NTT DATA BEST Hackathon 2026 ·
Politecnico di Torino
Tire-Road
Friction ID
Real-time tire-road friction identification using ESC gradient analysis and Burckhardt NLS classification — per wheel, per braking event, without stopping the vehicle.
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48 MATLAB simulations · 274,667 frames · Burckhardt NLS + ESC gradient identification
Dataset
About the Data
48 closed-loop braking simulations generated in MATLAB/Simulink across 8 road scenarios, 3 brake force distributions, and 2 controller modes.
48
Simulations
8 scenarios × 3 brake distributions × 2 modes
765k
Raw rows
Timestep ~1 ms · 29 columns: slip, μ, ESC signals, ground truth
20.6k
Prepared rows
ABS filter · α>0.01 · stride=10 · balanced per surface
3
Surfaces
Dry asphalt · Wet asphalt · Snow
Preprocessing pipeline
Raw 765k → ABS filter (abs_active=1) → 479k
→ Confidence filter (α > 0.01) → 340k
→ Slip range (0.002 ≤ s ≤ 0.55) → 310k
→ Stride=10 (removes autocorrelation) → 48k
→ Balance Snow≤12k, Dry/Wet≤6k → 20,616 rows
→ Confidence filter (α > 0.01) → 340k
→ Slip range (0.002 ≤ s ≤ 0.55) → 310k
→ Stride=10 (removes autocorrelation) → 48k
→ Balance Snow≤12k, Dry/Wet≤6k → 20,616 rows
Key signals per row
slip — wheel slip ratio (encoder)mu_noisy — friction coefficient (force estimation)g_esc — ESC gradient from LPF demodulatora_esc — ESC dither amplitudealpha — identifier confidence (0–1)surface — ground truth label
Why these preprocessing steps?
- ABS-active filter — only timesteps where the ABS is actively modulating brake force are retained. Outside of ABS intervention the tyre operates in the linear, low-slip regime where the Burckhardt curve is nearly flat and parameter estimation is ill-conditioned (Rajamani 2011, §5).
- Confidence filter α > 0.01 — the ESC identifier reports a convergence confidence α. Low-α samples indicate the algorithm has not yet stabilised; including them would inject outliers into the training set.
- Stride = 10 — consecutive timesteps at 1 ms are heavily autocorrelated. Subsampling at 10× decorrelates adjacent samples without losing scenario coverage, satisfying the persistent-excitation condition required for identifiability (Gustafsson 1997, §3).
- Surface balancing — Snow produces ~3× more ABS-active frames than Dry/Wet (lower peak friction → longer braking distance). Capping per-surface count prevents the classifier from being biased toward Snow.
Gustafsson 1997 — Automatica 33(6)Rajamani 2011 — Vehicle Dynamics and Control §5
How It Works
Animated NLS Curve Fitting
Watch the Burckhardt NLS fit converge in real time. Data points are drawn from a surface with additive Gaussian noise — the classifier identifies the surface once the fit stabilises.
c₁ (fitted)
—
c₂ (fitted)
—
c₃ (fitted)
—
Starting…
Reading this plot: the faded dashed curve is the true Burckhardt model for the selected surface — ground truth. The bright solid curve is the live NLS fit converging as noisy data accumulates. Each dot is one synthetic measurement with σ = 0.018 added Gaussian noise, matching realistic ABS wheel-speed and force-estimation error levels reported in the literature.
- NLS (Non-Linear Least Squares) minimises ∑(μfit(sᵢ) − μᵢ)² over (c₁, c₂, c₃) using a multi-seed grid search — three starting points covering Dry, Wet and Snow to avoid local minima.
- Classification fires once 50 points are accumulated. The fitted (c₁, c₂, c₃) vector is normalised and compared to the three surface prototypes via Euclidean nearest-neighbour. The dominant discriminant is c₂ — notice how Dry (c₂=24) and Wet (c₂=34) look visually similar but their curves peak at different slip values (s_opt ≈ 0.17 vs 0.13).
- Ice is the most distinctive: its extremely sharp rise (c₂=306) means the curve peaks at s_opt ≈ 0.03 — just 3% slip — after which friction plummets. This is why ice is so dangerous for ABS-equipped vehicles at higher slip.
Burckhardt 1993 — FahrwerktechnikGustafsson 1997 — Automatica 33(6)
Plots
Burckhardt Friction Curves
All three road surfaces plotted in the Burckhardt model space — note how c₂ separates them clearly (24 / 34 / 94). Peaks and optimal slip points are annotated.
Dry asphalt (c₁=1.28, c₂=23.99, c₃=0.52)
Wet asphalt (c₁=0.857, c₂=33.82, c₃=0.347)
Snow (c₁=0.195, c₂=94.13, c₃=0.065)
Ice (c₁=0.050, c₂=306.4, c₃=0.001)
The Burckhardt model (1993) represents the tyre–road friction coefficient μ as a function of wheel slip ratio s using three physically interpretable parameters:
- c₁ — asymptotic friction ceiling. Dry asphalt (c₁=1.28) can generate over 1.2g of braking force; ice (c₁=0.05) barely 0.05g.
- c₂ — curve sharpness and the key discriminant. A large c₂ means the curve rises steeply and peaks at very low slip. Surfaces are separated by nearly a decade: 24 (dry) → 34 (wet) → 94 (snow) → 306 (ice). This wide natural gap makes nearest-neighbour classification robust even with sensor noise.
- c₃ — post-peak slope. A small c₃ means friction stays high well past s_opt; a larger c₃ causes a sharper drop, making over-braking more dangerous.
Burckhardt 1993 — Fahrwerktechnik, Vogel-VerlagPacejka 2012 — Tire and Vehicle Dynamics §3Rajamani 2011 — Vehicle Dynamics and Control §5
Confusion Matrix — Batches (50 pts each)
Dry
Wet
Snow
Dry (pred)
17
0
0
Wet (pred)
0
17
0
Snow (pred)
0
0
48
82 batches total · 20% stratified hold-out · 0 misclassifications
F1 / Precision / Recall per Surface
F1 SCORE
Dry asphalt1.000
Wet asphalt1.000
Snow1.000
WHY PERFECT?
c₂ separates surfaces: 24 (dry) vs 34 (wet) vs 94 (snow). The nearest-neighbour distance in normalised (c₁,c₂,c₃) space has a large margin. Noise erodes this only above σ≈0.05.
Algorithm
Three-Layer ESC Identifier
Three layers fire in cascade — each activates when its precondition is met.
Layer 1 — Always active
Lookup Table
Maps observed peak friction μ_max to a coarse c₂ estimate via linear interpolation.
μ_max → c₂_coarse
→
Layer 2 — ESC gradient available
ESC-Gradient Analytic
Converts ESC demodulator output to friction gradient, solves analytically for c₁ and c₃.
g_esc → c₁, c₃
→
Layer 3 — Sufficient slip excitation
Brent Root-Finding
Solves for c₂ from two curve points using Brent's method (guaranteed convergence).
|s_probe − s_peak| > δ → c₂_fine
Burckhardt Friction Model
μ(s) = c₁ · (1 − e−c₂|s|) − c₃ · |s|
c₁ — friction amplitude ·
c₂ — curve sharpness (key discriminant: 24 dry / 34 wet / 94 snow) ·
c₃ — slope after peak
How the three layers work together:
- Layer 1 — Lookup Table is always active from the first braking event. It maps the observed maximum friction μ_max to a coarse c₂ estimate via linear interpolation over the four known surface presets. This gives an immediate, rough surface guess even before the ABS probes different slip values.
- Layer 2 — ESC Gradient Analytic activates once the Extremum Seeking Control demodulator has settled. The ESC dither signal adds a small sinusoidal perturbation to the brake slip set-point; the demodulator extracts the local gradient g_esc = dμ/ds at the current operating point. Sign convention:
g_true = −g_esc · 2 / a_esc. Knowing g_true plus a single (s, μ) measurement provides two constraints, enough to solve analytically for c₁ and c₃ — without ever needing to reach the friction peak. This works at any operating point, making it suitable for partial-braking manoeuvres (Tan et al. 2006). - Layer 3 — Brent Root-Finding refines c₂ when the ABS has probed two sufficiently different slip values (|s_probe − s_measured| > δ). Two curve points over-determine c₂; Brent's method solves the resulting scalar equation to tolerance 10⁻⁴ in at most 20 iterations — guaranteed convergence without derivative information (Press et al. 2007, §9.3).
Tan, Nesic & Mareels 2006 — Automatica 42(6)Gustafsson 1997 — Automatica 33(6)Press et al. 2007 — Numerical Recipes §9.3
Robustness
Sensor Noise vs Classification Performance
Drag the slider to add Gaussian noise (σ_μ) on top of the real data.
Understanding the noise sensitivity:
- σ_μ = 0 (baseline) — the raw data already contains realistic ABS sensor noise from the MATLAB/Simulink simulation. The classifier achieves perfect F1 because c₂ separation (24 / 34 / 94) is much larger than the NLS fitting error at this noise level.
- σ_μ = 0.010 — realistic vehicle sensors. This corresponds to approximately ±2% friction measurement error, typical of combined wheel-speed encoder quantisation and tire force estimation (Gustafsson 1997). F1 = 0.724 is the reference real-world operating point.
- Dry↔Wet confusion dominates because their c₂ values (24 vs 34) differ by only 10 units — a 30% gap. At high noise the NLS fit uncertainty in c₂ spans this gap, causing misclassification. Snow (c₂=94) sits ~60 units away from Wet, so even large NLS errors rarely cross the decision boundary.
- σ_μ = 0.050 — the critical threshold. Above this level the Dry/Wet NLS fit variance exceeds the c₂ margin. The practical implication: on degraded sensors (e.g., contaminated encoders), the system should report "Dry or Wet" rather than committing to one label.
Gustafsson 1997 — Automatica 33(6), §4Canudas-de-Wit et al. 2003 — Vehicle System Dynamics 39(3)
Robustness Comparison
Classifier Variants vs Noise
Monte Carlo simulation (60 batches × 8 σ levels × 2 axes) comparing four classifier strategies. Computed in-browser — click Run to start.
Baseline (batch=50, 3D NN)
Large batch (batch=100)
c₂-only classify (batch=50)
Majority vote ×3 (batch=50)
Not started
F1 vs σμ — friction noise (σs=0)
F1 vs σs — slip noise (σμ=0)
Two independent noise axes — why both matter:
- Left plot — friction noise σ_μ models inaccuracy in the force estimation chain: wheel torque sensor noise, tyre radius uncertainty, and load transfer estimation. This directly corrupts the μ values fed to NLS fitting.
- Right plot — slip noise σ_s models wheel-speed encoder quantisation and shaft compliance. Slip noise is typically smaller in practice (high-resolution encoders are cheap), but it distorts the shape of the fitted curve by misplacing points along the s-axis.
- Large batch (×2, 100 pts) — averaging more noisy points reduces the NLS fit variance by approximately √2. This is the most reliable improvement under both noise types.
- c₂-only classification — instead of comparing all three fitted parameters (c₁, c₂, c₃), only c₂ is used. Since c₁ and c₃ are far more sensitive to noise than c₂ (they control amplitude and slope, not shape sharpness), dropping them removes noise dimensions from the decision boundary.
- Majority vote ×3 — takes the most common prediction across three consecutive batches. This smooths single-batch outliers caused by an unlucky noisy window, at no computational cost beyond latency of two extra batches.
Åström & Wittenmark 1995 — Adaptive Control §6Gustafsson 1997 — Automatica 33(6)
Custom Data
Upload Your Own Dataset
Run the Burckhardt classifier on your own CSV file — processed entirely in-browser.
Drop CSV file here or click to browse
Accepts .csv files · No data leaves your machine
Required CSV file structure
slip— Wheel slip ratio, float, range 0.002 – 0.55 (required)mu_noisy— Measured friction coefficient, float (required)surface— Ground truth:Dry asphalt/Wet asphalt/Snow— for accuracy scoring (optional)alpha— ESC confidence 0–1; rows with α < 0.01 filtered out (optional)- — Column names are case-sensitive. Minimum 50 rows needed per window.
Literature
Key References
The theoretical foundation behind this work spans tire mechanics, extremum seeking control, and online parameter identification.
[1]
Fahrwerktechnik: Radschlupfregelsysteme
Vogel-Verlag, Würzburg, 1993
Burckhardt Model
[2]
Slip-based tire-road friction estimation
Automatica, vol. 33, no. 6, pp. 1087–1099, 1997
Friction Estimation
[3]
Dynamic friction models for road/tire longitudinal interaction
Vehicle System Dynamics, vol. 39, no. 3, pp. 189–226, 2003
Tire Dynamics
[4]
On non-local stability properties of extremum seeking control
Automatica, vol. 42, no. 6, pp. 889–903, 2006
ESC Theory
[5]
Vehicle Dynamics and Control, 2nd ed.
Springer Science & Business Media, 2011
ABS / Vehicle Dynamics
[6]
Tire and Vehicle Dynamics, 3rd ed.
Butterworth-Heinemann, Oxford, 2012
Magic Formula / Tire Model
[7]
Adaptive Control, 2nd ed.
Addison-Wesley, Reading, MA, 1995
Adaptive Identification
[8]
Numerical Recipes: The Art of Scientific Computing, 3rd ed. — §9.3 Van Wijngaarden–Brent method
Cambridge University Press, 2007
Brent Root-Finding
Team
Authors
