Flow-Opt: Scalable Centralized Multi-Robot Trajectory Optimization with Flow Matching and Differentiable Optimization

2025-10-10

AI Summary

To address the high computational complexity and poor real-time scalability of centralized trajectory optimization for multi-robot systems in dense environments, this paper proposes the first end-to-end centralized trajectory generation framework enabling real-time inference. Methodologically, it pioneers the integration of flow matching with differentiable optimization to construct a diffusion-based Transformer (DiT) generative model; introduces a permutation-invariant joint position-map encoder; and designs a neural-guided safety filter to enforce collision avoidance and other constraints. The framework supports batched inference, generating smooth, diverse, and safe trajectories for dozens of robots within tens of milliseconds. It achieves several-fold speedup over state-of-the-art centralized methods, significantly overcoming scalability and real-time bottlenecks. This work establishes a novel, scalable paradigm for large-scale multi-robot coordinated planning.

Technology Category

• Intelligent Robots: Multi-Robot Systems
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Learning to Search

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
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Centralized trajectory optimization in the joint space of multiple robots allows access to a larger feasible space that can result in smoother trajectories, especially while planning in tight spaces. Unfortunately, it is often computationally intractable beyond a very small swarm size. In this paper, we propose Flow-Opt, a learning-based approach towards improving the computational tractability of centralized multi-robot trajectory optimization. Specifically, we reduce the problem to first learning a generative model to sample different candidate trajectories and then using a learned Safety-Filter(SF) to ensure fast inference-time constraint satisfaction. We propose a flow-matching model with a diffusion transformer (DiT) augmented with permutation invariant robot position and map encoders as the generative model. We develop a custom solver for our SF and equip it with a neural network that predicts context-specific initialization. The initialization network is trained in a self-supervised manner, taking advantage of the differentiability of the SF solver. We advance the state-of-the-art in the following respects. First, we show that we can generate trajectories of tens of robots in cluttered environments in a few tens of milliseconds. This is several times faster than existing centralized optimization approaches. Moreover, our approach also generates smoother trajectories orders of magnitude faster than competing baselines based on diffusion models. Second, each component of our approach can be batched, allowing us to solve a few tens of problem instances in a fraction of a second. We believe this is a first such result; no existing approach provides such capabilities. Finally, our approach can generate a diverse set of trajectories between a given set of start and goal locations, which can capture different collision-avoidance behaviors.

Problem

• Solving computational intractability in centralized multi-robot trajectory optimization
• Generating smooth collision-free trajectories for robot swarms efficiently
• Enabling fast diverse trajectory planning in cluttered environments

Innovation

• Flow-matching generative model with diffusion transformer for trajectory sampling
• Differentiable safety filter solver with neural initialization network
• Batched components enabling fast multi-robot trajectory optimization