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This paper introduces a novel approach to generative grasping in robotics using Lie Group-constrained MeanFlow, which significantly accelerates the sampling process. By leveraging a training objective that combines algebraic consistency with Riemannian Conditional Flow Matching on the product Lie group, the method achieves reliable grasp generation in under five network evaluations. The results show that this approach matches the performance of existing state-of-the-art models while achieving up to 39 times faster inference, making it suitable for real-time applications in robotic manipulation.
Achieving grasp synthesis in less than five evaluations while maintaining state-of-the-art performance could revolutionize real-time robotic manipulation.
Grasp synthesis is a core task in robotic manipulation, for which the solution typically forms a multimodal distribution rather than a point estimate. Generative robotic grasping aims to learn this distribution with deep generative models such as diffusion and flow-based approaches. The iterative nature of such generative models makes them flexible and generalizable; however, multi-step sampling impedes the time-critical operation required in robotics. We devise an approach to fast generative grasping based on MeanFlow on the product Lie group $\mathcal{G} = \mathrm{SO}(3) \times \mathbb{R}^3$. The training objective couples a purely algebraic semigroup consistency condition with Riemannian Conditional Flow Matching on $\mathcal{G}$ that anchors the average velocity to the data distribution. The resulting Lie Group-constrained MeanFlow formulation samples reliable grasps in $\leq 5$ network evaluations, matching the grasp generation performance of state-of-the-art diffusion and flow-based models on the ACRONYM dataset at millisecond-scale inference latency (up to $39\times$ speed-up). We further demonstrate that the approach directly translates to real-world robotic grasping without additional training or domain adaptation, exhibiting robust grasp synthesis under observation noise.
