⚡ electrical engineering

Excitation-Aware On-Track System Identification at Full Scale

This paper identifies and resolves three critical defects in a full-scale on-track system identification pipeline—specifically a loss of excitation, non-identifiable peak factors, and a non-contractive feedback loop—to successfully recover accurate tire parameters and maintain stable vehicle control on surfaces with significantly reduced grip.

Original authors: Ebrahim Abdelghfar, Mohamed Elshalakani, Mohamed Abdelaziz, Sherif Said

Published 2026-10-08

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Ebrahim Abdelghfar, Mohamed Elshalakani, Mohamed Abdelaziz, Sherif Said

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Autonomous racing cars are not just fast; they are constantly guessing. To drive at the limit, a computer must know exactly how much grip its tires have on the road at any given moment. This grip changes with speed, temperature, and the condition of the asphalt, making it the most critical and elusive piece of information for the vehicle's brain. Traditionally, engineers would stop a race car, drive it in slow circles on a test track, and measure the tires to build a mathematical model. But in a real race, there is no time for a test track. The car must learn the tires while it is racing, using the data from a normal lap to figure out how the rubber is behaving. This process is called on-track system identification. It is a high-stakes game of inference: the car must deduce the invisible properties of its tires from the visible movements of its chassis, all while moving at high speed.

A recent study by researchers at Ain Shams University and the American University of the Middle East investigated a specific method for teaching a full-sized race car to learn its own tires while driving. They took a system that had worked well on a tiny, one-tenth scale model car and tried to transplant it directly onto a full-scale Formula Student vehicle. The expectation was that the method would scale up smoothly. Instead, the researchers discovered that the system was failing in a subtle but dangerous way. When moved to the full-size car, the identification pipeline was producing a model that looked correct on paper but was physically impossible, leading the car to believe it had far more grip than it actually possessed. The study, conducted entirely within a high-fidelity computer simulation, revealed that the failure was not due to bad math or noisy sensors, but to a fundamental flaw in how the system generated its own test data.

The core of the problem lay in a step where the system created a "virtual" test drive to analyze the tires. In the original small-scale setup, this virtual drive was sufficient to reveal the tire's limits. However, on the full-size car, the speed and steering angles used in this virtual simulation were too low to ever push the tires to their breaking point. Because the virtual test never asked the tires to work hard, the system could not see where the grip ended. It was like trying to guess the weight limit of a bridge by driving a bicycle across it; the bridge would never show signs of stress, so the guesser would never know how much weight it could actually hold. Consequently, the computer filled in the missing information by guessing, and it guessed a value that hit the maximum limit allowed by its programming. The system reported that the tires could handle nearly four times the force they were actually capable of. When the real car tried to drive at the speeds the computer thought were safe, it simply ran out of grip and left the track.

The researchers traced this failure to a concept known as "excitation." For a system to learn a property, it must be excited or stimulated enough to reveal that property. In the context of tire identification, the car must be driven hard enough to feel the edge of its grip. The virtual test drive used by the original system was too gentle for a full-sized vehicle. The researchers calculated that the virtual drive was only capable of demanding a fraction of the friction the tire could actually provide. Because the data never reached the peak of the tire's performance curve, the mathematical model could not distinguish between a tire with low grip and a tire with high grip. It simply settled on the highest possible answer allowed by its safety limits, creating a false sense of security.

To fix this, the team redesigned the identification pipeline to be "excitation-aware." They changed the system so that the virtual test drive would automatically adjust its speed and steering intensity based on how fast the car was actually driving on the real track. If the car was moving fast, the virtual test would become more aggressive, ensuring it demanded enough force to reveal the true limits of the tires. They also introduced a new safety check. Instead of just looking at the raw numbers the computer produced, they checked if the resulting model made physical sense. They verified that the calculated grip ceiling was not higher than the road could possibly support and that the car's steering behavior remained stable. If the model failed these physical checks, the system would reject it and keep using the previous, known-safe model rather than deploying a dangerous new one.

The results of these changes were dramatic in the simulation. On a static surface where the grip was constant, the corrected system learned the tire's stiffness with an error of less than 3.2 percent, whereas the old system was off by more than 100 percent. More importantly, the team tested the system on a surface where the grip was slowly fading, simulating a track that was getting wet or worn down. The old system, stuck on its false high-grip estimate, failed to notice the loss of traction. It continued to drive at speeds that were no longer safe, causing the car to spin off the track during the second lap. The corrected system, however, detected the fading grip. It realized the tires were losing their hold and the controller re-clamped the reference speed profile against the new, lower limits. This allowed the vehicle to complete three full laps with the same level of precision as before, simply by adjusting its speed to the changing conditions.

The study highlights a critical lesson for autonomous vehicles: a model that fits the data perfectly is not necessarily a model that understands the physics. The researchers found that simply checking if a number falls within a safe range is not enough; the system must also ensure that the data it uses to learn was actually capable of testing those limits. By forcing the system to ask the right questions of the tires—questions that are hard enough to reveal the truth—they were able to prevent the car from trusting a lie. While these results were achieved in a simulation, the logic of the fix is based on physical laws that apply to real cars. The researchers conclude that for autonomous racing to be safe and effective, the car must be designed to actively seek out the limits of its own capabilities, rather than assuming those limits are what the computer says they are.

Technical Summary: Excitation-Aware On-Track System Identification at Full Scale

Problem Statement
On-track system identification aims to learn tire models from ordinary racing laps to avoid the logistical costs of dedicated off-track maneuvers. While a residual-learning pipeline proposed by Dikici et al. [6] demonstrated success on a 1:10 scale platform, this paper investigates its transferability to a full-scale Formula Student vehicle (269.6 kg, 1.53 m wheelbase). The study identifies that the baseline pipeline fails at full scale due to a loss of excitation inherent in its "virtual-data" step. Specifically, the synthetic rollout used to generate training data for the tire fit is constrained by the rollout configuration (speed and steering sweep) rather than the tire's actual capabilities. This leads to a situation where the friction coefficient ( $\mu$ ) the synthetic data can demand is lower than the tire's peak, causing the optimizer to resolve the remaining degrees of freedom by sliding coefficients onto box constraints. Consequently, the identified model reports a grip ceiling nearly four times the plant's actual capability, leading to controller failure and the vehicle leaving the track.

Methodology
The study utilizes a CARLA simulation environment with a PhysX-based wheeled-vehicle model as the ground truth plant. The identification pipeline follows a four-stage loop: (1) training a residual network on recorded lap data; (2) performing a virtual, quasi-steady steering rollout with the corrected model; (3) fitting Pacejka coefficients to the synthetic rollout forces; and (4) updating the nominal model.

The paper introduces three primary methodological corrections to address the identified failure modes:

Excitation-Aware Rollout: The authors derive a reachable-friction bound, $\mu_{reach} \approx v^2 \delta_{sweep} / (gL)$ , which dictates the maximum friction the synthetic rollout can demand. They demonstrate that the baseline's fixed low-speed rollout (4 m/s) caps $\mu_{reach}$ at 0.43, insufficient for the full-scale tire. The corrected pipeline selects rollout speed from the measured lap (clamped at a 15 m/s floor) and warns if $\mu_{reach}$ falls below the prior's peak.
Structural Identifiability Corrections:
- Peak Factor Pinning: Analysis shows that in the quasi-steady virtual rollout, the Pacejka fit depends on parameters $B, C, D$ only through their product ( $BCD$ ). Thus, the peak factor $D$ is structurally unidentifiable from the rollout alone. The corrected method measures $D$ directly from the recorded lap using a proprioceptive brush-model estimator (based on force curve curvature) and pins it for the co-identification loop.
- Relaxed Fixed-Point Iteration: The loop where each fit generates the trajectory for the next fit is a positive feedback path, not a contraction. The authors introduce a relaxation factor ( $\beta = 0.20$ ) to dampen the update, preventing error compounding.
Admissibility Gates: Instead of checking individual coefficient bounds, the pipeline gates models on derived physical quantities: axle cornering stiffness, understeer sign, critical speed, and the grip ceiling relative to the trajectory's lateral demand.

Key Results
The corrected pipeline ("Excitation-S4D-Pinn") was compared against the inherited configuration ("Baseline-NN-MSE") on two surfaces: a static surface ( $\mu=0.70$ ) and a decaying surface where grip drops from 0.70 to 0.35 under the moving vehicle.

Static Surface: The corrected pipeline identified axle cornering stiffness within 3.2% (front) and 1.4% (rear) of the ground truth and recovered the peak factor to within 11%. In contrast, the baseline configuration pinned the peak factor $D$ to its upper bound (2.0) in every cycle, overstating stiffness by 118–132% and resulting in an axle force RMSE 10–12 times higher. The corrected model reduced MPC lateral tracking error by 32%.
Decaying Surface: The baseline configuration failed to detect the loss of grip, maintaining a 2.0 g ceiling estimate while the plant's grip dropped to 0.53 g, causing the vehicle to leave the track in the second lap. The corrected pipeline tracked the decay rate to within 7% and the absolute level to within 10.9–17.4% (accounting for one cycle of transport lag). By correctly identifying the falling grip, the controller re-clamped the reference speed profile from 0.51 g to 0.30 g, allowing the vehicle to complete three laps with unchanged lateral tracking error for 18% of the lap time.

Significance and Claims
The paper claims that the failure of the baseline pipeline at full scale is not a tuning issue but a fundamental identifiability problem caused by the virtual-data step's configuration. The primary contribution is the derivation of the reachable-friction bound and the subsequent architectural changes that ensure the pipeline does not silently converge to a degenerate solution.

The authors emphasize that per-coefficient box constraints are insufficient for admissibility; a fit can satisfy all bounds while being physically degenerate (e.g., coefficients resting on bounds while the product yields a plausible but incorrect stiffness). Therefore, they advocate for gating on derived physical quantities at the model-to-controller interface. The study concludes that while the specific numerical values are tied to the CARLA/PhysX plant, the structural insights regarding excitation loss, the $BCD$ degeneracy, and the necessity of damping the identification loop are generalizable to any implementation of the virtual-steady-state-data strategy. The results are presented as simulation-based observations, with the authors noting that hardware replication is required to confirm transferability to physical vehicles.

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