## 1 Introduction  
Fickle driving behaviors can easily lead to increased carbon emissions and energy consumption [1], which then becomes a source of global warming and the greenhouse effect. In order to build a eco-friendly transportation system, the application of electric vehicles and advanced driving strategies is necessary [2]. In this case, energy efficient driving, also known as \"eco-driving\", is an important way to achieve energy conservation and emission reduction for vehicles [3]. It is usually implemented by avoiding sudden acceleration and reducing idling time [4], whereas frequent acceleration/deceleration, slow movements, and idling are the main factors affecting vehicular energy consumption. Generally, both freeway [5, 6] and signalized intersections of urban roads are the primary scenarios for eco-driving [7, 8], but the intersection scenario is more challenging because of the uncertainty of the changing signal phase and the evolving road traffic. Traffic signals and vehicle queues impose spatial and temporal constraints on the movement of the vehicle needed to be controlled (i.e., the ego vehicle) [9]. However, with the support of advanced vehicle-to-infrastructure (V2I) communication and vehicle-to-vehicle (V2V) communication, the uncertainty can be attenuated to help the vehicle make better decisions to cross the conflict area [10]. Scholars have presented many methods to realize eco-driving in the proximity of signalized intersections. More specifically, most of the existing works utilize signal phase and timing (SPaT) information so that the ego vehicle can achieve the energy-saving goal [11]. The SPaT data acquired by the ego vehicle through V2I communication includes the current phase and the phase changing time, which can guide the vehicle to adjust its acceleration to avoid a red light. Leveraging the SPaT data, the majority of previously proposed studies obtain the control law of the vehicle by formulating an optimal control problem [12; 13; 14]. More specifically, [PERSON] and [PERSON] [15] reported a multi-objective adaptive cruise control (ACC) system to reduce idle time and fuel consumption by formulating an optimization-based control algorithm. [PERSON] et al. [16] considered the powertrain dynamics of a CV and solved the eco-driving problem numerically by combining the multi-stage driving rule and the Dijkstra algorithm to get an approximated optimal trajectory. [PERSON] et al. [17] introduced a connected and automated vehicle (CAV)-based method targeted for a signalized corridor scenario. The CAVs in their paper can receive SPaT and serve as leaders or followers in a string to achieve cooperative eco-driving. [PERSON] et al. [18] put forward a framework for CV passing through semi-actuated signalized intersections. They applied a simple algorithm to predict the signal changing time with the premise that the logic of signal timing is known, so the trajectory of the ego vehicle can be planned. [PERSON] et al. [19] also proposed a SPaT-based trajectory planning approach, which was designed in a modular and scalable fashion. They carried out a series of comprehensive sensitivity analyses to explore the fuel-optimum configuration of the traffic phase and system penetrating rate. Moreover, [PERSON] et al. [20] built a queue discharge prediction model and controlled the ego vehicle according to the queue estimation results. Dynamic programming (DP) and model predictive control (MPC) are used to design the general speed profile of the vehicle and compute the explicit control solution, respectively. Besides, some researchers extend the control framework to the platoon-based situations, which also utilized SPaT data to further reduce the energy consumption of the vehicles [21; 22]. In addition to these optimization-based methods, some rule-based methods are also implemented, aiming at reducing the computation complexity. In general, the rule-based frameworks divided the running of CVs into several categories with regard to vehicular position and traffic signal status [23; 24].