Dexterous Skill Discovery via Topology-Aware Wasserstein Dependency

Dexterous manipulation remains a fundamental challenge in robotics, with current approaches depending on human supervision in the form of demonstrations or task specifications such as engineered rewards, goals, and curricula. While unsupervised reinforcement learning holds the promise of discovering dexterous skills autonomously, state-of-the-art methods have yet to be applied successfully to high-degree-of-freedom manipulators such as multi-fingered hands. We argue that this limitation stems from two key factors: existing methods lack effective inductive biases to prioritize object interaction over agent motion, and they fail to respect the non-Euclidean topology of object configuration space \(\mathrm{SE}(3)\). To address these limitations, we propose a novel Wasserstein dependency measure between skills and object motions, formulated in the Lie algebra \(\mathfrak{se}(3)\). Our approach, topology-aware skill discovery (TopSkill), enables the discovery of core manipulation skills—such as multi-axial object translation and rotation—without demonstrations or task specifications. Across a range of embodiments, including non-prehensile pushers, parallel-jaw grippers, and multi-fingered hands, our method learns dexterous behaviors where previous approaches struggle, marking a significant step toward autonomous robotic dexterity.