Mapping Tire-Road Friction Coefficients Along Driven Trajectories

Risto Ojala

cs.ROOct 9, 2026

Mapping Tire-Road Friction Coefficients Along Driven Trajectories

Authors: Risto Ojala

Organizations: Energy and Mechanical Engineering, Aalto University, Espoo, Finland

Abstract

Information of the tire-road friction coefficient is critical for intelligent vehicle systems, as friction establishes the limits at which the vehicle can be manoeuvred without loss of control. While there is extensive literature on online friction estimation, no previous studies have explored post-processing and mapping friction coefficients along a driven trajectory based on recorded sensor data. Mapped friction information could be shared by connected vehicles, enabling proactive measures in low-friction areas. This paper presents an offline post-processing method, FrictionMap, for mapping friction coefficients from recorded driving data. The method operates on commonly available on-board vehicle sensor information, and requires only a basic vehicle parameter set and a slip threshold as prior knowledge. FrictionMap runs an extended Kalman filter combined with a Rauch-Tung-Striebel smoother to estimate vehicle dynamics. Data points where the friction limit is observable are identified by filtering points based on tire slip. A Gaussian process is fitted to these points to acquire a continuous estimate of the friction coefficient along the trajectory. FrictionMap is validated via a simulation study, and shown to outperform commonly used online friction estimation techniques. The code implementation and the simulation benchmark are released as open-source after paper acceptance to enable further research.

Figures & tables

Fig. 1: High-level illustration of the proposed FrictionMap solution. Given recorded vehicle on-board sensor data as an input, the solution estimates the tire-road friction coefficient $\mu$ as a function of the distance $d$ along the driven route.

Fig. 2: Overview of the proposed friction mapping pipeline, FrictionMap.

Fig. 3: Driven trajectory of the simulation dataset, with vehicle speed and friction patches visualized. Values above the plot indicate the exact friction coefficient at each patch.

Variable	Definition	Value
$m$	vehicle mass	1669 kg
$I_{z}$	vehicle yaw inertia	1356 $\text{kgm}^{2}$
$J_{w}$	combined wheel inertia	2.198 $\text{kgm}^{2}$
$l_{f}$	distance from CoG to front axle	1.388 m
$l_{r}$	distance from CoG to rear axle	1.388 m
$R$	tire dynamic radius	0.3236 m

TABLE I: Values used for the model parameters.

Fig. 4: Noisy measurement signals of the simulation dataset.

Fig. 5: Friction estimates of the FrictionMap Gaussian process posterior compared against the ground truth reference values.

Fig. 6: State estimation accuracy of the EKF + RTS smoother in FrictionMap.

Method	MAE	RMSE	PICP ( $1\sigma$ ) a
Joint EKF (linear)	0.279	0.341	0.289
Joint EKF (Dugoff)	0.259	0.325	0.384
Cascaded EKF (linear)	0.287	0.343	0.078
Cascaded EKF (Dugoff)	0.288	0.350	0.089
Joint EKF, adaptive (linear)	0.143	0.186	0.883
Joint EKF, adaptive (Dugoff)	0.136	0.179	0.900

TABLE II: Results of the friction estimation accuracy benchmark. Best value in each column is bolded.

Method	MAE	RMSE	PICP ( $1\sigma$ ) a
FrictionMap w/o RTS smoother	0.059	0.096	0.731
FrictionMap w/o GP	0.072	0.136	-
FrictionMap w/ $\nu=0.5$	0.051	0.088	0.809
FrictionMap w/ $\tau=0.10$	0.055	0.089	0.732
FrictionMap [ours]	0.050	0.087	0.754

TABLE III: Ablation study of different design choices in the architecture. Best value in each column is bolded.

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Open paper AskPDF arXiv

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.

Abstract

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