# Exploring Safety-Stability Tradeoffs in Cooperative CAV Platoon Controls with Bidirectional Impacts
## 1 Introduction  
Platoon control aims to minimize speed variations among vehicles while ensuring consistent and secure spacing between them [1]. This approach offers a promising solution to several pressing concerns of today's road transportation due to its potential to increase highway capacity, enhance safety, and reduce fuel consumption [2]. The recent advent of CAV technologies has received much attention in platoon control, largely owing to the pivotal role of communication and information technologies, including advanced sensors, 5G network and a variety of communication protocols [34]. These technologies significantly enhance platoon safety and stability [5, 6]. Leveraging communication technology, platoon controls can be developed based on Cooperative Adaptive Cruise Control (CACC), typically comprising four components [1, 2]: (1) vehicle dynamics, especially longitudinal vehicle dynamics, which depict the behavior of each vehicle in the longitudinal direction, (2) information exchange that describes how vehicles communicate with other vehicles, including the exchanged information and information flow topology (IFT) that determines the configuration of V2V communicationlinks in vehicle platoon, (3) a controller that uses information from other vehicles in the platoon to devise control strategies, and (4) formation geometry that describes the spatial arrangement of vehicles within the platoon. Among the four components, information exchange is crucial, facilitated by advanced information and communication technologies that support different information flow topologies for effective communication in CAV platoon control [7]. Various information topologies offer both benefits and challenges to the design and analysis of multi-vehicle systems, such as predecessor following topology, predecessor-leader following topology, multiple predecessor following topology, and bidirectional topology [8]. Among them, bidirectional topology stands out as popular and extensively applied in various studies due to its simple structure. In bidirectional topology, the subject vehicle adjusts its velocity by not only following the preceding vehicle but also taking into account the dynamics of the following vehicle. CAV platoon controls employing bidirectional topology are also referred to as bidirectional car-following control models. Existing bidirectional models primarily aim to improve overall platoon stability by integrating abundant information from vehicles traveling behind. However, the incorporation of increasingly complex layers of information into these models comes with its drawbacks. One significant oversight in this pursuit of enhanced stability is the neglect of safety analysis--an essential aspect that remains under-explored. The emphasis on stability often overshadows the potential safety implications of adding complexity to control protocols. It is crucial to acknowledge that the reception of back-looking information from following vehicles can affect the dynamics of preceding vehicles, leading to significant safety concerns. Current studies are examining the tradeoff between safety and stability in automated vehicles [9], but the impact of bidirectional communication on this tradeoff is not thoroughly understood yet. Additionally, there is a lack of comprehensive investigation into the diverse effects resulting from different types of information in current research. To address these research gaps, this study introduces a novel framework utilizing the concept of phase shift to examine the influence of back-looking information on platoons considering both stability and safety aspects. Employing the proposed framework, this research analyzes how spacing information and velocity difference information affect CAV platoon safety and stability. Theoretical analysis reveals that incorporating spacing information of the following vehicle improves both platoon string stability and safety. In contrast, adopting velocity difference information enhances either safety or stability, but not both simultaneously.