Quadruped locomotion provides a natural setting for understanding when model-free learning can outperform model-based control design, by exploiting data patterns to bypass the difficulty of optimizing over discrete contacts and the combinatorial explosion of mode changes. We give a principled analysis of why imitation learning with quadrupeds can be inherently effective in a small data regime, based on the structure of its limit cycles, Poincaré return maps, and local numerical properties of neural networks. The understanding motivates a new imitation learning method that regulates the alignment between variations in a latent space and those over the output actions. Hardware experiments confirm that a few seconds of demonstration is sufficient to train various locomotion policies from scratch entirely offline with reasonable robustness.
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Fig. 1: Overview of our approach. We consider the offline imitation learning that collects a small batch of expert demonstration data, and then train deep neural network policies only from the batch without finetuning in simulation or on hardware. We propose new imitation methods with Latent Variation Regularization (LVR) that enforces the matching of the local structure between the control problem and the neural networks. The trained policies are directly tested on hardware platforms with varying ground conditions.
Fig. 2: Illustration of the first-order variation requirement in neural policies. Around expert trajectories of stable walking, the local stabilizing control laws are linear at both continuous (analyzed through trajectory stabilization) and discrete jump states (analyzed through Poincaré sections). This structure matches with the local smooth pieces in deep neural networks that are approximately independent because of sparsity in the large parameter space. Thus the local feedback requirements can be readily enforced through imitation learning that regularize local variations in the latent space.
Fig. 3: Real-world deployment of quadruped policies trained with minimal expert data. The upper left shows expert demonstration. Using the same data, behavior cloning (bottom left) fails to walk, whereas our Latent Variation Regularization (LVR, right column) produces stable forward and sideways walking. LVR further shows robust performance, such as walking backwards on grass by training on data from walking backwards on flat indoor ground.
Fig. 4: Left: training pointwise imitation loss, where both BC and LVR rapidly converge to similar values. Right: control performance on forward and sideways walking with varying dataset sizes. LVR achieves expert-level performance with ≤ 1 trajectory, whereas BC requires substantially more demonstrations to approach similar returns. Purple line denotes the expert policy performance.
Fig. 5: PCA visualization of latent states ht , where projection axes are obtained from PCA on consecutive differences δht=ht+1−ht . Points are connected in temporal order and colored by cosine similarity of δht with the first principal component (PC1). Left: expert forward-walking trajectory showing structured trot dynamics with two alternating gait modes. Right: an OOD rollout where BC (top) collapses while LVR (bottom) preserves coherent orientation bundles and separates ill-conditioned late states. See details in Section VI-B .
Fig. 6: t-SNE visualization (perplexity 15) of the expert training trajectory in state space (left) and the corresponding latent feature spaces learned by BC (top) and LVR (bottom). Points are colored by timestep index in the original trajectory. For the feature-space plots, the left column shows embeddings near initialization, while the right column shows embeddings at convergence. BC embeddings remain fragmented throughout training, whereas LVR progressively organizes local neighborhoods into a coherent loop structure that mirrors the periodic gait cycle observed in the state space.
Fig. 7: Robustness evaluation of forward walking under increasing terrain roughness. Both BC and LVR are trained on the same demonstrations collected on flat ground and then evaluated on terrains with varying roughness scales. The purple line indicates expert performance on flat terrain, and the black line marks the walkability threshold below which locomotion fails. Rendered images show representative behaviors of the expert (I), LVR (II), and BC (III) policies. LVR sustains high performance across a wider range of roughness levels, whereas BC rapidly deteriorates once the environment deviates from the training condition.
Closed-loop learned locomotion is established on commercial quadrupeds but remains uncommon at the sub-kilogram scale. Continuous-rotation legs give MiNI-Q, a 270 g quadruped, access to supporting configurations on either side of the body. We exploit this range with a single posture-conditioned reinforcement-learning policy that runs entirely onboard. A continuous joint-space reference on the torus T8 and its gravity-conditioned transformation connect upright walking, inverted walking, and landing recovery without state machines or phase switching. Coordinated posture and release curricula train this behavior family; identified actuation, cross-engine validation, and embedded execution support hardware transfer. The same sub-100k-parameter network tracks forward velocity with RMSE of 0.037 m/s upright and 0.050 m/s inverted, resumes walking in 24 of 30 release trials, and operates with four interchangeable foot geometries across four indoor surfaces. Hardware experiments and simulation ablations connect these capabilities to the representation, conditioning, and training choices that exploit the platform's motion range. Demonstration videos and supplementary material are available on the project website: https://submissionreview.github.io/around-the-world/.
Arturo Flores Alvarez, Nathan Lintu, Dennis Hong
Robotics and Mechanisms Laboratory (RoMeLa), University of California, Los Angeles (UCLA)
We present MimicAgent, a prompt-to-trajectory generation framework for learning dynamic quadruped skills. Although reward shaping is extensively used when training quadruped policies, navigating the resulting reward landscape is notoriously difficult, requiring hours of "graduate student descent". Eureka attempts to automate reward design with LLMs, but we find that it struggles to generalize across diverse skills and morphologies. Our key observation is that it is far easier for a human - and by association, an LLM - to generate reference motions than to shape reward functions. Our hypothesis is motivated by the success of example-guided RL for humanoids, which exploits large-scale motion capture datasets as references for training locomotion policies. Unlike humanoids, quadrupeds lack such reference motion data. Towards this end, we propose MimicAgent, an agentic harness that, given a skill prompt, generates quadruped reference trajectories with coding agents. These coarse reference trajectories are then used to train example-guided RL policies that are deployable in simulation and in the real-world. Notably, we find that when prompting Claude Fable 5.1 within our agentic harness, 87% of prompts yield semantically aligned reference trajectories.
Lucky Kant Nayak, Narayanan Palghat Parameswaran, Neehar Peri +1
Animal demonstrations provide quadruped robots with natural and distinctive gait styles that are difficult to specify through hand-crafted rewards. However, their narrow directional coverage leaves little style-consistent supervision for backward, lateral, and turning commands. We present OmniMimic, a training framework that turns directionally limited animal demonstrations into a single multi-gait policy over target per-axis velocity ranges. OmniMimic first combines temporal reversal, constrained dynamics completion, and sagittal reflection to construct robot-specific kinematic and physical supervision beyond the observed directions. It then expands commands progressively from the demonstrated velocity distribution toward the target per-axis bounds, and uses a shared actor with soft-gated, gait-specialized residual experts to balance reusable locomotion skills with gait-specific corrections. Across four gaits in simulation, OmniMimic reduces mean foot-position RMSE at forward and backward reference velocities by 12.9% and velocity-tracking RMSE on a uniform Cartesian command grid by 63.1%, compared with the matched APEX baseline. The project page is at https://OmniMimic.github.io.
Sheng Wu, Guoqiang Zhao, Zhe Yang +7
School of Artificial Intelligence and Robotics, Hunan University, China · China Mobile Group Hunan Company Ltd., China · National Engineering Research Center of Robot Visual Perception and Control Technology, Hunan University, China