Koopman Operator Framework for Modeling and Control of Off-Road Vehicle on Deformable Terrain

2026-03-30

AI Summary

This work addresses the high computational cost of high-fidelity dynamics models for off-road vehicles on deformable terrain, which hinders their use in real-time control. The authors propose a hybrid modeling paradigm that integrates physical priors with data-driven learning: five-degree-of-freedom simulation data generated from Bekker-Wong theory is combined with real-vehicle measurements to train a Koopman operator via recursive subspace identification, thereby approximating the nonlinear terrain–vehicle system as a linear dynamical model. To enhance data efficiency and generalization, informative training segments are selected using Grassmannian distance. The resulting model demonstrates strong short-term prediction stability and robustness to minor terrain perturbations. When embedded within a constrained model predictive controller, it enables efficient tracking of highly dynamic trajectories while satisfying steering and torque constraints.

Abstract

This work presents a hybrid physics-informed and data-driven modeling framework for predictive control of autonomous off-road vehicles operating on deformable terrain. Traditional high-fidelity terramechanics models are often too computationally demanding to be directly used in control design. Modern Koopman operator methods can be used to represent the complex terramechanics and vehicle dynamics in a linear form. We develop a framework whereby a Koopman linear system can be constructed using data from simulations of a vehicle moving on deformable terrain. For vehicle simulations, the deformable-terrain terramechanics are modeled using Bekker-Wong theory, and the vehicle is represented as a simplified five-degree-of-freedom (5-DOF) system. The Koopman operators are identified from large simulation datasets for sandy loam and clay using a recursive subspace identification method, where Grassmannian distance is used to prioritize informative data segments during training. The advantage of this approach is that the Koopman operator learned from simulations can be updated with data from the physical system in a seamless manner, making this a hybrid physics-informed and data-driven approach. Prediction results demonstrate stable short-horizon accuracy and robustness under mild terrain-height variations. When embedded in a constrained MPC, the learned predictor enables stable closed-loop tracking of aggressive maneuvers while satisfying steering and torque limits.

Problem

• Koopman operator
• deformable terrain
• off-road vehicle
• predictive control
• terrmechanics

Innovation

• Koopman operator
• deformable terrain
• physics-informed learning
• subspace identification
• model predictive control