# An Eco-Driving Controller Based on Intelligent Connected Vehicles for Sustainable Transportation
## 2 The Cooperative Car-Following System Based on Eco-Driving
### The Car-Following Model Based on Eco-Driving for ICVs
#### 2.3.1 The Spacing Policy for ICVs  
The car-following model focused on the influences between preceding vehicles and the following vehicle. When the velocity of the preceding vehicle changes, the velocity of the following vehicle needs to be changed simultaneously to ensure safety. The car-following model will be formulated based on the kinematics of vehicles and will further be quantitatively analyzed. Then, the optimal spacing between two vehicles and vehicular velocity will be achieved, accordingly. As shown in Figure 4, the vehicle \(i\) is the preceding vehicle and the vehicle \(i+1\) is the following vehicle. All vehicles in this model share state information through wireless communication. Compared with the traditional constant safety (CS) spacing, the constant time headway (CTH) considers the relationship between the spacing of two vehicles and the real-time velocity. In this paper, the CTH is considered as the desired spacing between the preceding vehicle and the following vehicle. The desired spacing is expressed as Equation (1):  
\[d_{\text{tar}}(t)=d_{0}+hv(t) \tag{1}\]  
where \(d_{0}>0\) is the minimum safe spacing that needs to be maintained when two vehicles are standstill, \(h>0\) is the time gap that needs to be maintained between two vehicles, and \(v(t)\) represents the velocity of the vehicle at the moment \(t\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Title** & **Byte Length** & **Contents** \\ \hline VehID & 1 & Vehicular identification number \\ VehLoc & 2 & Position \\ VehDis & 2 & Spacing \\ VehVel & 2 & Velocity \\ VehAcc & 2 & Acceleration \\ Time & 4 & Timestamp \\ Angle & 2 & Front steering angle \\ \hline \hline \end{tabular}
\end{table} 
Table 1: V2X communication protocols of the cooperative car-following system. Figure 4: The spacing policy for ICVs. 2.3.2. The Fuel Consumption and Emission Model for ICVs  
A fuel consumption and emission model is very important for evaluating the effectiveness of the eco-driving controller, which can be estimated by velocity and acceleration [25] as in Equations (2) and (3):  
\[C(t)=\alpha+\beta_{1}P_{T}(t)+\left(\beta_{2}ma^{2}(t)v(t)\right)_{a>0} \tag{2}\]  
\[P_{T}(t)=\max\Bigl{\{}0,d_{1}v(t)+d_{2}v^{2}(t)+d_{3}v^{3}(t)+ma(t)v(t)\Bigr{\}} \tag{3}\]  
where \(C(t)\) denotes the instantaneous fuel consumption, \(\alpha\) stands for the idle fuel consumption, \(\beta_{1}\) and \(\beta_{2}\) are constant efficiency factors, \(P_{T}(t)\) indicates the total power of the vehicle,\(m\) is the mass of the vehicle\(d_{1}\), \(d_{2}\) and \(d_{3}\) are resistance coefficients, and \(a(t)\) is the acceleration of the vehicle at the moment \(t\). The real-time emission rate of an ICV can be expressed by the measure of effectiveness (MOE) [26; 27; 28]. [PERSON] et al. [29] presented that the real-time MOE of a vehicle at moment \(t\) is a function of the real-time velocity \(v(t)\) and acceleration \(a(t)\), which can be expressed as Equation (4):  
\[\ln(MOE_{e})=\sum_{i=0}^{3}\sum_{j=0}^{3}(K_{i,j}^{e}\times v(t)^{i}\times a(t )^{j}) \tag{4}\]  
where \(MOE_{e}\) is real-time emission rate, \(K_{i,j}^{e}\) represents the model regression coefficient for \(MOE_{e}\), \(i\) is the power exponent of velocity, and \(j\) is the power exponent of acceleration. 2.3.3. The Eco-Driving Controller for ICVs  
We define \(\Delta r(t)\) and \(\Delta v(t)\) as the current spacing and velocity difference between the \(i\)-th vehicle and its preceding vehicle; the formulation of the current spacing and velocity difference can be expressed as Equations (5) and (6):  
\[\Delta r(t)=r^{i-1}(t)-r^{i}(t) \tag{5}\]  
\[\Delta v(t)=v^{i-1}(t)-v^{i}(t) \tag{6}\]  
where \(r^{i}(t)\) and \(r^{i-1}(t)\) represent the displacement of the \(i\)-th vehicle and its preceding vehicle, and \(v^{i}(t)\) and \(v^{i-1}(t)\) represent the velocity of the \(i\)-th vehicle and its preceding vehicle.