# Distributed Attitude Synchronization for Spacecraft Formation Flying via Event-Triggered Control
## 1 Introduction
Event-triggered functions can be divided into state trigger functions [18; 19], time trigger functions [20], and dynamic trigger functions [21] according to the variables on which the trigger function depends. Time trigger functions have the disadvantages of low precision in realizing state coordination and the need for global state information of the formation system, and dynamic trigger functions have the shortcoming that it is difficult to rule out Zeno behavior, while state trigger functions are convenient for the design of the control system and physical implementation. Thus, state trigger functions have been extensively utilized in the field of consensus control for SFF. [PERSON] et al. [18] proposed two event-based control algorithms which were updated at the trigger instants of itself and its neighbors. [PERSON] et al. [19] discussed the distributed synchronization control for nonlinear multi-agent systems subject to unknown control directions and disturbances and proposed a Zeno-free event-triggered strategy to save communication resources. However, the above event-driven strategies proposed in the literature [18; 19] need to be continuously calculated in the calculation of the trigger threshold, while the continuous calculation of the event-triggered threshold consumes some resources. Scholars have given some solutions to this problem. [PERSON] and [PERSON] [22] designed an event-based controller for first-order multi-agent systems to achieve average synchronization, and the proposed event-triggered strategy did not require consecutive status information of its adjacent agents. For linear multi-agent systems under connected undirected topologies, [PERSON] et al. [23] constructed a feedback control strategy using the estimation of its neighbors' state information to realize state coordination. In addition, it should be noted that the controllers developed in the literature [22; 23] are designed for linear systems and based on feedback control technology, which means that these controllers are not suitable for SFF systems with nonlinear characteristics. [PERSON] et al. [24] proposed a fault-tolerant synchronization controller for nonlinear multi-agent systems via event-triggered control, backstepping control, and adaptive control. [PERSON] et al. [25] designed an attitude coordinated control algorithm for SFF systems in the context of limited communication resources based on sliding mode control and event-driven control. Nevertheless, there are still few research studies related to the distributed event-triggered attitude consensus control for SFF systems. Therefore, it is highly desirable to design a novel event-based controller for nonlinear SFF systems to save resources of spacecraft in the formation. In this paper, a novel distributed attitude coordination control scheme is constructed for SFF on the basis of the event-driven control method, such that state errors of SFF can reach the reference neighborhood around the origin cooperatively under the limitation of energy and computation resources. Firstly, a distributed event-based attitude cooperative controller is designed for SFF systems with limited energy and computation resources to achieve attitude synchronization. Subsequently, a novel event-triggering mechanism without requiring successive status of its adjacent spacecraft is established to further save energy and computing resources. Unlike the cooperative controllers developed in the literature [10; 11; 12; 13; 14; 15; 16], the event-driven coordinated controller does not need to be updated continuously, which greatly reduces energy and computational resources. In contrast to the event-based consensus controllers [18; 19], the event-triggering function only relies on the latest neighbors' state information, implying that no continuous calculation is required in the calculation of the trigger condition. Compared with the event-driven coordination controllers [22; 23], the event-based coordinated controller is suitable for nonlinear SFF systems. The rest of this paper is organized as follows.