## 2 Materials and Methods
### Model Integration  
Considering that the vehicle dynamic model is constructed in the form of state-space equation, the driver's NMS dynamic expressed as transfer functions should be converted to the state equation. From the aspect of theoretic analysis, the n-order transfer function can be decomposed into the product of several one-order transfer functions. Then the system state variable diagram is formed in series by one-order transfer functions [25]. In this way, the HVSC state equation form the block diagram can be constructed as shown in Figure 3.  
A total of 17 state variables are defined in Figure 3.The physical sense of \(\delta_{\text{sw}}\), \(\dot{\delta}_{\text{sw}}\), \(T_{\alpha\alpha}\), \(T_{\xi\varepsilon}\), \(T_{rc}\), \(T_{\alpha\alpha}\), \(\theta_{\text{lim}b}\), \(\theta^{\prime}_{\text{lim}b}\), \(T_{\text{c}cl}\), \(T_{\text{int}}\), \(T_{\text{a}cl}\), \(T_{\text{a}cl}\), \(T_{\text{g}ot}\) and \(T_{\text{sp}}\) represents the steering wheel angle, steering wheel angular rate, arm active contraction torque, reference contraction torque, contact contraction torque, reflex contraction torque, leg motion, leg motion rate, leg contact contraction torque, leg intrinsic contraction torque, leg active contraction torque, leg GTO feedback torque and leg spindle feedback torque respectively. Noteworthily, the physical value of some state variables cannot be obtained directly from the sensor. Therefore, a state observer based on UKF is proposed to estimate these variables. The relationship between state variables and measurable variables was elaborated on in the following content [26]. First, the muscle contraction force \(F_{i}\) is deduced based on [PERSON] muscle theory as follows:  
\[ \begin{array}{ll}F_{i}&=F_{\text{ce}}+F_{\text{pe}}=F_{\text{max}}[a(i)f_{a} (\varepsilon)+f_{p}(\varepsilon)]\\ &=F_{\text{max}}[a(i)e^{-[2.7272778\times\text{ln}(\varepsilon+1)]^{2}}+0.03(e^ {\varepsilon\varepsilon}-1)]\end{array}  \tag{17}\]  
where \(F_{ce}\) represents muscle contraction force; \(F_{pe}\) infers to the elastic force; \(F_{\text{max}}\) indicates the muscle maximum contraction force; \(a(i)\) is the muscle activation; \(f_{a}(\varepsilon)\) and \(f_{p}(\varepsilon)\) infer to the active and passive contraction of the muscle; \(\varepsilon\) represents deformation degree of the muscle during contraction. Afterward, the weighted analysis method is used to calculate the arm active contraction torque \(T_{aca}\) and leg active contraction torque \(T_{acl}\) applied to the steering wheel and pedal respectively as follows:  
\[\left\{ \begin{array}{l}T_{aca}=(F_{1}n_{1}+F_{2}n_{2}+\cdots+F_{i}n_{i})/R_{a}; i=6\\ T_{acl}=(F_{1}n_{1}+F_{2}n_{2}+\cdots+F_{i}n_{i})/R_{i};i=4\end{array} \right. \tag{18}\]  
where \(n_{i}\) infers to the weight coefficient of muscle force; \(R_{a}\) and \(R_{l}\) represent the radius of the steering wheel and pedal rotation. For the arm dynamic model, the arm reflex contraction torque \(T_{rc}\) can be deduced based on \(T_{aca}\) and assist torque \(T_{as}\) applied on the steering wheel, which can be express as Equation (19):  
\[T_{rc}=T_{aca}-T_{as} \tag{19}\]  
The arm reference contraction torque \(T_{\xi c}\) and arm contact contraction torque \(T_{cca}\) can be described as follows:  
\[T_{\xi c}+T_{caa}+K_{a}(\theta_{sw}-\hat{\theta}_{sw})=T_{dr} \tag{20}\]  
\[T_{caa}=T_{sw}-T_{dis} \tag{21}\]  
where \(K_{a}\) represents the active stiffness; \(T_{dr}\) infers to the steering wheel torque; \(T_{sw}\) infers to the torque applied on the steering wheel; \(T_{dr}\) indicates the steering torque of vehicle; \(T_{dis}\) is the torque perturbation from the sensor. Figure 3: Block diagram of HVSC model.