In this paper, we present a novel approach towards feasible dynamic grasping by leveraging Gaussian Process Distance Fields (GPDF), SE(3) equivariance, and Riemannian Mixture Models. We seek to improve the grasping capabilities of robots in dynamic tasks where objects may be moving. The proposed method combines object shape reconstruction, grasp sampling, and grasp pose selection to enable effective grasping in such scenarios. By utilizing GPDF, the approach accurately models the shape and physical properties of objects, allowing for precise grasp planning. SE(3) equivariance ensures that the sampled grasp poses are equivariant to the object's pose. Additionally, Riemannian Gaussian Mixture Models are employed to test reachability, providing a feasible and adaptable grasping strategy. The sampled feasible grasp poses are used as targets for novel task or joint space reactive controllers formulated by Gaussian Mixture Models and Gaussian Processes, respectively. Experimental results demonstrate the effectiveness of the proposed approach in generating feasible grasp poses and successful grasping in dynamic environments. (Video: https://www.youtube.com/watch?v=wjIVrwTzTOc&t=70s)

翻译：本文提出了一种新颖的动态抓取可行方法，通过结合高斯过程距离场（GPDF）、SE(3)等变性与黎曼混合模型，旨在提升机器人在物体可能移动的动态任务中的抓取能力。所提方法融合了物体形状重建、抓取采样与抓取姿态选择，以实现在此类场景下的高效抓取。通过利用GPDF，该方法精确建模物体的形状与物理属性，从而实现精准的抓取规划。SE(3)等变性确保采样得到的抓取姿态相对于物体姿态具有等变性。此外，采用黎曼高斯混合模型评估可达性，从而提供一种可行且自适应的抓取策略。采样得到的可行抓取姿态被用作目标，分别输入到由高斯混合模型和高斯过程构建的新型任务空间或关节空间反应控制器中。实验结果表明，所提方法能够生成可行的抓取姿态，并在动态环境中实现成功抓取。（视频链接：https://www.youtube.com/watch?v=wjIVrwTzTOc&t=70s）