Real-time estimation of vehicle-tire-road friction is critical for allowing autonomous race cars to safely and effectively operate at their physical limits. Traditional approaches to measure tire grip often depend on costly, specialized sensors that require custom installation, limiting scalability and deployment. In this work, we introduce RAGE, a novel real-time estimator that simultaneously infers the vehicle velocity, slip angles of the tires and the lateral forces that act on them, using only standard sensors, such as IMUs and RADARs, which are commonly available on most of modern autonomous platforms. We validate our approach through both high-fidelity simulations and real-world experiments conducted on the EAV-24 autonomous race car, demonstrating the accuracy and effectiveness of our method in estimating the vehicle lateral dynamics.
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Fig. 1: Unimore Racing’s Dallara EAV-24 during the 2024 Abu Dhabi Autonomous Racing League at Yas Marina F1 circuit. Photo by Ian Bundey.
Fig. 2: Schematic representation of the dynamic single-track model.
Fig. 3: Sensor setups for the Dallara EAV-24. While the car is equipped with additional sensors, only the ones used in this study are shown.
Fig. 4: Simulated double lane change maneuver. The simulator outputs slip angles and lateral forces for all four tires. For the single-track model, slip angles are averaged and forces summed per axle.
Fig. 5: Simulated spin on wet asphalt ( μ=0.6 ), the car brakes from 65 m/s before a left turn, but reduced grip causes rear instability and a 135° spin.
Fig. 6: Estimated Pacejka peak coefficient D under three different road friction levels.
Fig. 7: Front and rear tire Pacejka model fitted over time. The sequence of model parameters captures the changing tire behavior and lateral dynamics throughout the lap.
Fig. 8: Estimated lateral forces during the hot-lap. RAGE tracks lateral forces accurately, with minor errors due to neglecting the limited-slip differential and combined slip effects.
Fig. 9: RAGE outputs compared with reference data obtained from the optical sensor, covering a complete lap of the Yas Marina F1 track. The lateral acceleration estimate is computed combining the front and rear lateral tire forces obtained from the Pacejka model with the online-estimated parameters.
Fig. 10: The estimated tire cornering stiffness shows a correlation with tire temperature and pressure, and exhibits periodic variations aligned with the circuit layout. The color-coded stiffness values correspond to specific segments of the track layout displayed on the right.
In this work, we present RAGE-XY, an extended version of RAGE, a real-time estimation framework that simultaneously infers vehicle velocity, tire slip angles, and the forces acting on the vehicle using only standard onboard sensors such as IMUs and RADARs. Compared to the original formulation, the proposed method incorporates an online RADAR calibration module, improving the accuracy of lateral velocity estimation in the presence of sensor misalignment. Furthermore, we extend the underlying vehicle model from a single-track approximation to a tricycle model, enabling the estimation of rear longitudinal tire forces in addition to lateral dynamics. We validate the proposed approach through both high-fidelity simulations and real-world experiments conducted on the EAV-24 autonomous race car, demonstrating improved accuracy and robustness in estimating both lateral and longitudinal vehicle dynamics.
Operating autonomous vehicles at the absolute limits of handling requires precise, real-time identification of highly non-linear tire dynamics. However, traditional online optimization methods suffer from "cold-start" initialization failures and struggle to model high-frequency transient dynamics. To address these bottlenecks, this paper proposes a novel vision-augmented, iterative system identification framework. First, a lightweight CNN (MobileNetV3) translates visual road textures into a continuous heuristic friction prior, providing a robust "warm-start" for parameter optimization. Next, a S4 model captures complex temporal dynamic residuals, circumventing the memory and latency limitations of traditional MLPs and RNNs. Finally, a derivative-free Nelder-Mead algorithm iteratively extracts physically interpretable Pacejka tire parameters via a hybrid virtual simulation. Co-simulation in CarSim demonstrates that the lightweight vision backbone reduces friction estimation error by 76.1 using 85 fewer FLOPs, accelerating cold-start convergence by 71.4. Furthermore, the S4-augmented framework improves parameter extraction accuracy and decreases lateral force RMSE by over 60 by effectively capturing complex vehicle dynamics, demonstrating superior performance compared to conventional neural architectures.
Zhiping Wu, Cheng Hu, Yiqin Wang +2
State Key Laboratory of Industrial, Zhejiang University, Hangzhou 310027, China
Accurate estimation of the tire-road friction coefficient (TRFC) is critical for ensuring safe vehicle control, especially under adverse road conditions. However, most existing methods rely on naturalistic driving data from regular vehicles, which typically operate under mild acceleration and braking. As a result, the data provide insufficient slip excitation and offer limited observability of the peak TRFC. This paper presents a high-slip-ratio control framework that enables automated vehicles (AVs) to actively excite the peak friction region during empty-haul operations while maintaining operational safety. A simplified Magic Formula tire model is adopted to represent nonlinear slip-force dynamics and is locally fitted using repeated high-slip measurements. To support safe execution in car-following scenarios, we formulate a constrained optimal control strategy that balances slip excitation, trajectory tracking, and collision avoidance. In parallel, a binning-based statistical projection method is introduced to robustly estimate peak TRFC under noise and local sparsity. The framework is validated through both closed-loop simulations and real-vehicle experiments, demonstrating its accuracy, safety, and feasibility for scalable, cost-effective roadway friction screening.
Zhaohui Liang, Hang Zhou, Heye Huanh +1
Civil & Environmental Engineering Department, University of Wisconsin, Madison, Madison, WI