BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching
For robotic motion planning, BridgeFlow provides a practical solution that combines equivariance with real-time inference, overcoming a key trade-off in learning-based planners.
BridgeFlow introduces a fast and strictly SE(2)-equivariant motion planning framework using flow matching, achieving up to 15x inference speedup and 2x higher valid trajectory rate over state-of-the-art diffusion baselines, with robust generalization to unseen environments and spatial transformations.
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.