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This paper introduces BridgeFlow, a novel generative motion planning framework that achieves strict SE(2) equivariance without the computational overhead of specialized architectures. By employing a lightweight task-centric canonicalization module and a Brownian bridge informative prior, BridgeFlow significantly enhances inference speed and trajectory validity in robotic motion planning. Evaluations show that it outperforms state-of-the-art diffusion baselines, achieving up to a 15x speedup and a 2x higher valid trajectory rate while maintaining robust generalization across diverse environments.
Achieving a 15x speedup in motion planning without sacrificing equivariance could redefine real-time robotics applications.
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.
