Actions Need Not Align: Predictive Consequence-Aware Transfer across Embodiments

Learning from heterogeneous robot experience promises more data-efficient and reusable manipulation policies, yet incompatible native action spaces make cross-embodiment sharing difficult. Existing approaches often address this heterogeneity by making actions comparable through shared or explicitly aligned action representations. We instead explore whether transfer can be organized around the predictive consequences of native actions without explicitly aligning their control representations. We formulate cross-embodiment learning as an abstraction-dynamics-grounding problem and introduce Predictive Dynamics with Embodiment Grounding (PDEG). PDEG preserves each robot's native action space: embodiment-specific motion adapters expose heterogeneous trajectories to shared temporal abstraction and predictive modeling, while embodiment-conditioned queries retrieve control-relevant information from the shared predictive representation and ground it back into native controls. By sharing predictive computation rather than an explicitly aligned low-level action code, PDEG requires neither predefined joint correspondence, paired cross-embodiment demonstrations, cross-robot retargeting, nor a hand-designed common geometric action space. Experiments across three embodiments and three real-world manipulation tasks show positive cross-embodiment transfer under fixed target-robot data budgets.