# Cooperative Multi-UAV Collision Avoidance Based on a Complex Network
## 1 Introduction  
Collision is an inherent problem in unmanned aerial vehicle (UAV) systems [1; 2; 3; 4; 5; 6]. Path planning is important in performing different tasks. Therefore, the demand for the collision avoidance (CA) of UAVs has emerged. With increasing UAV cluster densities, it has become more difficult to perform multi-UAV collaborative tasks, especially if collision avoidance requirement cannot be met. Therefore, the effective planning of flight trajectories and collision avoidance among UAV flight trajectories has become critical in UAV clusters for safe and smooth operation [7]. Various conflict detection and resolution (CDR) theories with different techniques have been proposed to solve this problem. In conventional aviation, several widely used CA systems exist. For example, the traffic alert and CA system (TCAS) is recognized worldwide as an airborne collision avoidance system, and it is the last line of the CDR approach. Technological development has enabled the increase in air traffic density to be mitigated [8; 9]. Many studies regarding UAV collision avoidance have been performed in recent years [10; 11; 12]. CDR and the optimization of different resolutions have been discussed widely by many researchers and practitioners. These methods can be classified into two primary types of algorithms: Geometric and path planning. Geometric algorithms focus on analyzing the relationship between UAVs and intruders within a specific space to implement passive CA operations. Meanwhile, path planning algorithms focus on obtaining a path for an optimalconnection between the start and end points with minimal security constraints [13; 14; 15]. Dimensionality, direction selection, the number of participants, and resolutions are four key elements that should be considered for a UAV's CDR. A detailed summary of publications regarding the different methods of CA is provided in Table 1.  
Geometric algorithms exploit state information such as the location, velocity, and the heading of UAVs and intruders to geometrically perform the CA operation. [PERSON], [PERSON], and [PERSON] (2008) [16] demonstrated a typical example of this approach, in which a single resolution maneuvering logic called'vector sharing resolution' was proposed. This method calculates the subtraction of two UAVs' movement vectors in a two-dimensional space and adjusts the trajectories of the UAVs based on the shortest distance vector obtained. Another instant of this method can be found in [17] by [PERSON] et al. In contrast, this paper solves the problem of obstacles being irregular objects. A collision cone approach is employed by which the irregularly shaped moving objects can be modelled through general quadric surfaces and dynamic inversion-based avoidance strategies can be derived. The limitations of this type of method is the need for information from the intruder UAV, as well as sensitivity to noise from the input data of the sensors. Path planning algorithms include sampling-based, artificial heuristic, numerical optimization, and decoupled path planning approaches. Each method exhibits its own strength over others in certain aspects. The philosophy of sampling-based approaches is transforming the path-planning problem to obtain a suitable problem from a limited quantity of candidates that is a continuous state space. [PERSON] and [PERSON] (2017) [18] presented a method based on the closed-loop rapidly exploring random tree algorithm and three variations of it. Artificial heuristic approaches are highly advantageous during the optimization process, and typical methods include the genetic algorithm [19], particle swarm optimization [20], and artificial bee colony optimization [21]. Numerical optimization approaches rely on some geometric trajectory calculations and aim to obtain an optimal path with respect to a specific objective in the solution sense. The relevant methods include mixed integer linear programming [22], nonlinear programming [23], Dynamic programming [24], quadratic programming [25], and Pontryagin's minimum principle [26].