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

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

Derek You, Zafir Shamsi, Keqin Wang, Christine Allen-Blanchette · N/A · 2026

locomotion reinforcement-learning
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Summary

Actuator degradation turns quadruped locomotion into a coordination problem requiring joints to compensate for lost actuation. Prior work suggests that morphology-aware graph policies improve learning and generalization under body perturbations.

Abstract Summary

Actuator degradation turns quadruped locomotion into a coordination problem requiring joints to compensate for lost actuation. Prior work suggests that morphology-aware graph policies improve learning and generalization under body perturbations. We ask whether these benefits can be strengthened by explicitly modeling higher-order mechanical structure. We represent the Unitree Go1 as a cell complex with limb- and body-level rank-2 cells and apply Hodge-based message passing. Under degradation training, the node-edge-face Hodge actor achieves the highest return on unseen actuator degradations, with higher survival and lower velocity-tracking error. These results support higher-order morphology as a useful inductive bias for whole-body compensation under actuator degradation.

Key Points

  • Actuator degradation turns quadruped locomotion into a coordination problem requiring joints to compensate for lost actuation.
  • Prior work suggests that morphology-aware graph policies improve learning and generalization under body perturbations.
  • We ask whether these benefits can be strengthened by explicitly modeling higher-order mechanical structure.
  • We represent the Unitree Go1 as a cell complex with limb- and body-level rank-2 cells and apply Hodge-based message passing.
  • Under degradation training, the node-edge-face Hodge actor achieves the highest return on unseen actuator degradations, with higher survival and lower velocity-tracking error.

Preliminaries

The Unitree Go1 is a 12-DoF quadruped with four three-joint legs attached to a rigid trunk (see Fig. 1 ). Each leg comprises a hip abduction/adduction joint and hip and knee flexion/extension joints. Two properties motivate the higher-order representation in Sec. III-C .

First, each leg acts as a mechanical unit: foot placement depends jointly on all three joints, so lost actuation at one must be compensated for by the others.

Preliminaries — Higher-Order Morphology Priors for Quadruped Reinforcement Learning Under Actuator Degradation
Figure 1 : Go1 higher-order morphology. (a) The twelve actuated joints form the 0-cells; sixteen 1-cells give eight serial couplings, four around the hip ring, and four dashed virtual closures that let each leg bound a face. The five shaded 2-cells are one per limb plus the body cell spanned by the four coplanar hips. (b) The same cells at the true Go1 joint positions, with distant limbs faded. Only the node-edge-face actor propagates through rank-2 cells. The legend maps each mark to its rank: a ring is a 0-cell, a solid line a 1-cell, a dashed line a virtual 1-cell, and a filled patch a 2-cell.

Method

The Go1 cell-complex construction is shown in Fig. 1 . Each node (0-cell) corresponds to one of the twelve joints on the robot. Eight kinematic edges (1-cell) connect adjacent joints along the four legs. Four additional edges connect the hip joints around the body, while four hip-calf edges close the four limb cycles.

Method — Higher-Order Morphology Priors for Quadruped Reinforcement Learning Under Actuator Degradation
Figure 2 : Node-edge-face Hodge actor. Left: the policy observes trunk velocity, angular velocity, projected gravity, and joint-wise angle, velocity, and previous action. Centre: these signals and the velocity command form $o_{t}\in\mathbb{R}^{48}$ and are reshaped into joint-wise features $X_{t}\in\mathbb{R}^{12\times 20}$. Right: $X_{t}$ initializes node, edge, and face states $H_{0}\in\mathbb{R}^{12\times d}$, $H_{1}\in\mathbb{R}^{16\times d}$, and $H_{2}\in\mathbb{R}^{5\times d}$. Each Hodge block performs same-rank message passing through the corresponding Hodge operators and cross-rank communication through incidence matrices $B_{1}$ and $B_{2}$. After $L$ residual blocks, the rank-0 states are decoded by a shared actor head to parameterize the joint action $a_{t}\in\mathbb{R}^{12}$.

Experiments

All experiments use the Unitree Go1 problem setting described in Sec. III-B . All actor variants share the same critic, reward, domain randomization, optimization setup, and training budget. Each policy is trained for 400M environment steps with seeds $\{11,12,13\}$. We compare five parameter-matched actor architectures: MLP-C : centralized MLP mapping the global 48-D observation directly to all joint outputs.

MLP-D : factorized per-joint MLP with shared weights and no inter-joint message passing.

Experiments — Higher-Order Morphology Priors for Quadruped Reinforcement Learning Under Actuator Degradation
Figure 3 : In-regime learning curves. Evaluation episode returns under the healthy (left) and degraded (right) regimes. In the healthy regime, MLP-C performs best, with Hodge-F and Hodge-L slightly behind. Under degradation, Hodge-F achieves the strongest performance.

Sources and Demonstrations

Figures are reproduced from You et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.

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