Multi-fidelity Gaussian processes for terramechanical modeling

Abstract

Many natural phenomena and processes remain poorly understood and analytically intractable. One such example is the contact dynamics between non-Newtonian fluids—such as soft soils—and rigid bodies, like wheels. This issue becomes particularly critical in scenarios where the use of large wheels, tracks, or tires is constrained, such as during planetary rover missions. To better anticipate the terrain conditions a rover may encounter, researchers have developed a range of terramechanical models. These models vary in their levels of fidelity, computational cost, and applicability. Given the complexity and variability of wheel-soil interactions, this domain presents an ideal use case for machine learning-based surrogate modeling. Such surrogates aim to approximate the behavior of complex dynamical systems without requiring explicit formulation through differential equations. Existing studies in wheel-soil contact dynamics span both real-world experiments and a spectrum of simulation approaches—from fast empirical models to computationally intensive discrete element methods. In this context, a multi-fidelity modeling framework is particularly promising. By integrating information from diverse sources—ranging from low-fidelity, low-cost simulations to high-fidelity but expensive and sparse data—machine learning models can be trained to deliver fast yet accurate predictions. This work introduces a multi-fidelity Gaussian Process surrogate model designed to predict the dynamic interactions between wheels and soft soil, including the forces and torques acting on the wheel. Specifically, it focuses on the prediction of forces and torques acting on the wheel during motion. The work details the process of dataset generation, analysis, and surrogate model construction, incorporating existing physical knowledge and domain-specific intuition. Furthermore, it includes uncertainty quantification to assess model robustness. The proposed model is evaluated from both quantitative and qualitative perspectives—statistically, in terms of predictive accuracy, and mechanistically, as a viable terramechanical surrogate. This research aims to answer whether a multi-fidelity approach can indeed produce a surrogate that is both computationally efficient and sufficiently accurate, and how it compares to state-of-the-art terramechanical simulations in terms of performance and limitations.