System Identification for Dynamic Modeling of Large Steering Angle Vehicles

Technical Summary: System Identification for Dynamic Modeling of Large Steering Angle Vehicles

Problem Statement
The paper addresses the challenge of modeling autonomous vehicles with exceptionally high maneuverability, specifically bumper cars capable of steering angles up to approximately 115°. Standard vehicle models, such as the linearized Newton-Euler or kinematic bicycle models, rely on small-angle assumptions and neglect significant tire slip. These assumptions fail in the bumper car domain, where large steering angles induce pronounced nonlinear dynamic effects and transitions between forward and backward motion. Consequently, existing models either lack the accuracy required for planning-based collision avoidance (e.g., Model Predictive Control) or suffer from prohibitive computational stiffness that prevents real-time deployment. The authors aim to develop a system identification framework that balances modeling fidelity, computational efficiency, and physical interpretability for this specific experimental domain.

Methodology
The authors propose a comparative study of three modeling paradigms: purely physical (white-box), purely data-driven (black-box), and hybrid (grey-box) approaches.

1. Physics-Based Models (White-Box):

   • Newton-Euler Model: A dynamic bicycle model was tailored to the bumper car's geometry and actuation. It incorporates a piecewise linear tire force model to balance simplicity and accuracy, avoiding complex parameterizations like the Magic Formula which are difficult to identify from limited high-slip data. The model accounts for longitudinal drag and motor forces.
   • Kinematic Model: An extended kinematic formulation was derived where the system state includes the front-wheel velocity (directly actuated) rather than just the Center of Gravity velocity. This formulation explicitly incorporates tire slip, moving beyond the slip-free assumption of standard kinematic models.

2. Data-Driven System Identification:

   • Black-Box Models: Two Multilayer Perceptron (MLP) architectures were trained to minimize Normalized Mean Squared Error (NMSE). A Nonlinear AutoRegressive model with eXogenous inputs (NARX-MLP) modeled velocity evolution directly, while a Kinematic-MLP (K-MLP) modeled the state transition of the extended kinematic variables.
   • Grey-Box Models:
     • SINDy (Sparse Identification of Nonlinear Dynamics): The kinematic state transition was approximated using a sparse linear combination of candidate functions derived from physical insights (e.g., motor throttle behavior, rolling resistance, and slip dynamics).
     • Hybrid K-SINDy-MLP: To overcome the accuracy limitations of the sparse SINDy library, a residual MLP was added to the SINDy model. This hybrid approach learns the correction terms (residuals) to the physics-based SINDy prediction, combining interpretability with the approximation power of neural networks.

Key Contributions

1. Tailored Physical Models: The authors adapted Newton-Euler and kinematic bicycle models to handle large steering ranges and low-speed dynamics, including specific discretization choices for stable multi-step prediction and a piecewise linear tire force model.
2. Progressive Identification Framework: The paper systematically explores the transition from black-box to grey-box representations. It demonstrates how embedding physical structure (via SINDy) into learned models improves interpretability and reduces the complexity required for the neural network component.
3. Hybrid Architecture: The proposal of the K-SINDy-MLP model, which integrates a physics-informed kinematic backbone with a data-driven residual network, offers a novel trade-off between accuracy, computational speed, and interpretability.

Experimental Results
Validation was performed using one hour of driving data collected in a 7×12 m arena using an OptiTrack motion-capture system. The models were evaluated based on prediction accuracy (NMSE) and computational runtime.

• Accuracy: The purely black-box K-MLP achieved the highest accuracy (NMSE $4.594 \times 10^{-3}$). The hybrid K-SINDy-MLP achieved comparable accuracy ($4.765 \times 10^{-3}$), significantly outperforming the purely physical Newton-Euler model ($5.973 \times 10^{-3}$) and the linearized version.
• Computational Efficiency: The SINDy-based models were the fastest. The K-SINDy-MLP required 81.1 ms per prediction step, which is substantially faster than the Newton-Euler model (303.7 ms) and comparable to the black-box MLPs.
• Performance in Extreme Regimes: In scenarios involving steering angles exceeding 90° (transitioning between forward and backward motion), the K-SINDy-MLP model substantially outperformed the Newton-Euler baseline, which failed to accurately predict the trajectory under these conditions.

Significance and Claims
The paper claims that the hybrid K-SINDy-MLP approach successfully addresses the trade-off between model accuracy and computational requirements. It demonstrates that physics-informed neural network models can surpass purely physical baselines in accuracy while maintaining lower computational costs, making them suitable for real-time applications like collision avoidance in high-maneuverability environments. The authors emphasize that embedding physical laws into the learning process not only improves accuracy but also enhances model interpretability and adaptability, which is crucial for systems influenced by variable factors such as cyclically changing passenger loads. The work suggests that for high-steering-angle vehicles, purely physical models are often too computationally stiff for real-time use, while purely data-driven models lack the necessary physical consistency; the hybrid approach offers a viable middle ground.