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

Kartik Loya, Phanindra Tallapragada

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.

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

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.

Paper Structure

This paper contains 18 sections, 41 equations, 14 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Dynamic Modeling of the Vehicle–Terrain System
  3. Single-track (bicycle) dynamics model
  4. Half-car suspension model
  5. Wheel-Terrain Interaction Modeling
  6. Koopman Operator Identification Framework
  7. Koopman Theory and Finite Linear Embeddings
  8. Brief Review on Subspace Identification Methods
  9. Simulation and Results
  10. Vehicle simulation dataset and training
  11. Model Prediction Performance
  12. Model Generalization Under Terrain Elevation Perturbations and Maneuver Diversity
  13. Koopman-Based Model Predictive Control
  14. Prediction model
  15. MPC optimization problem
  16. ...and 3 more sections

Figures (14)

  • Figure 1: Longitudinal dynamics using single-track (bicycle) dynamic model
  • Figure 2: Vertical dynamics using half-car suspension model
  • Figure 3: Wheel-terrain interaction model
  • Figure 4: Sandy loam soil results for Koopman model selection and prediction: (a) RMSE versus refresh time, (b) open-loop RMSE growth with time, (c) normalized RMSE versus model order $r$ (dotted line: mean across outputs), and (d) eigenvalue spectrum of the identified Koopman $A$ matrix (unit circle shown for reference).
  • Figure 5: Sample trajectory prediction on sandy loam soil.
  • ...and 9 more figures