Tyre–Road Friction Estimation for EV Traction Control

The problem

Traction, ABS and stability controllers work best when they know the available road friction, but friction can change suddenly from dry to wet or gravel. Conventional vehicles estimate it poorly because engine and brake torques are uncertain. EV motors provide accurate, fast torque information, making friction estimation more practical, but the estimator must work with small excitation and noisy signals.

Objectives

• Build a vehicle plant with Magic Formula tyres and surface transitions.
• Implement slip-slope and Kalman-filter friction estimators using motor torque and wheel speed.
• Compare estimator accuracy, convergence time and sensitivity to excitation and noise.
• Adapt a traction controller's slip target using the estimate and evaluate the benefit.
• Characterise when each estimator is reliable.

What you need

Key concepts

Slip-slope method

At low slip, normalised traction force rises roughly linearly with slip, and the slope correlates with road surface. Estimating the slope with recursive least squares lets the controller infer friction before reaching the limit.

Force-based estimation

Tyre force is estimated from motor torque and wheel acceleration, Fx = (T − J·dω/dt)/R, then compared with a tyre model to estimate peak friction.

Excitation

Friction is observable only when tyres produce meaningful force. In gentle cruising there is little information, so estimators must handle low excitation.

Adaptive slip target

Traction control can choose a slip target near the friction peak for the estimated surface, instead of a conservative fixed value.

Step-by-step guide

1. 1

   Define the problem and benchmarks

   Choose an example single-motor EV and define test scenarios: acceleration on dry, wet, gravel and snow-like surfaces, sudden transitions between surfaces and gentle driving with low excitation. Define metrics: estimation error of peak friction, convergence time after a transition, false alarm rate and traction-control benefits. List baseline estimators from literature to compare against. Fix the surface parameter sets in advance.

   Checkpoint: A scenario list, metric definitions and literature baselines documented.

2. 2

   Build the plant and sensors

   Assemble a vehicle model from the Vehicle Dynamics Blockset with Magic Formula tyres, applying friction scaling to represent surfaces and switching it at set distances. Model the motor as a torque source with known torque plus small error, and add wheel-speed sensor noise and quantisation, and an accelerometer for vehicle acceleration. Log the true friction scaling as the reference for estimator evaluation, and check slip values on each surface.

   Checkpoint: Plant runs all scenarios with realistic sensor noise and visible tyre slip differences between surfaces.

3. 3

   Estimate tyre force

   Estimate longitudinal tyre force from motor torque and filtered wheel acceleration. Estimate vehicle speed from non-driven wheels or accelerometer integration with correction. Compare estimated force and slip with the plant's true values and quantify errors. Use a low-pass or filtered-derivative estimate of wheel acceleration, because differentiating a noisy wheel speed amplifies noise. Check the estimate during acceleration and during regenerative braking, since both provide excitation. Record errors as RMS and peak values across scenarios.

   Checkpoint: Force and slip estimates within stated errors of the true values across scenarios.

4. 4

   Slip-slope estimator

   Implement recursive least squares with a forgetting factor to estimate the slope of normalised force against slip in the low-slip region. Map slope to surface class or peak friction using a calibration from simulation. Tune the forgetting factor to trade tracking speed against noise. Restrict data to the low-slip region where the relationship is near linear, and freeze the estimate when excitation is too small. Record the calibration mapping from slope to friction so the method can be reproduced.

   Checkpoint: Slope estimates that separate dry, wet and low-friction surfaces in steady acceleration tests.

5. 5

   Kalman-filter estimator

   Implement an extended or unscented Kalman filter with states for vehicle speed, wheel speed and a friction scaling parameter modelled as a random walk. Use a Magic Formula tyre model in the measurement or process equations. Tune noise covariances and compare convergence with the slip-slope method. Choose the random-walk variance of the friction state to balance convergence speed against noise. Freeze or slow the update when excitation is low, and compare the filter's covariance with actual error to check consistency.

   Checkpoint: Friction estimate converges after transitions with a stated convergence time.

6. 6

   Compare estimators

   Run all scenarios with both estimators and baselines. Compute metrics including error, convergence time and false alarms. Plot estimated against true friction across transitions. Identify conditions where each estimator is reliable or poor, especially under low excitation. Use identical sensor noise and scenarios for all estimators. Present convergence times as distributions where scenarios are repeated with different noise seeds. Highlight cases where an estimator gives confident but wrong results, because these are the most dangerous for a controller relying on them.

   Checkpoint: A comparison table and plots across scenarios with reliability conditions identified.

7. 7

   Monte Carlo robustness

   Run a Monte Carlo study varying sensor noise, torque error, tyre parameters and vehicle mass. Report distributions of estimation error and convergence time. Identify which uncertainties matter most. Use parsim if Parallel Computing Toolbox is available, or a scripted loop otherwise, and fix random seeds so the study can be repeated. Present histograms of error and convergence time for each estimator, and compute the sensitivity of error to each uncertain input by regression on the samples. State the number of runs and confidence intervals.

   Checkpoint: Distributions and sensitivity ranking from at least a few hundred runs.

8. 8

   Adaptive traction control

   Implement a traction controller that limits wheel slip using motor torque, first with a fixed conservative slip target and then with a target adapted from the friction estimate. Compare acceleration performance and slip overshoot on each surface and transition. Use the same controller gains in both cases so only the slip target differs. Test transitions from high to low friction especially carefully, since the estimate lags the surface change and the target may briefly be too high. Report slip overshoot and acceleration.

   Checkpoint: Adaptive control improves acceleration on high-friction surfaces without larger slip overshoot on low friction.

9. 9

   Safety logic and fallback

   Add confidence measures from estimator covariance or residuals and fall back to conservative targets when confidence is low. Test with low-excitation driving and sudden transitions. Make sure wrong estimates cannot drive the controller into unsafe slip. Define confidence from innovation size, covariance or excitation level, and test thresholds across scenarios. Compare performance with and without fallback in transitions, and show that fallback trades some performance for safety. Document the logic clearly, since it is the part a safety review would examine.

   Checkpoint: Fallback activates in low-confidence cases and slip stays within limits in all scenarios.

10. 10

    Report and publishable findings

    Present the plant, estimators, comparisons, robustness study and traction-control application. State limitations: simulated tyres and surfaces, no camber or temperature effects and no real-vehicle data. Discuss how experiments on a test vehicle could validate the findings. Include estimator equations, tuning, scenario definitions and Monte Carlo set-up. Present results in tables and plots with confidence intervals, and state which conclusions depend on the simulated tyre model. Release scripts and parameters for reproducibility.

    Checkpoint: A thesis chapter with reproducible scripts and quantified estimator comparison.

Testing & validation

• Force and slip estimation accuracy.
• Estimator accuracy and convergence across surfaces and transitions.
• Monte Carlo distributions of error and convergence.
• Traction-control performance with adaptive slip target.
• Fallback behaviour under low confidence.

Expected results

Two EV friction estimators compared on accuracy, convergence and robustness, with an adaptive traction controller that uses the estimate safely.

Take it further

• Add lateral excitation and estimate friction from steering and lateral dynamics.
• Fuse estimates from several wheels and vehicle sensors.
• Use machine-learning surface classification alongside model-based estimation.
• Validate with data from a vehicle or test rig.

Viva and review questions

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