BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching

2026-07-16

AI Summary

Existing learning-based motion planning methods struggle to simultaneously achieve SE(2) equivariance and real-time inference efficiency, often hindered by reliance on complex equivariant architectures or the absence of built-in symmetry. This work proposes BridgeFlow, a novel framework that uniquely integrates a lightweight task-centric normalization scheme with flow matching to rigorously enforce SE(2) equivariance within standard neural network architectures. By leveraging a Brownian bridge prior and context-aware minibatch optimal transport, BridgeFlow constructs an efficient flow field, further enhanced with classifier-free guidance to improve adaptability to diverse environments. Experiments in 2D cluttered scenes and on a 7-DoF Franka robotic arm demonstrate that, compared to state-of-the-art diffusion baselines, the proposed method achieves up to 15× faster inference, doubles the rate of valid trajectories, and exhibits strong generalization to unseen environments and arbitrary spatial transformations.

Abstract

In robotic motion planning, equivariance to rigid body transformations is crucial for robust spatial generalization. However, current learning-based planners face a critical dilemma: they either lack inherent equivariance, treating transformed tasks as novel scenarios, or enforce it via computationally expensive specialized architectures that bottleneck real-time inference. To break this trade-off, we propose BridgeFlow, a fast and strictly SE(2)-equivariant generative motion planning framework. Rather than relying on heavy equivariant networks, BridgeFlow achieves exact spatial equivariance via a lightweight task-centric canonicalization module, enabling generalization using standard architectures. To further accelerate inference, we pair a Brownian bridge informative prior with context-aware mini-batch optimal transport. This constructs a straightened vector field that minimizes transport costs and stabilizes training. Furthermore, environmental awareness is explicitly embedded via Classifier-Free Guidance. Evaluations in dense 2D environments and on a 7-DoF Franka manipulator demonstrate that BridgeFlow achieves up to a 15x inference speedup and a 2x higher valid trajectory rate over state-of-the-art diffusion baselines, alongside robust generalization to entirely unseen environments and arbitrary spatial transformations.

Problem

• motion planning
• SE(2)-equivariance
• spatial generalization
• real-time inference
• learning-based planning

Innovation

• SE(2)-equivariance
• flow matching
• canonicalization
• Brownian bridge
• Classifier-Free Guidance