## 1 Introduction  
Unmanned Aerial Vehicles (UAVs) have shown great potential in aerial photography, plant protection, disaster relief, route inspection, and other fields [1; 2; 3; 4]. Compared with helicopters, UAVs have a better flexibility, simpler mechanical structure, and stronger maneuverability. However, the common quadrotor UAV is a typical nonlinear and dynamically unstable system, and the trajectory tracking is easily affected by internal uncertainties from the control model and external disturbances from the flight environment. Many nonlinear control methods have been implemented to solve these problems in space and time, such as back-stepping, sliding mode control, and a combination of them [5; 6; 7; 8]. The back-stepping method can enhance the adaptability and robustness of the quadrotor system, but it has the problem of over-parameterization with an increase in the instructions [9; 10; 11]. Then, the sliding mode controller in the outer loop position subsystem was developed to ensure a robust tracking performance, even under the internal uncertainty and external disturbance of the time-varying control mode [12]. However, there is a serious chattering tendency in the presence of unmodeled actuator dynamics. Therefore, their hybrid control techniques were proposed to ensure the accuracy of trajectory tracking in the case of disturbance and to improve the system stability using the Lyapunov stability analysis. The above closed-loop and nonlinear control methods work well, and they greatly reduce the control cost in practical UAV applications. However, they have the common defects of oscillation and the overshoot phenomenon, which reduce the accuracy of trajectory tracking, and long-time overshoot will cause serious problems to the physical system. To address these shortcomings, some researchers have also used neural networks to learn the quadrotor dynamics via offline or online means because neural networks have superior capabilities of self-learning and high-efficiency optimal solutions [13; 14; 15]. A novel nonlinear controller using neural networks and output feedback was implemented to learn the complete dynamic characteristic of the control system, including uncertain nonlinear terms such as aerodynamic friction and blade flapping [16]. An iterative learning algorithm that exploits the previous trajectory data was proposed to anticipate the recurrent disturbances of the system and proactively compensate for them. This approach is applied to quadrotor vehicles, and trajectory tracking can be achieved by a pure feedforward adaptation of the input signal [17]. However, these data-based control algorithms are still based on feedback control mechanisms and enhanced by reduplicative operating conditions and controlled environments. According to the above questions, the trajectory implementation of intelligent creatures inspires us and offers a possible similar solution to overcome some drawbacks of oscillation and overshoot. Intelligent creatures train themselves many times in order to be familiar with the limits of their maneuverability in different states and make a feasible trajectory planning strategy in accordance with their capability. The biologically inspired heuristic method has also been used for UAVs or the swarm control strategy [18; 19; 20]. A novel tracking control strategy that integrates a bio-inspired back-stepping controller and a torque controller is presented. It takes into account system measurement noise and robot dynamic constraints, and avoids the shortcomings of large velocity jumps and overshoot problems in conventional back-stepping control [18]. A metaheuristic swarm coordination method of UAVs used in target search is based on flocking and stigmergy to provide robust formation control and dynamic environmental information sharing, respectively. The quality of the resulting cooperation is better in terms of swarm formation, search efficiency, strategy, and scalability [19]. Intelligent animals adopt a combination of open-loop and closed-loop control modes.