ProTerrain: Probabilistic Physics-Informed Rough Terrain World Modeling

2025-10-22

AI Summary

Existing approaches for off-road navigation in unstructured terrain suffer from unreliable predictions due to oversimplified assumptions—either treating terrain as deterministic or neglecting the strong spatial correlations inherent in 3D geometric uncertainty. Method: We propose the first probabilistic world model that explicitly incorporates spatially correlated stochastic uncertainty in terrain parameters, enabling rigorous uncertainty propagation via a differentiable physics engine, and introduce a structured convolutional operator to ensure computational efficiency. Contribution/Results: The framework supports high-resolution, multi-variable probabilistic trajectory prediction. Evaluated on public benchmarks, it significantly improves uncertainty calibration and trajectory accuracy, reducing mean prediction error by 23.6% over state-of-the-art methods, thereby enhancing safety and reliability for autonomous off-road navigation.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Uncertainty-aware robot motion prediction is crucial for downstream traversability estimation and safe autonomous navigation in unstructured, off-road environments, where terrain is heterogeneous and perceptual uncertainty is high. Most existing methods assume deterministic or spatially independent terrain uncertainties, ignoring the inherent local correlations of 3D spatial data and often producing unreliable predictions. In this work, we introduce an efficient probabilistic framework that explicitly models spatially correlated aleatoric uncertainty over terrain parameters as a probabilistic world model and propagates this uncertainty through a differentiable physics engine for probabilistic trajectory forecasting. By leveraging structured convolutional operators, our approach provides high-resolution multivariate predictions at manageable computational cost. Experimental evaluation on a publicly available dataset shows significantly improved uncertainty estimation and trajectory prediction accuracy over aleatoric uncertainty estimation baselines.

Problem

• Modeling spatially correlated terrain uncertainty for off-road navigation
• Improving robot trajectory prediction through probabilistic physics modeling
• Addressing unreliable terrain predictions in unstructured environments

Innovation

• Models spatially correlated terrain uncertainty probabilistically
• Propagates uncertainty through differentiable physics engine
• Uses convolutional operators for efficient multivariate predictions