Autonomous Drifting with 3 Minutes of Data via Learned Tire Models

Authors: Franck Djeumou, Jonathan Y.M. Goh, Ufuk Topcu, Avinash Balachandran · ICRA 2023

Licences

Open Access
Paper: CC BY 4.0

Everything below draws on the full paper under its CC BY 4.0 licence; its figure is credited to the authors.

TL;DR

Neural ODE and ExpTanh tire models that enforce the S-shaped force curve and friction limit replace a Fiala brush model in drifting NMPC, cutting lateral tracking error over 4× on a real car.

Why it matters

A tire model that fits from a few minutes of driving data means a vehicle can be re-identified after a tire change without specialised tire testing facilities. The learned models captured coupling with vehicle state that the single-axle brush model misses, and the controller converged in fewer gradient iterations with them. This matters for any controller that works at the friction limit, from drifting to emergency obstacle avoidance.

Problem

Tire forces near the limits of adhesion are nonlinear and coupled with suspension, weight transfer and other chassis effects. Controllers for drifting and emergency manoeuvres usually lump each axle into a single analytical tire model such as the Fiala brush model, which misses these higher-order effects. Black-box neural tire models lose physical guarantees and had not been tested on a full-size car at the handling limits.

Proposed solution

The authors learn axle tire forces from vehicle state measurements with a neural ODE whose learned second derivative and inflection points enforce the S-shaped force curve, with a soft penalty on exceeding the estimated friction limit. ExpTanh, a closed-form subset of these solutions, is cheap to evaluate and differentiate for real-time control. Both models take selected vehicle states (yaw rate, speed, sideslip) as features and are used as drop-in replacements for the Fiala model in an existing drifting NMPC.

Key insights

Constraining the sign of the learned second derivative between learned inflection points guarantees the S-shaped tire curve while leaving its exact form to the data
ExpTanh needs only two exp evaluations, against three arctan evaluations for the Magic Formula, and its maximum can be found analytically
Adding yaw rate, speed and sideslip as features lets the axle model absorb chassis effects such as weight transfer and camber, which shifted and flattened the learned curves
A smoother, more accurate tire model reduced NMPC gradient iterations; with the Fiala model iterations tripled in the transition from drifting to grip driving
Retraining ExpTanh after a tire change took under 15 s on a laptop GPU, while the unchanged Fiala model degraded on the new tires

Main results

Offline, NODE and ExpTanh prediction errors were at least 1.5× denser around zero mean error than Fiala and Magic Formula (Fig. 4 caption); the introduction states up to 2× denser
Training on a dataset of 306,887 state measurements (~1 hour) took ~27 minutes for NODE and ~4 minutes for ExpTanh on a laptop GeForce RTX 2060
Slalom drifting with sideslip references up to 43° at 31–45 mph: ExpTanh tracked the path (e and ∆ϕ) up to 3.5× better and sideslip up to 1.5× better than Fiala in RMS error, with fewer steering oscillations
Figure-8 drifting after a rear tire change, with ExpTanh retrained on ~3 minutes of manual driving: more than 4× lower RMS lateral error and more than 2× better sideslip tracking than Fiala on both tire sets
The Bridgestone tire + Fiala run was ended early because the safety driver was uncomfortable with the tracking error

Limitations

Forces are estimated only for cases where front longitudinal force can be assumed zero (rear-wheel drive, no front torque), chosen for simplicity
The NODE model is slow to train and evaluate, so for control it was replaced by a network trained to mimic its solutions, which cost some tracking accuracy
The feature set is one choice; the authors note other selections may suit other vehicles
Reference trajectories were still computed with the Fiala model, and the comparison dataset was collected on the same surfaces in similar summer weather
Online updating of the tire curves during driving is left to future work

Field impact

Finalist for the ICRA 2023 Outstanding Dynamics and Control Paper award, with 47 citations. The authors publish videos of the experiments; the paper does not state a code or data release.

Abstract

Near the limits of adhesion, the forces generated by a tire are nonlinear and intricately coupled. Efficient and accurate modelling in this region could improve safety, especially in emergency situations where high forces are required. To this end, we propose a novel family of tire force models based on neural ordinary differential equations and a neural-ExpTanh parameterization. These models are designed to satisfy physically insightful assumptions while also having sufficient fidelity to capture higher-order effects directly from vehicle state measurements. They are used as drop-in replacements for an analytical brush tire model in an existing nonlinear model predictive control framework. Experiments with a customized Toyota Supra show that scarce amounts of driving data – less than three minutes – is sufficient to achieve high-performance autonomous drifting on various trajectories with speeds up to 45mph. Comparisons with the benchmark model show a 4× improvement in tracking performance, smoother control inputs, and faster and more consistent computation time.

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