Robot manipulation policies are typically tied to specific robotic hand embodiments, limiting the transfer of learned behaviors across platforms with different kinematic structures. In this work, we propose the Unified Hand Action Space (UHAS), a sphere-based unified action representation for cross-embodiment dexterous manipulation. UHAS represents robotic hand actions as geometric deformations of a canonical sphere and uses a Cascade Inverse Kinematics (CIK) algorithm to map the shared representation to embodiment-specific joint configurations. Using reinforcement learning, we train dexterous manipulation policies directly in the proposed action space for in-hand cube reorientation tasks. We evaluate our method in both simulation and real-world experiments across multiple robotic hands, including the Allegro Hand, LEAP Hand, Shadow Hand, and MANO Human Hand. Experimental results demonstrate effective dexterous manipulation, zero-shot transfer to unseen hands, rapid finetuning across embodiments, and successful real-world deployment. Our experiments show that the proposed UHAS representation enables stable dexterous control and cross-embodiment policy transfer across robotic hands.

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