CMR: Contractive Mapping Embeddings for Robust Humanoid Locomotion on Unstructured Terrains

2026-02-03

AI Summary

This work addresses the insufficient robustness of humanoid robots operating in unstructured terrains, where perception noise and model mismatch often degrade performance. To this end, the authors propose the Contractive Mapping Representation (CMR) framework, which integrates contrastive representation learning with Lipschitz regularization to embed high-dimensional observations into a latent space that exhibits perturbation-attenuating properties. By explicitly constraining perceptual sensitivity while preserving task-relevant geometric structures, CMR can be seamlessly incorporated as an auxiliary loss into deep reinforcement learning pipelines. Experimental results across multiple high-noise humanoid locomotion tasks demonstrate that CMR significantly outperforms existing approaches, achieving superior stability and disturbance rejection capabilities.

Technology Category

• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Computer Vision: Representation Learning for Vision
• Machine Learning: Representation Learning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Robust disturbance rejection remains a longstanding challenge in humanoid locomotion, particularly on unstructured terrains where sensing is unreliable and model mismatch is pronounced. While perception information, such as height map, enhances terrain awareness, sensor noise and sim-to-real gaps can destabilize policies in practice. In this work, we provide theoretical analysis that bounds the return gap under observation noise, when the induced latent dynamics are contractive. Furthermore, we present Contractive Mapping for Robustness (CMR) framework that maps high-dimensional, disturbance-prone observations into a latent space, where local perturbations are attenuated over time. Specifically, this approach couples contrastive representation learning with Lipschitz regularization to preserve task-relevant geometry while explicitly controlling sensitivity. Notably, the formulation can be incorporated into modern deep reinforcement learning pipelines as an auxiliary loss term with minimal additional technical effort required. Further, our extensive humanoid experiments show that CMR potently outperforms other locomotion algorithms under increased noise.

Problem

• humanoid locomotion
• unstructured terrains
• disturbance rejection
• sensor noise
• model mismatch

Innovation

• contractive mapping
• robust locomotion
• contrastive representation learning
• Lipschitz regularization
• observation noise