Tire Road Friction Coefficient Estimation for Individual Wheel Based on Two Robust PMI Observers and a Multilayer Perceptron
Bibliographic record
Abstract
The tire-road friction coefficient (TRFC) is critical to the control of assisted and autonomous vehicles. However, direct measurement of TRFC by existing sensors is impossible. In this paper, we aim to develop a scheme to estimate TRFC based on the mathematical model and measurable vehicle states. To address this issue, we first develop a vehicle dynamics model and a wheel rotation dynamics model. Based on the two models, we propose two robust proportional multiple-integral (PMI) observers for the longitudinal and lateral tire-force estimation. To reduce the conservative of conventional H∞ observer, a novel optimization problem is formulated and solved by particle swarm optimization (PSO) algorithm to determine the observer gain. Next, an multilayer perceptron (MLP) is trained to estimate TRFC from the estimated tire forces, slip rate, and slip angle. However, based on data analysis, we find that the tire forces are not sensitive to the TRFC when the slip ratio and slip angle are relatively low, and these data frames would degrade the performance of MLP. To balance the performance and generalization ability of MLP, we determine the threshold for slip ratio and slip angle to exclude the insensitive data frames and train the MLP with the remaining data. Finally, the proposed scheme is verified under different scenarios. The simulation results demonstrate that the proposed method could estimate the TRFC more accurately than the traditional method. Furthermore, the proposed method has the advantage that its estimation does not depend on the initial states.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".