# Spacing Allocation Method for Vehicular Platoon: A Cooperative Game Theory Approach
## 1 Introduction  
Cooperative control of multi-vehicles in platoon and its extended application in intelligent transportation technology are considered as efficient measures to solve nuisance to motorists, consumes less fuel, and likely causes less accidents [1]. The main control objective of the platoon is to maintain the desired space and form a pre-specified formation called spacing policy. The studies on related field reveal that the profit of vehicular platoon will be significantly affected by spacing policy [2]. Spacing policy aims to ensure a proper distance between the nearest vehicles and prevent malicious insertion of the vehicles outside the platoon. Current spacing policies, including constant distance (CD) policy, constant time headway (CTH) policy, and non-linear distance (NLD) policy are widely used to analyze the macro performance of the platoon combined with their distributed controllers [3; 4; 5]. Due to the complex physical environment and difficulties in modelling for platoon, the researches onspacing policy mainly focus on the string ability and attempt to attenuate and recover from a speed disturbance [6]. According to the use of global information or local information to make decisions, the spacing strategy can be divided into integrated spacing policies and distributed spacing policies. The integrated spacing policies aim to maximum overall benefit, and the distributed spacing policies intense to get optimal monomer benefit. However, ignoring the fairness of the benefit allocation of each vehicle will reduce the motivation to constitute the platoon. Besides, the desired profit is difficult to be modelled as explicit functions, and the solving process of the nonlinear optimal problem makes it even harder to achieve a reliable performance. Therefore, the theory of multiple-agents-system (MAS) is introduced to decoupling the interaction of the vehicles [7]. The MAS is widely used in the platoon control which derived from the research of the bionics on fish, birds and flocks [8]. Bionic motion principles are concluded from the investigation of the flocks, including collision avoidance, velocity matching and center gathering, with which the motion of the agents will achieve consistent control performance. Considering the consistency control of MAS as the optimization problem of spacing policies and fairly allocate the profit to vehicles in platoon is an effective method to address aforementioned research gap. To fill the research gap, we attempt to propose a fair spacing policy based on cooperative game theory instead of a distributed space policy. The main contributions of this paper are as follows:  
1. To evaluate the behaviors of the vehicles in platoon, we propose a flock's model according to the bionic motion principles with the information from the nearest vehicle, which can be used to achieve a longitudinal consistency control performance for the vehicle platoon. 2. A general expression of the motion controller is derived from the proposed flock's model which can ensure the local stability, string stability and traffic flow stability. 3. By modifying and applying the Sharpley value, \(\tau\) value and the average lexicographic value, the inter-vehicle spacing is fairly allocated to the vehicles in the platoon with proposing characteristic function specified by platoon's structure. The rest of the paper is organized as follows. We summered the relative literature of spacing policy and the cooperative game theory used in transportation, based on which, the limitations and difficulties of current methods are concluded in Section 2. Section 3 presents a flock's model based on bionic behaviors. In Section 4, the proposed model is considered as a profit function, and then the methodology of spacing allocation for vehicle platoon is presented based on cooperative game model. Besides, a general motion controller is derived to satisfy local stability, string stability, and traffic stability. The simulation experiments and results analysis are shown in Section 5. We conclude the paper in Section 6.