## 1 Introduction  
Swarm robotics is a research field of the multi-robot system inspired by the self-organizing behavior of social animals such as birds, bees, fish, and so forth [1]. Formation control is one of the essential topics of the cooperative behavior of those systems [2]. The goal is to deploy robots regularly and repeatedly within a specific distance from each other to obtain the desired pattern, and then maintain it during movement. The members in the swarm are usually homogeneous with low complexity, only equipped with local sensing and communication devices with decentralized architecture. Swarms can be used for missions such as virgin territories exploration [3], contamination detection or tracking, and disaster search and rescue [4]. We have shown a formation-based distributed processing paradigm for collaborative searching of swarms in a scanner-like manner with a moving line formation [5]. We also extended this paradigm to more general cases not only for line formation but also for V-shaped formations [6]. In those works, the moving formations are treated as a sensor network with dynamically changing positions, so that multi-dimensional based algorithms could be applied in a distributed way. In this paper, we deal with how to get those formations under the constraints of limited visual sensing and communication abilities of each swarm member. Formation forming problem is a well-studied problem in swarm robotics field. There are many state-of-the-art methods to deal with this problem. There are macroscopic collective behavior-inspired methods such as structured approaches (leader-follower [7], virtual structure [8]), behavior-based methods (finite state machine [9], potential fields [10], and consensus-based control [11]. In addition, multicellular mechanism-inspired formation control has also been developed, such as morphogen diffusion [12], reaction-diffusion model [13], chemotaxis [14], gene regulatory networks [15], etc. A more detailed review was published by [PERSON] et al. [16]. However, sensors equipped in swarms are limited not only by the sensing range but also by the field of view (FOV) [17]. Under the condition of limited FOV, the connectivity of the members cannot be maintained if the omnidirectional sensing model is still applied, thus the above formation control strategies might be invalid under this constraint. In biological research, the way geese or other big birds fly together in formations is a widely studied phenomenon [18]. Many researchers believe that those species flying in such a way can reduce the flight power demands and energy expenditure, as well as improve orientation abilities by communication within groups [19; 20]. Some other works hold the different opinion that this phenomenon is constrained by the visual factors and the formations might be a by-product of the limited field of view of the following birds during flying [21]. The members of the team are communicating indirectly based on their sensed information, which means the communication is also constrained by the FOV [22]. According to [PERSON]'s research on flying geese [23], the visual field for each eye of a flying goose is \(135^{\circ}\) with a binocular overlap of \(20^{\circ}\), as shown in Figure 1. This means the members in a swarm could only follow others in this visual field, which causes the line or V-shape formations during moving. This paper illustrates a formation forming control strategy inspired by flying geese. This work studies the V-shape formation forming control problem with limited visual field constraints of sensing and communication inspired by flying geese. The leader broadcasts the heading angle directly to the members in a specific range, while each member in this range also broadcasts the heading with some other simple statuses.