BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching
arXiv:2607.14725
BridgeFlow is a generative motion planning method that achieves exact SE(2) equivariance through a lightweight canonicalization step and uses a Brownian bridge prior with optimal transport to speed up inference, enabling fast and robust planning for robots in unseen environments.
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.
Accepted to the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2026). 8 pages, 7 figures