Higher-Order Morphology Priors for Quadruped Reinforcement Learning Under Actuator Degradation

An animal with a weakened limb does not necessarily switch its gait, instead it unloads the affected limb, re-coordinates the remaining limbs, and scales its response with injury severity. This graded adaptation allows locomotion to persist despite partial loss of limb strength, rather than requiring a discrete transition between healthy and failed. Inspired by this behavior, we propose SG-CPG, a central pattern generator (CPG) for quadruped locomotion under continuous actuator degradation. SG-CPG preserves a frozen healthy CPG policy and introduces two severity-driven gates: a residual gate that re-coordinates all four legs and an amplitude gate that progressively shortens the weakened leg's stride as degradation increases. We emulate progressive degradation through two mechanisms: lowering the joint torque ceiling (ceiling mechanism) and scaling its low-level controller gains (gain mechanism), representing distinct forms of actuator weakening. Our simulations on a Unitree Go2 show that SG-CPG maintains a trot gait with 100% survival across an omnidirectional command schedule under 95% joint strength loss while tracking commands within 8%. Under a lowered torque ceiling, removing either severity path, the residual's severity observation or the amplitude gate, raises clipping at the weakened joint from 4.4% to 13.6% and 26.3% of steps at an 80% loss. On a real Go2, SG-CPG survives 28 of 29 forward and turning trials with up to 93% calf torque degradation. These results show that severity-gated adaptation can extend a healthy locomotion policy to progressive actuator degradation without treating the fault as a discrete failure.

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.

Learning-based quadrupedal locomotion typically relies on complex reward formulations that entangle task specification, operational limits, gait preference, and terrain adaptation within a single optimization objective. We instead treat these functions through distinct mechanisms: rewards for task specification, constraints for operational limits, energy minimization for gait preference, and exteroceptive perception for adapting energy use to terrain difficulty. We show that these components jointly enable efficient, terrain-adaptive locomotion, and that removing each component exposes a distinct failure mode. Our formulation removes explicit gait priors (including air-time, contact-count, and foot-clearance targets) in favor of emergent behavior. Compared to a conventional complex-reward baseline, our formulation achieves comparable terrain traversal while reducing cost of transport by 56% and operational-limit violations by 96%. The resulting policies transfer zero-shot to a physical Unitree Go2 using LiDAR-based elevation mapping. Project website with videos: https://tinyurl.com/locomposition.