Beyond Topology: A Morphological Symmetry Graph Representation for Locomotion Policy Learning

Reinforcement learning has enabled impressive locomotion skills on articulated robots, but common policy representations remain only weakly aligned with robot physics. Generic networks ignore kinematic structure, while graph-based policies encode connectivity without specifying how physical quantities transform across symmetric body parts. We introduce a morphological symmetry graph representation for locomotion policy learning and instantiate it in MS-PPO. Starting from the robot's topological graph, our representation augments each observation and action space with the permutation and sign transformations induced by morphological symmetry. This yields a symmetry-equivariant graph actor and a symmetry-invariant graph critic, enforcing the desired policy and value constraints by construction rather than through reward shaping or data augmentation. We evaluate MS-PPO on a variety of locomotion tasks using both Unitree Go2 quadruped and Unitree G1 humanoid, including command tracking, asymmetric joint failures, out-of-distribution command generalization, and zero-shot sim-to-real deployment. Experiments show improved symmetry generalization, robustness, sample efficiency, and model efficiency over topology- and symmetry-aware baselines.