Means of Obtaining Mamdani Fuzzy Model of Car Driver’s Dynamics

Mihálik, Ondrej; Fiedler, Petr · 2022 · OpenAlex-citations

DOI: 10.13164/eeict.2022.243

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Summary

This paper addresses the challenge of creating an interpretable, non-linear model of human driver dynamics during elementary driving tasks, specifically lane-changing maneuvers on a motorway. While previous research often relied on linear models or complex black-box approaches like neural networks, this study aims to generalize existing linear models by incorporating a Mamdani fuzzy system to capture non-linearities. The authors seek to overcome the limitations of manual fuzzy model identification, which is subjective and irreproducible, by developing a deterministic, data-driven identification algorithm. The methodology employs a Hammerstein model structure, combining a static fuzzy non-linearity with linear dynamics. The linear component is based on a transfer function representing the driver as a derivative controller with reaction delay and bandwidth limitations. The non-linear component is a simple Mamdani fuzzy system with three rules corresponding to left, centered, and right car positions. To ensure interpretability and facilitate mathematical optimization, the authors impose symmetry constraints on the membership functions, reducing the non-linearity to two parameters. Crucially, the authors derive closed-form analytical equations for the fuzzy system’s input-output relationship. These explicit formulae allow for the calculation of exact gradients, enabling the use of efficient derivative-based minimization algorithms (specifically the Trust Region Algorithm) to minimize the quadratic error between the model output and measured simulator data. Experimental results demonstrate that the proposed fuzzy Hammerstein model achieves higher accuracy than the original linear model. The quadratic error for the fuzzy model was 21.1%, compared to 24.1% for the linear model. The identified parameters for the linear dynamics were similar in both models, but the fuzzy model introduced specific non-linear characteristics, such as a zone of smaller gain for small errors, reflecting human behavior where minor deviations require less corrective steering. The use of analytical derivatives significantly improved the convergence speed and reliability of the identification process compared to derivative-free methods like the Nelder-Mead algorithm. The significance of this work lies in providing a robust, reproducible method for identifying Mamdani fuzzy models, which are typically difficult to optimize due to their non-differentiable nature. By deriving explicit formulae, the authors enable the use of standard gradient-based optimization techniques. The resulting model offers a balance between accuracy and interpretability, allowing researchers to visualize and understand the driver’s reasoning process through graphical membership functions. This approach provides a foundation for modeling more complex driving tasks, such as acceleration and deceleration, by extending the fuzzy component to handle multiple inputs.

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• Theoretical Contribution: computational model