# Distributed Attitude Synchronization for Spacecraft Formation Flying via Event-Triggered Control
## 1 Introduction  
In the last few years, spacecraft formation flying (SFF) has become increasingly popular, owing to its wide range of applications, such as earth monitoring [1], space-based synthetic aperture radar [2], and gravitational field measurement [3]. In addition, compared with the traditional large spacecraft, SFF can bring lots of benefits, including the lower cost involved in research and development (R&D) and launching [4], better flexibility, and higher robustness [5]. In addition, the formation control of multi-spacecraft systems has been extensively studied and many outstanding contributions for SFF have been made by researchers and scholars. For example, [PERSON] et al. [6] designed a distributed attitude control law for SFF in the context of unknown external disturbances to ensure that attitude errors cooperatively arrive at the reference neighborhood in finite time. [PERSON] et al. [7] constructed a novel distributed attitude consensus control algorithm with finite-time convergence for SFF via homogeneous theory under undirected communication graphs. [PERSON] et al. [8] investigated the optimal coordinated control method of SFF subject to collision avoidance among spacecraft and proposed optimal control algorithms on the basis of the state-dependent Riccati equation to avoid collisions and achieve optimal performance states. Moreover, many advanced control schemes for single spacecraft have been given by researchers [9], but there are still many challenges in applying them to multi-spacecraft systems. Therefore, the formation control of SFF is worthy of further study. The consensus control has received considerable attention from various scientific communities in recent years [10]. For the consensus control problem, a variety of solutions can be found in the literature. [PERSON] et al. [11] designed a feedback control lawfor multiple spacecraft systems in the case that only a certain subgroup of spacecraft have access to the main control objective. For multi-agent systems in the presence of actuator failures and unknown perturbations, [PERSON] et al. [12] addressed the fault-tolerant formation control problem under time-varying weighted topologies. [PERSON] et al. [13] designed a distributed attitude cooperative control strategy for SFF systems subject to time delays and the state errors could converge to zero asymptotically under the proposed controller. [PERSON] et al. [14] constructed two distributed attitude synchronization control algorithms for multi-spacecraft systems subject to external disturbances to achieve attitude coordination in finite time. [PERSON] et al. [15] proposed a finite-time coordinated control method for second-order multi-agent systems with disturbances to achieve the main control objectives, including collision avoidance, the compensation of uncertainties, and finite-time convergence. [PERSON] et al. [16] developed an adaptive image-based controller for robot formation systems in the context of visibility constraints to realize the system stability. It should be emphasized that the coordination controllers proposed in the literature [10; 11; 12; 13; 14; 15; 16] are needed to be continuously updated, which will consume lots of energy and computational resources. Although the electronic technology has developed rapidly in recent years, the computing resources on the spacecraft are still limited. Moreover, it is well known that energy on the spacecraft is very precious. In light of this, the constraints on energy and computation resources should be emphasized in the design of the consensus controller. The traditional method to decrease computing and energy resources is to make the digital controller take actions periodically. However, compared with event-triggered technology, this method has the disadvantages of lack of flexibility and scalability [17]. Therefore, the event-based control strategy has attracted extensive interest of experts and scholars, and numerous event-based research results are given by researchers.