## 1 Introduction  
Over the past few years, Unmanned Aerial Vehicles (UAVs) of type quadrotors or quadcopters have seen an increasing interest since their wide range of civilian and military applications. These quadrotors are considered the most complex flying machines due to many physical effects influencing their dynamics including aerodynamic effects, gravity, gyroscopic effects, friction, and inertia. However, they have advantages over conventional helicopters. Given that the left and the right motors rotate clockwise, and the front and the rear motors rotate counterclockwise, gyroscopic effects and aerodynamic torques tend to cancel in trimmed flight. Many researchers modeled the quadrotor using the formalisms of Newton-Euler [1; 2] and Euler-Lagrange [2; 3; 4]. For both methods, the quadrotor modeling is regarded as a delicate task and the model obtained using these approaches is strongly nonlinear, fully coupled, under-actuated (Six Degrees of Freedom System (6-DOF) with only four actuators) and dynamically unstable with complex behavior. In this work, we adopt the most used formalism of Newton-Euler to define the dynamics of the quadrotor. Regarding the quadrotor's control, there are several types of research done both in linear and nonlinear control methods [5; 6; 7]. For practicality, the linear controllers, especially PID (Proportional, Integral, and Derivative)/PD (Proportional and Derivative)/ PI (Proportional and Integral), are easy to design and simple to tune, which perform better in practical implementation [8]. In literature, PIDs are the most used for quadrotor control [2; 9; 10]. However, tuning the parameters of these controllers is very important to get best performances. In this scope, classical methods can be used. They include the methods of [PERSON] [11], [PERSON] [12], [PERSON] [13], Cohen-Coon, Reference Model (RM) [14, 15], and many other techniques. Nature-inspired optimization algorithms can effectively resolve complex problems compared to classical and statistical methods. Some of these algorithms proposed in the literature are Genetic Algorithm (GA) [16, 17], Particle Swarm Optimization (PSO) [18], Ant Colony Optimization (ACO) [19], Artificial Bee Colony (ABC) [20], and Cuckoo Search (CS) [21, 22]. GA is inspired by the crossover, mutation, and recombination principles of genetics. PSO algorithm is inspired by social behavior patterns of organisms that live and interact within large groups. It incorporates swarming behaviors observed in flocks of birds and schools of fish. ACO is inspired by ants' behavior in seeking food sources. The ABC algorithm is based on the natural behavior of honeybee swarm, and CS algorithm is motivated by the aggressive breeding of a bird called 'cuckoo'. The PSO method has shown superior performances. It has features such as a straightforward algorithm, rapid convergence, easy implementation, and is computationally efficient when applied to a diverse set of optimization problems [15]. In CS, immigration and environmental specifications have the advantage to help cuckoos' groups to converge and reach the best places for breeding and egg laying [21]. Another advantage of CS compared to PSO and GA is that it uses a smaller number of parameters to be tuned, which makes it more adaptable [21]. Due to these advantages, PSO and CS are still successfully applied in recent works for control problems [23, 24, 25], and PSO is especially used in tuning PID controllers for quadrotor's control [26, 27]. Therefore, regarding PSO and CS programs, there are many common points. Both use the same initialization matrices of particles in n-dimensional research space for PSO and nests with \(D\) eggs (problem's dimension) for CS. The fitness function evaluates the quality of particles and nests in the same way. Then, the velocities of displacement of particles and nests are calculated in different ways for PSO and CS, which generates differences in the convergence speeds of both algorithms.