# Topology Control of Low-Connection UAV Laser Network with Virtual Nodes
## 1 Introduction  
With the widespread application of drone technology in the military, civilian, and commercial sectors, unmanned aerial vehicle (UAV) networks are facing unprecedented challenges, such as the growing demand for transmission bandwidth and increasingly prominent data security issues. These challenges pose significant tests to the existing radio frequency communication technologies [1, 2, 3]. Laser communication technology utilizes lasers as carriers to achieve information transmission in free space, featuring high bandwidth, high directionality, low intercept rates, and low interference [2, 3, 4, 5]. These advantages demonstrate great potential for high data transmission rates, resistance to electromagnetic interference, and enhanced communication security. As a result, space laser communication technology is gradually becoming an important choice for information transmission in space information networks.  
However, the introduction of laser communication technology has also presented new issues to UAV ad hoc networks, particularly in the critical research area of network topology control. Network topology control is a crucial aspect of UAV networking, involving the construction and maintenance of an efficient and stable communication network structure in a dynamically changing spatial environment. The high directionality of laser communication demands precise alignment and tracking during the communication process, thus significantly increasing the cost of switching between communication nodes. Thisbecomes a critical issue that must be considered in the dynamic communication process among UAV nodes. Furthermore, this characteristic of laser communication renders traditional neighbor discovery processes inapplicable as they typically rely on omnidirectional signal propagation.  
Despite the significant progress achieved by many research institutions in the field of UAV laser communication technology [6; 7; 8; 9], constructing a proximity graph that is suitable for the characteristics of laser networks remains an urgent problem to be solved. Due to the high cost of alignment and acquisition in laser communication, the time-division multiplexing technology traditionally used in radio frequency communication is not easily applicable to laser communication. This means that, within a certain period, a communication module can only communicate with one other module. Consequently, the number of connections a UAV can have is dependent on the number of laser communication modules it is capable of carrying. Regarding UAV laser networks, the power and payload capacity of the UAVs themselves are limited, making it difficult to connect multiple UAVs simultaneously by simply adding more laser communication modules. This imposes an upper limit on the degree of the nodes in the neighbor graph.  
Most past researchers have focused on reducing network redundancy while attempting to maintain the overall performance of the original graph. Consequently, many methods have not effectively constrained the node degree limits in worst-case scenarios. Although researchers worldwide have achieved numerous advancements aimed at increasing the connection limits of laser communication modules [10; 11; 12], they still struggle to meet the stringent node degree requirements imposed by traditional neighbor graph planning algorithms.  
The main contributions of this paper are as follows:  
1. To address the issue of low node degree limits in laser networks, we designed a virtual node topology control algorithm (VNTC) that constrains the upper limit of the node degree to 4.
2. Sufficient conditions necessary for the operation of the algorithm on two-dimensional topological graphs are provided.
3. An analysis and resolution of the issues related to unmatched nodes and boundary conditions within the algorithm are presented, and the effectiveness of the algorithm is verified through simulations.