Training Cross-Morphology Embodied AI Agents: From Practical Challenges to Theoretical Foundations

While theory and practice are often seen as separate domains, this article shows that theoretical insight is essential for overcoming real-world engineering barriers. We begin with a practical challenge: training a cross-morphology embodied AI policy that generalizes across diverse robot morphologies. We formalize this as the Heterogeneous Embodied Agent Training (HEAT) problem and prove it reduces to a structured Partially Observable Markov Decision Process (POMDP) that is PSPACE-complete. This result explains why current reinforcement learning pipelines break down under morphological diversity, due to sequential training constraints, memory-policy coupling, and data incompatibility. We further explore Collective Adaptation, a distributed learning alternative inspired by biological systems. Though NEXP-complete in theory, it offers meaningful scalability and deployment benefits in practice. This work illustrates how computational theory can illuminate system design trade-offs and guide the development of more robust, scalable embodied AI. For practitioners and researchers to explore this problem, the implementation code of this work has been made publicly available at https://github.com/airs-admin/HEAT