Short-Horizon Position Accuracy of Single-Track Models: Implications for Motion Planning of Autonomous Vehicles

Technical Summary: Short-Horizon Position Accuracy of Single-Track Models

Problem Statement
Accurate and computationally efficient vehicle models are critical for the motion planning of autonomous vehicles, particularly within Model Predictive Control (MPC) frameworks. In MPC, the vehicle model predicts future trajectories to compute control actions; therefore, model fidelity directly influences trajectory feasibility and safety. While high-fidelity models exist, they are often too computationally expensive for online use, leading many researchers to rely on single-track (bicycle) models. However, the positional accuracy of these models has not been systematically evaluated against real-world measurements across various driving maneuvers. Historically, vehicle dynamics research has focused on acceleration and yaw-rate responses rather than position accuracy, which is essential for tasks requiring tight tolerances, such as parking or low-speed maneuvering. This paper addresses the gap between the autonomous driving and vehicle dynamics communities by evaluating the short-horizon positional accuracy of different single-track model variants against real vehicle data to inform model selection for MPC.

Methodology
The study utilizes a 2011 Nissan Leaf ZE0 instrumented with an Oxford Technical Solutions (OxTS) RT3000 v3 GNSS-INS system and a CANedge2 data logger. The vehicle parameters, including mass, center of gravity (CG) location, and yaw inertia, were identified through physical measurements and standard methods. Cornering stiffnesses were identified via least-squares fitting of experimental data within the linear tire regime, while Magic Formula (MF) tire parameters were derived from flat plank tire test facility data.

Three single-track model variants were evaluated:

1. Kinematic Model: Neglects tire slip and assumes rotation about an instantaneous center.
2. Linear Dynamic Model: Includes lateral and yaw dynamics with linear tire behavior (constant cornering stiffness).
3. Nonlinear Dynamic Model: Includes lateral and yaw dynamics with nonlinear Magic Formula tires and quasi-static longitudinal load transfer.

The models were tested across seven driving scenarios (S1–S7), ranging from constant-speed figure-eights to steady-state cornering at lateral accelerations up to 6 m/s², U-turns, and roundabout navigation. For each scenario, the models were initialized with measured states at 100 ms intervals and simulated over a 5-second prediction horizon. The predicted trajectories were compared against ground truth measurements, decomposing the global error into longitudinal and lateral components relative to the vehicle's heading.

Key Results
The evaluation yielded the following findings regarding positional accuracy:

• Kinematic vs. Dynamic Models: The kinematic model performed substantially worse than both dynamic models, exhibiting errors approximately two to six times larger in most scenarios. This discrepancy is most pronounced in steady-state cornering at higher lateral accelerations (4 m/s² and 6 m/s²), where the kinematic model fails to capture speed-dependent understeer effects due to the neglect of tire slip.
• Linear vs. Nonlinear Dynamic Models: Contrary to the expectation that higher fidelity yields higher accuracy, the linear and nonlinear dynamic models demonstrated comparable accuracy across all tested scenarios. The relative differences were in the centimeter range, with absolute errors in the decimeter range.
• Reason for Similarity: The comparable performance is attributed to two factors: (1) tire slip angles in most scenarios remained within or near the linear region (front slip < ±3°, rear slip < ±2°), where the linear and nonlinear force responses align; and (2) longitudinal accelerations were limited, resulting in negligible load transfer effects.
• Parameter Identification Impact: In the high-acceleration scenario (S4, 6 m/s²), the nonlinear model unexpectedly produced larger errors than the linear model. This was attributed to the quality of parameter identification; the nonlinear model's parameters were scaled to match linear stiffness but deviated at high slip levels where friction limits dominate. This suggests that increasing model complexity without accurate parameter identification can degrade performance.

Significance and Contributions
The paper's primary contribution is providing empirical insight into the trade-offs between model complexity, parameterization quality, and positional accuracy for MPC applications. The authors conclude that for the tested operating conditions (passenger car, moderate speeds, and lateral accelerations), the linear dynamic model offers the best trade-off. It provides significantly better accuracy than the kinematic model while avoiding the increased parameterization effort and potential identification uncertainties of the nonlinear model, without sacrificing positional accuracy.

The study emphasizes that model selection should be driven by the expected operating conditions and the ability to accurately identify parameters, rather than a default assumption that higher-fidelity models are inherently superior. The authors note that future work is required to evaluate these models in closed-loop MPC applications and to extend the analysis to conditions involving combined slip, higher speeds, and autonomous trucks, where payload variability and longer prediction horizons may alter the optimal model choice.