## 4 Experiments
### Integrated Longitudinal Navigation  
Algorithm 5 depicts the integrated longitudinal control system for the implementation of GLOSA/RBS/EAD. The results of said algorithm are presented in terms of navigation success rate and power regeneration. Both generated control methods are based on empiric and expert knowledge. A fixed-step solver was selected with different sampling times for the physical elements \((t_{s})\) and the control methods \((t_{Ds})\) (Table 3). The rule- and FIS-based controllers were tested and validated in a variety of initial speeds and initial light status time. The complete performance data of the rule- and FIS-based longitudinal navigation systems can be found in Table 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Notation** & **Default Setting** \\ \hline Initial pose [m] & \(X_{i}=[x_{i},y_{i}]\) & \([0,0]\) \\ Initial steering angle [rad] & \(\delta\) & 0 \\ Initial velocity [m/s] & \(\dot{X}_{i}=[\dot{x}_{i},\dot{y}_{i}]\) & min: \([0,0]\) \\  & & max: \([13,0]\) \\ Goal pose [m] & \(X_{f}=[x_{f},y_{f}]\) & \([300,0]\) \\ Green light duration [s] & \(t_{Lg}\) & 16 \\ Yellow light duration [s] & \(t_{Ly}\) & 4 \\ Red light duration [s] & \(t_{Lr}\) & 20 \\ Initial light & \(L_{s}\) & \(L_{s}\in[t_{Lg},t_{Ly},t_{Lr}]\) \\ Vehicle sample time [s] & \(t_{s}\) & 0.001 \\ Rules and FIS sample time [s] & \(t_{Ds}\) & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Environment parameters.  
Figure 7: Road layout.  
The rule-based system successfully completed 96.43% of the tests. The cases in which the intersection was not successfully crossed were due to extreme situation such as the following: The vehicle was traveling at very high speeds at the _approaching_ zone of the intersection and the status of traffic light was _green_. Then, there was not enough road to decrease the longitudinal speed and make a stop during the sequence change to _yellow_ and _red_. The fuzzy system had a similar success rate to the rule-based, 95.9%. The performance in terms of speed and acceleration of both control systems is comparable. Likewise, navigation complies with comfort as the acceleration never surpasses the \([-9.6,4.905]\) m/s\({}^{2}\) interval. Completion time is consistent with the the longitudinal velocity and throttle.  
```
1:Initialize the control methods mentioned in Section 3
2:Define ego vehicle and environment
3:Start V2X communication
4:for\(t=0,1,2,\dots,T\)do
5: Retrieve SPaT data
6: Retrieve pose data
7:if navigation = rules then
8: Compute selected \(\tau_{norm}\)
9:else if navigation = FIS then
10: Compute \(X_{r}\) and \(\dot{x}_{norm}\)
11: Fuzzify crisp values
12: Use knowledge base according to \(L_{s}\)
13: Defuzzify linguistic value
14: Compute selected \(\tau_{norm}\)
15:endif
16: Apply a \(\tau_{max}\) gain
17: Input the \(\tau\) setpoint to the electric motor
18: Apply the motor torque to the vehicle powertrain
19:endfor
```  
**Algorithm 5** Integrated data acquisition and control algorithm for the connected electric vehicle  
Three samples of the performed tests on rule- and FIS-based controllers are presented: one for \(L_{s}=\) green with starting time \(t=0\) s and initial speed \(\dot{x}_{i}=0\) m/s (Figure 8), another one for \(L_{s}=\) yellow with starting time \(t=0\) s and initial speed \(\dot{x}_{i}=5\) m/s (Figure 9), and, finally, for \(L_{s}=\) red with starting time \(t=15\) s and initial speed \(\dot{x}_{i}=11\) m/s (Figure 10). The samples are evaluated with the pose \(X\) and velocity \(\dot{x}\) metrics. The pose plot depicts the world-based road in meters for \(x\) against time. It also shows the position of the intersection and the current status \(L_{s}\) of the traffic light. The velocity plot illustrates the velocity behavior of the CEV through time. Each test is described in the next paragraphs.