# Exploring Safety-Stability Tradeoffs in Cooperative CAV Platoon Controls with Bidirectional Impacts
## 2 Literature Review  
The exchange of vehicle dynamics information is pivotal for CAV platoon control. The most commonly used vehicle dynamics information includes velocity and spacing [10; 11; 12]. Other types of vehicle information are also considered, such as acceleration [13], traffic jerk [14; 15], visual angle [16], and electronic throttle opening angle [17; 18]. Abundant vehicle information can facilitate platoon control design to achieve better platoon performances in a coordinated manner. This research focuses on bidirectional car-following control models. Existing bidirectional models primarily depend on two prevalent types of vehicle dynamic information to maintain harmonized speeds with constant time headways: spacing, which is the distance between the target vehicle and the following vehicle, and the velocity difference between the target and following vehicles [19]. Table 1 categorizes existing bidirectional car-following control models into three categories by types of back-looking information utilized, including spacing information only, velocity difference information only and both types of information. The first category of bidirectional car-following control models utilizes spacing information only. Spacing information is widely used since it can be easily measured by sensors. For example, [PERSON] et al. extended the optimal velocity model (OVM) by introducing a back-looking optimal velocity function. The modified model takes into account one preceding and one following vehicle, and it has been shown to improve traffic stability compared to the traditional OVM model [20]. [PERSON] et al. extended the OVM model by considering the headway of multiple preceding and following vehicles. The study examined the linear stability of the modified model, revealing that it displayed dynamic properties capable of mitigating velocity fluctuations [21]. [PERSON] et al. proposed an extension of the OVM model that takes into account an arbitrary number of vehicles ahead and one vehicle following. Linear stability analysis was conducted to demonstrate the enhanced stabilizing effect [22]. [PERSON] et al. extended the full velocity difference (FVD) model by considering the driver's sensory memory and the back-looking effect [23]. [PERSON] et al. further incorporated the bidirectional FVD models with the driver's visual angle [24]. [PERSON] et al. improved the FVD model by accounting for the time-delayed velocity difference and back-looking effect [25]. [PERSON] et al. introduced a new bidirectional distance-balanced model that was built upon the Intelligent Driver Model (IDM). This model aims to balance the distance between the host vehicle and its nearest preceding and following vehicles. The authors conducted analyses on the local stability and string stability of the proposed model [26]. The second category solely utilizes velocity difference information. Models in this category are relatively rare. [PERSON] et al. were the first to propose a bidirectional car-following control model using velocity differences, taking into account both the velocity difference between the target vehicle and the preceding vehicle and the velocity vehicle between the target vehicle and the following vehicle. It was found that the local and string stability conditions improved as the weights of the forward-looking and back-looking decisions increased [27]. Research in the third category combines spacing and velocity difference information when designing car-following control models. [PERSON] et al. presented a new extension of the OVM model that considers an arbitrary number of preceding and following vehicles. The study found that the back-looking effect can help to stabilize traffic flow [28]. [PERSON] et al. proposed an extension of the OVM model that considers bidirectional visual fields and multiple anticipations. A stability analysis of the model revealed that multiple anticipations can enhance the stability of traffic flow.