## 6 Experimental Study Using a Driving Simulator
### Evaluation Method  
The key performance indicator for the system validation is proposed in two categories. First, the evaluation indicator related to the vehicle collision avoidance performance--EAPI (Emergency Avoidance Performance Index)--was used [28]. Next, to evaluate the overall performance of the closed-loop driver-vehicle system, the driver model parameter identification method was used [25]. \(\bullet\) Emergency Avoidance Performance Index, (EAPI):  
Here, the index called EAPI is determined as the area which is integrated along the curve of steering angle with respect to the yaw rate. It is generally known that the better the vehicle handling quality, the smaller the value of EAPI [28]. \[S=\frac{1}{2}\int_{0}^{T}\left(\delta_{sw}{}^{2}+r^{2}\right)d\left(\tan^{-1} \left(\frac{r}{\delta_{sw}}\right)\right)=\frac{1}{2}\int_{0}^{T}\left(\delta _{sw}\,r-\delta_{sw}\,r\right)dt. \tag{38}\]  
\(\bullet\) Driver model steering operation 1 st-order delay time constant \(T_{r}\)[25]:  
Generally the driver model parameter is affected by the vehicle dynamics characteristics, as the driver has adaptation characteristics according to [PERSON] crossover driver model description [28]. If the vehicle has good responsiveness with respect to the steering angle, the driver can be in a relaxed mood and his/her time constant \(T_{r}\) increases. On the other hand, if the vehicle has bad responsiveness, the driver has to concentrate to control the vehicle; hence the handling quality from the driver's viewpoint deteriorates. Here, the paper will use the identified parameter in a specific driving scenario to discuss about the handling quality in a quantitative way. The driver model steering operation delay time constant \(T_{r}\) can be identified from the measured data of the lane change experiment. The procedure of the calculation of the parameter \(T_{r}\) can be expressed as follows. From Equation (36), the relationship between the driver steering wheel angle and the vehicle motion can be rewritten as follows  
\[(T_{r}s+1)\delta_{sw}(s)=h_{d}\{y_{OL}(s)-\left(y_{c}(s)+T_{p}V(s)\psi(s)\right)\}. \tag{39}\]  
Here, from the measurement data of steering wheel angle \(\delta_{sw}^{*}\), the lateral displacement \(y_{c}^{*}\), the constant vehicle velocity \(V^{*}\), the vehicle yaw angle \(\psi^{*}\), and the deviation \(e\) between the actual steering wheel angle and the predicted steering wheel angle from the vehicle motion exists as the following equation. \[e(s)=(1+T_{r}s)\delta_{sw}^{*}(s)+h_{d}({y_{c}}^{*}(s)-y_{OL}(s))+h_{d}T_{p}V^{ *}(s)\psi^{*}(s). \tag{40}\]  
Figure 18: Condition of the double-lane change test course. However, the parameters \(T_{r}\), \(h_{d}\), and \(T_{p}\) can be set to minimize this deviation, the parameter set which gives the minimum steering deviation is treated as the driver individual parameter set. Take the Inverse Laplace transformation of Equation (40), the following expression can be obtained. \[e(t)=\delta_{sw}^{*}+T_{r}\frac{d\delta_{sw}^{*}}{dt}+h_{d}(y^{*}-y_{\text{OL }})+h_{d}T_{p}V^{*}\psi^{*}. \tag{41}\]  
Next, the following cost function \(J\), as the integral square of the deviation of the steering wheel angle with respect to the predicted value, is set to identify the driver model parameters \(T_{r}\), \(h_{d}\), and \(T_{p}\). \[J=\int_{0}^{T}e^{2}dt=\int_{0}^{T}\biggl{[}\delta_{sw}^{*}+T_{r}\frac{d\delta_ {sw}^{*}}{dt}+h_{d}(y^{*}-y_{\text{OL}})+h_{d}T_{p}V_{x}{}^{*}\psi^{*}\biggr{]} ^{2}dt. \tag{42}\]  
Then, by the following calculation process, the driver model parameters \(T_{r}\), \(h_{d}\), and \(T_{p}\) are determined to minimize the cost function \(J\). \[\frac{\partial J}{dT_{r}}=0,\frac{\partial J}{dh_{d}}=0,\frac{\partial J}{d(h _{d}T_{p})}=0, \tag{43}\]  
\[\left[ \begin{array}{c}T_{r}\\ h_{d}\\ h_{d}T_{p}\end{array} \right]=-A_{driver}{}^{-1}B_{driver} \tag{44}\]  
where, the matrices \(A_{driver}\) and \(B_{driver}\) are calculated from the collected measurement data in discrete form as follows  
\[A_{driver}=\left[