## 4 Numerical Experiments
To perform a better analysis of our proposed optimal driving strategy for a platoon in Section 4, a certain external disturbance is applied to the leading vehicle of the platoon at 30 s, and the advantages of the optimal driving strategy in this paper are analyzed by observing the changes in the following vehicles in the platoon. The disturbance period lasts for 60 s and the simulation step is 0.1 s with the largest control acceleration and deceleration of 2 m/s\({}^{2}\) and \(-\)2 m/s\({}^{2}\), respectively. To verify the advantages of our proposed potential field-based optimization method in Section 4, the constant spacing strategy in [PERSON] (2015) and the constant time headway strategy in [PERSON] et al. (2020) are applied for comparison and analysis. Figure 11 shows the comparison results in term of velocity, acceleration and gap distance under three different control strategies. Figure 8: The velocities of the CAVs during the platoon formation process: (**a**) lateral velocity; (**b**) longitudinal velocity (scenario II). Figure 11a-c show the changes in velocities of all vehicles in the platoon under three different control strategies. The velocity tracking effects of the constant time headway strategy and the potential field-based strategy are better, while the constant spacing strategy has a larger velocity deviation, with a maximum deviation of 1.42 m/s. Figure 11d-f display the changes in accelerations of all vehicles in the platoon under three different control strategies. In the constant spacing strategy, the acceleration fluctuation changes the most, and the acceleration fluctuation of the constant time headway strategy has the best convergence effect. However, at the beginning of the disturbance, the acceleration fluctuates greatly. Figure 10: The velocities of the CAVs during the platoon formation process: (**a**) lateral velocity; (**b**) longitudinal velocity (scenario III). Figure 9: The trajectories of the CAVs during the platoon formation process (scenario III). Figure 11: _Cont._  
Figure 11: Comparison results under three different control strategies. (**a**) Velocity changes in the constant spacing strategy: (**b**) Velocity changes in the constant time headway strategy: (**c**) Velocity changes in in the potential field-based strategy; (**d**) Acceleration changes in the constant spacing strategy; (**e**) Acceleration changes in the constant time headway strategy; (**f**) Acceleration in the potential field-based strategy; (**g**) Gap distance changes in the constant spacing strategy; (**h**) Gap distance changes in the constant time headway strategy; (**i**) Gap distance changes in the potential field-based strategy. Figure 11g-i depict the change in the gap distance between each adjacent vehicle under three different control strategies. It can be found that in the constant time headway strategy, the gap distance value is generally higher than the other strategies. This is because in this strategy, the gap distance will increase as the velocity increases. This control strategy is to ensure the speed and acceleration tracking effect of the vehicle with a large traffic efficiency sacrifice. In contrast, we can find that the control optimization strategy based on the G-SPF model proposed in this paper shows obvious advantages in terms of improving traffic efficiency. In order to compare the three strategies more intuitively, we summarize the comprehensive performance of the platoon in terms of efficiency, safety and comfort under different strategies, as shown in Table 3.  
The average time headway (s/veh) represents the average headway between adjacent vehicles in the platoon that is obtained by calculating the headway based on the vehicle gap distance and velocity at each moment. Compared with the constant spacing and constant time headway control strategies, the simulation results show that our proposed method can strengthen the traffic capacity by approximately 48.8% and 26.6%, respectively.