IDENTIFICATION OF A DRIVER STEERING MODEL, AND MODEL UNCERTAINTY, FROM DRIVING SIMULATOR DATA

Vehicle active safety systems are designed to improve driving safety while the driver is still in control of the vehicle. For the design of such systems, driver-controller interaction can be significant and should not be neglected. Pilutti @1# shows that a lane departure warning system can be improved by considering variations in driver state. An active controller that uses direct intervention of vehicle motion will lend to driver-controller interaction issued, and generally requires a thorough investigation of driver behavior before active safety controllers can be implemented @2‐4 # For vehicle lateral control, the steering wheel angle is the primary means for control actuation. Many driver models try to approximate the real driver’s road tracking performance, assuming certain driver inputs and outputs. Several driver models have been developed in the literature ~e.g., @5‐9#!. A well-known result from human factors research is the ‘‘crossover’’ model @5,6#. The crossover model states that the open loop frequency response of the driver-vehicle combination approximates that of transfer function v c /s around the crossover frequency, where v c is the crossover frequency. Many driver models can be regarded as different realizations of the crossover model ~e.g., @7,8#!. These models have similar characteristics around the crossover frequency and differ more at higher and lower frequency ranges. Models of the driver steering control, based on system identification, which can be used for on-line implementation have also been reported in @10,11#. Although these models approximate the driver behavior well, no driver model is expected to represent the real driver completely. Furthermore, for the purpose of controller design, it is common practice to use a low-order driver model. Therefore, it is reasonable to expect that significant driver model uncertainty exists. This driver model uncertainty can have a significant effect on the performance of the designed control system. To successfully design an active safety controller, including warning and direct intervention, it is necessary to obtain a reasonable representation of this driver model uncertainty. The uncertainty can be used to represent the difference between one real driver and the driver model at any instant in time, or to represent the change in driving behavior with time. On a larger scale, the uncertainty can also be used to represent the variation across several different drivers if the designed system is to be used by different drivers. However, studies of driver model uncertainty have not been reported in the literature. This article aims to develop a model for the driver model uncertainty using the measured data from real drivers driving a fixed-base driving simulator. In general, model uncertainty can be divided into structured uncertainty ~e.g., parametric uncertainty! and unstructured uncertainty ~e.g., additive uncertainty due to unmodeled dynamics!. Driver model uncertainty includes contributions from: model order, parameter uncertainty, and nonlinearity @12#. In this study, the parametric uncertainty is used to represent the variation of driver behavior during a period of time. The unstructured uncertainty is used to account for unmodeled dynamics and nonlinearity of the real driver. Intuitively, higher order models can capture additional dynamic characteristics of the real driver, and can be considered more ‘‘complete.’’ If a linear low order model is used for the driver, the difference in model order will contribute to the model uncertainty. From the controller design viewpoint, the parametric uncertainty may be dealt with using adaptive control techniques and the unstructured uncertainty may be addressed using robust control techniques. The contribution of this research work is a new approach to compute the driver model with parametric and unstructured uncertainty from driving simulator data. 2 Identification of Driver Model From Simulator Data In this study it is proposed to use system identification techniques and driving simulator data to obtain a driver model and the model uncertainty. We consider a black-box driver model where the lateral deviation from the centerline of the road ~y! is treated as the input of the driver. The driver’s output is the steering wheel angle ~d!. The idea of this model is shown schematically in Fig. 1. The objective of this research is to obtain a nominal driver model (Gd) with parametric uncertainty and unstructured model uncertainty ~D! from the driving simulator data. This idea is shown in Fig. 2, where an additive model uncertainty is used. It is noted that the measured d is not completely related to the input signal y. Therefore, a disturbance term e8 is used to represent the portion of the data that cannot be included in D. In order to understand the identification results more clearly, it is helpful to examine the data in more detail.