchical generative framework for multi-robot motion planning. At the macroscopic level, to generate efficient global guidance, we formulate the multi-robot motion as time-varying Gaussian Mixture Model (GMM) density fields. We develop a tailored Diffusion Transformer that employs structured temporal attention to capture long-range dependencies, generating coherent macroscopic distribution trajectories. To jointly optimize transport efficiency, safety, and smoothness, a cost gradient guidance mechanism integrates Wasserstein distance, Conditional Value at Risk (CVaR), and Gaussian process priors into the diffusion sampling process. At the microscopic level, a probabilistic mapping strategy is employed to generate individual reference trajectories, facilitating flexible split-and-merge behaviors. Finally, a distributed model predictive controller is developed for real-time trajectory tracking and collision avoidance. To mitigate tracking errors caused by execution uncertainties, we introduce a closed-loop replanning mechanism via generative inpainting. This allows the planner to periodically regenerate the future trajectory anchored to the current actual state of the system. Extensive simulations demonstrate CHORD’s superior scalability, computational efficiency, trajectory quality, and safety, maintaining high-quality performance with up to 500 robots while achieving a reduction of nearly three orders of magnitude in computation time compared to state-of-the-art baselines. Real-world experiments further validate its effectiveness and practical applicability. Note to Practitioners—This work addresses the computational and safety challenges of large-scale multi-robot trajectory planning. Traditional methods often fail to deliver real-time performance or high-quality trajectories when coordinating hundreds of robots in cluttered environments. CHORD introduces a hierarchical generative framework that integrates macroscopic multi-robot guidance with microscopic control. Unlike open-loop approaches, it incorporates a reactive inpainting mechanism to ensure closed-loop execution against disturbances. This ensures scalable, efficient, and safe planning, significantly reducing computation time and trajectory length. The approach is well-suited for time-critical applications like disaster response, environmental monitoring, and industrial automation.