Connectivity-Aware Exploration of Robotic Grasp Spaces

Robotic grasping is typically formulated as the problem of identifying successful actions from a space of candidate grasp poses. However, the organization of successful actions within this space has received less attention. We study the multiscale structure of viable robotic grasps in SE(3) and investigate whether this structure can be exploited for more efficient exploration. Using a large-scale grasp dataset, we show that successful grasp sets exhibit heterogeneous and reproducible connectivity structure across objects. We then introduce a connectivity-aware sampling strategy that incrementally explores the currently observed grasp space by prioritizing potential bridges between components, structural frontiers, boundary extensions, and geometric novelty. In controlled reconstruction experiments, the method recovers the connectivity structure of successful grasp sets substantially more efficiently than random sampling and farthest-point sampling. We further evaluate whether connectivity acquired under hidden grasp viability can improve subsequent grasp discovery, and whether structural experience from previously explored objects can be retrieved and transferred to unseen objects. These results suggest that the spatial organization of viable actions provides information relevant to grasp-space exploration beyond the viability of individual candidate actions. More broadly, they motivate structure-aware exploration as a means of exploiting the geometry of viable action spaces in robotic manipulation.