Steered Axle Friction Estimation Using Pneumatic Trail
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Solution Overview
Problem
Existing methods for estimating road friction are computationally demanding and lack accuracy, particularly in real-time applications for automated or autonomous vehicles, necessitating improved mathematical modeling for safer vehicle control.
Innovation Solution
A computationally efficient method using nonlinear functions of the pneumatic trail, such as Fy = μFz tanh³(a - 9tp²/a) or Fy = μFz arctanh³(a - 9tp²/a), combined with corrections for caster trail, to estimate road friction coefficients, along with tolerance ranges and threshold evaluations for reliable vehicle control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If linear regression model is used for friction estimation, then computational simplicity is achieved, but estimation accuracy deteriorates
Solution Approach 1:
The patent transforms the friction estimation problem by changing the functional form from linear to nonlinear, specifically using tanh³ and arctanh³ functions of the pneumatic trail. This parameter transformation allows the model to capture the true nonlinear relationship between steering torque and friction coefficient, significantly improving accuracy while maintaining computational feasibility through the use of standardized mathematical functions.
2Measurement precision
If complex nonlinear models are used for friction estimation, then estimation accuracy is improved, but computational load increases
Solution Approach 1:
The patent employs computationally inexpensive mathematical functions (tanh³ and arctanh³) that can be evaluated rapidly on embedded vehicle processors. These functions serve as efficient approximations that capture nonlinear behavior without requiring heavy computational resources, making them suitable for real-time implementation in resource-constrained automotive environments.
3Measurement precision
If caster trail correction is applied, then estimation accuracy is improved, but model complexity increases
Solution Approach 1:
The patent separates the caster trail effect as a distinct correction term that can be extracted and applied independently to the main friction estimation model. By isolating this geometric correction component, the system can improve accuracy through the correction term while keeping the core estimation algorithm relatively simple and modular, allowing for easier implementation and tuning.
Data Source
AI summary
A road friction coefficient of a vehicle is estimated by obtaining substantially contemporaneous values associated with a steering angle for a steered axle of the vehicle, a lateral acceleration, a yaw acceleration, an alignment torque and an axle load on the steered axle; estimating a lateral tire force on the basis of the steering angle, lateral acceleration, and yaw acceleration; deriving a pneumatic trail from the alignment torque and estimated lateral tyre force; and estimating a road friction coefficient from the lateral tire force, the axle load, and the pneumatic trail. In embodiments, the derivation of the road friction coefficient includes evaluating a nonlinear function of the pneumatic trail.