  This paper introduces a novel approach to improve robotic grasping in dynamic
environments by integrating Gaussian Process Distance Fields (GPDF), SE(3)
equivariant networks, and Riemannian Mixture Models. The aim is to enable
robots to grasp moving objects effectively. Our approach comprises three main
components: object shape reconstruction, grasp sampling, and implicit grasp
pose selection. GPDF accurately models the shape of objects, which is essential
for precise grasp planning. SE(3) equivariance ensures that the sampled grasp
poses are equivariant to the object's pose changes, enhancing robustness in
dynamic scenarios. Riemannian Gaussian Mixture Models are employed to assess
reachability, providing a feasible and adaptable grasping strategies. Feasible
grasp poses are targeted by novel task or joint space reactive controllers
formulated using Gaussian Mixture Models and Gaussian Processes. This method
resolves the challenge of discrete grasp pose selection, enabling smoother
grasping execution. Experimental validation confirms the effectiveness of our
approach in generating feasible grasp poses and achieving successful grasps in
dynamic environments. By integrating these advanced techniques, we present a
promising solution for enhancing robotic grasping capabilities in real-world
scenarios.
