LatentMimic: Terrain-Adaptive Locomotion via Latent Space Imitation

Zhiquan Wang; Yunyu Liu; Dipam Patel; Ayush Kumar; Aniket Bera; Bedrich Benes

cs.ROApr 7, 2026

LatentMimic: Terrain-Adaptive Locomotion via Latent Space Imitation

Authors: Zhiquan Wang, Yunyu Liu, Dipam Patel, Ayush Kumar, Aniket Bera, Bedrich Benes

Organizations: Department of Computer Science, Purdue University, USA

Abstract

Developing natural and diverse locomotion controllers for quadruped robots that can adapt to complex terrains while preserving motion style remains a significant challenge. Existing imitation-based methods face a fundamental optimization trade-off: strict adherence to motion capture (mocap) references penalizes the geometric deviations required for terrain adaptability, whereas terrain-centric policies often compromise stylistic fidelity. We introduce LatentMimic, a novel locomotion learning framework that decouples stylistic fidelity from geometric constraints. By minimizing the marginal latent divergence between the policy's state-action distribution and a learned mocap prior, our approach provides a conditional relaxation of rigid pose-tracking objectives. This formulation preserves gait topology while permitting independent end-effector adaptations for irregular terrains. We further introduce a terrain adaptation module with a dynamic replay buffer to resolve the policy's distribution shifts across different terrains. We validate our method across four locomotion styles and four terrains, demonstrating that LatentMimic enables effective terrain-adaptive locomotion, achieving higher terrain traversal success rates than state-of-the-art motion-tracking methods while maintaining high stylistic fidelity.

Figures & tables

Fig. 1 : Left to right: Stair terrain, Noisy terrain, Wavy terrain.

Fig. 2 : Overview of LatentMimic: a) We first pretrain a motion encoder to encode the motion transitions into a latent space and a motion predictor to predict the future motion transitions based on a mocap dataset. These two networks together form our Latent Prior Module . b) We then perform imitation policy learning using a mimic reward that measures the KL-divergence between the simulated and target transition in the latent space to learn the desired motion style. c) We introduce an anchor reward and a terrain adaptation replay buffer to enhance terrain traverse while preserving the desired motion style. These components aid learning and enable effective adaptation across diverse terrains. Note: The latent prior module is trained in both b) and c).

Fig. 3 : A target motion predicted from flat terrain data may result in collisions when applied to stairs.

Fig. 4 : The input of our policy consists of proprioceptive observation, historical data, and encoded target motion $z_{\text{target}}$ .

Fig. 5 : The latent mimic reward: both the simulated and the predicted target motions are encoded into the latent space, and their KL-divergence is computed.

Fig. 6 : Terrain Adaptation Module: the current policy

\pi_{\theta}

and the style policy

\pi_{\theta_{\text{styles}}}

takes the same observation to output the action distribution. Transitions with top

10\%

rewards are stored to fine-tune the motion predictor.

Parameter	Randomization Range
Terrain Friction	$[0.5,1.25]$
Additional Base Mass	$[-1.0\ \text{kg},1.0\ \text{kg}]$
COM Displacement	$[-0.15\ \text{m},0.15\ \text{m}]$
Motor Strength Factor	$[0.9,1.1]$
$K_{P}$ Gain Factor	$[0.8,1.3]$
$K_{D}$ Gain Factor	$[0.5,1.3]$

TABLE I : Domain Randomization Parameters applied during the training process to ensure sim-to-real robustness.

Metric	Method	Pace	Pace Backwards	Trot	Trot Backwards
Base Position $(\text{m})\downarrow$	Our	$\mathbf{0.0338}$	$\mathbf{0.0734}$	$\mathbf{0.1437}$	$\mathbf{0.3445}$
	LIA	0.5838	0.3523	0.3519	0.6876
	AMP	0.4684	0.4547	1.4965	4.9182
Joint Angles $(\text{rad})\downarrow$	Our	0.1386	$\mathbf{0.1061}$	$\mathbf{0.1474}$	$\mathbf{0.1511}$
	LIA	0.2712	0.1624	0.3611	0.1786
	AMP	$\mathbf{0.0842}$	0.1772	0.1952	0.1702

TABLE II : Tracking errors of four different locomotion styles on flat terrain. The best performance is in bold. Errors are measured using mean squared errors (MSE). Joint angle and velocity errors are computed per joint.

Fig. 7 : The figure shows the t-SNE visualization of latent motion features of four different motion styles.

Fig. 8 : The left figure depicts a frame of pace in which the robot moves its legs laterally (left front and left hind together). The right figure shows a trotting frame in which the robot moves its legs diagonally (left front and right hind).

TABLE III : Robots’ success rate of traversing different terrains. Each row shows the maximum level the robot can reach with a specific success rate. Note: All methods achieve a 100% success rate on flat terrain.

Pace max level	our	w/o TA
Stairs	45	18
Noise	64	64
Waves	64	43

TABLE IV : Ablation Study: Our model can achieve the maximum level with and without the terrain adaptation module for locomotion style pace.

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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.

Abstract

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