RecMorph: Topology-Guided Spatial Recurrence for Generalized Morphology Control

Generalized morphology control requires a single policy to transform information across limbs with different physical roles, coordinate whole-body motion, and remain efficient as body size grows. Existing communication mechanisms address these requirements only partially. We introduce RecMorph, a topology-guided spatial recurrent architecture that uses recurrent sequence computation to jointly perform cross-limb communication and representation transformation. A depth-first traversal converts the kinematic tree into a morphology-derived sequence, along which shared bidirectional transitions progressively transform limb information before action decoding. Residual preservation, RMS normalization, and input-dependent channel modulation stabilize this repeated spatial transformation, yielding linear token complexity at fixed model width and depth. Across five UNIMAL tasks, RecMorph achieves the strongest mean final training performance among the evaluated generalized morphology controllers and the highest measured inference throughput on FT, while generalizing to unseen variations and bodies with up to 30 limbs. We further migrate representative generalized controllers from UNIMAL benchmarks to a four-platform quadruped setting. RecMorph achieves the best macro-averaged performance under nominal and high friction, reduces nominal velocity RMSE by 43.5% relative to specialist MLPs, and one shared policy completes 40 physical Go1/Go2 trials without falls. These results show that topology-guided recurrent transformation provides an effective and efficient communication mechanism for Generalized Morphology Control and remains effective when transferred from procedural bodies to physical robot platforms. Code and experimental resources are publicly available at https://github.com/quanruirao/RecMorph.