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

Reinforcement learning (RL) algorithms classically suffer from poor sample efficiency. In robotics, a recent line of work has emerged addressing this problem by encoding physics priors in the learning process. However, most of these approaches are validated on well-defined, low-dimensional benchmark systems rather than high-dimensional robots with complex nonlinear dynamics. In this paper, we introduce \textit{SKooP (Symmetric Koopman Predictions)}, an approach combining the advantages of morphological symmetries with those of a Koopman model learned via autoencoder to enhance policy learning. SKooP learns a Koopman model of the system dynamics alongside the policy. The resulting Koopman predictions are used as privileged observations for the critic, allowing the agent to learn based on smoother, more informative features. We also incorporate group symmetries into the actor, critic, encoder and decoder networks to produce a highly equivariant policy. The SKooP approach is validated via in-depth analysis of the learned Koopman models and symmetric policies to showcase how each of these influences the agent's performance. We also show that the learned policies are transferable to different simulation environments. Our results show that SKooP consistently reduces convergence time and increases the learned reward for multiple challenging bipedal locomotion tasks on a quadruped robot. Project page: https://evelyd.github.io/SymmetricKoopmanPredictions

Mobile manipulation requires coordinated control of high-dimensional, bimanual robots. Imitation learning methods have been broadly used to solve these robotic tasks, yet typically ignore the bilateral morphological symmetry inherent in such systems. We argue that morphological symmetry is an underexplored but crucial inductive bias for learning in bimanual mobile manipulation: knowing how to solve a task in one configuration directly determines how to solve its mirrored counterpart. In this paper, we formalize this symmetry prior and show that it constrains optimal bimanual policies to be ambidextrous and equivariant under reflections across the robot's sagittal plane. We introduce a $\mathbb{C}_2$-equivariant flow matching policy that enforces reflective symmetry either via a regularized training loss or an equivariant velocity network. Across planar and 6-DoF mobile manipulation tasks, symmetry-informed policies consistently improve sample efficiency and achieve zero-shot generalization to mirrored configurations absent from the training distribution. We further validate this zero-shot generalization capability on a real-world manipulation task with a TIAGo++ robot. Together, our findings establish morphological symmetry as an effective, generalizable, and scalable inductive bias for ambidextrous generative policy learning.

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.