## 1 Introduction  
### Control Problem of Aerial Robots  
Aerial robots have become increasingly popular in recent decades. Quadrotors, in particular, have piqued the attention of the scientific community, with several important discoveries and applications proposed and tested. Despite significant advancements, aerial robot control is still regarded as a very active field of research. Aerial robot controllers, on the one hand, need the ability to acquire, process, and calculate forces to apply to vehicle actuators in a very time-critical way. The flight controllers for aerial robots, on the other hand, should be able to resist failures and respond to changes in payload and disturbances. Flight control systems for aerial robots are usually implemented using proportional integral derivative (PID) control algorithms [1]. PIDs have proved their acceptable performance in some circumstances, such as racing drones, where fast control responses are crucial. A PID controller works close to optimally in stable settings and environments. Hence, most commercial aerial robot flight controllers use PIDs for both attitude and altitude control. However, PID controllers are unable to properly control a robot when faced with unexpected dynamics disturbances (such as variable payloads) [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. External disturbances (e.g., wind) can also reduce the accuracy of trajectory tracking by weakening attitude controller performance. The problem is that model-free controllers are unable to fully cover the complicated variations in nonlinear dynamics behavior of a quadrotor, causing the controller to lose stability and robustness [13]. This problem motivated some researchers to develop optimal and nonlinear model-based controllers to control aerial robots. Nonlinear Model Predictive Control (NMPC) is one of the most widely used optimal model-based control algorithms in many recent research works. The controller, as the name implies, uses a model of the system to forecast the future behavior of the robot in response to the current control input. A model predictive controller has some advantages over its model-free counterparts. Not only does the controller outperform its model-free equivalents in terms of control performance, but it also has the ability to take into account some constraints, which is a key element in some flight maneuvers such as obstacle avoidance [14]. Despiteits benefits over previous model-free techniques, MPC is vulnerable to failure when the prediction model of the controller does not account for fluctuations in the dynamical system under control. When it comes to controlling an aerial robot, it should be noted that the aerial robot controller needs to control both the altitude and the attitude of the robot. In order to implement a full optimal model-based controller for an aerial robot, some researchers proposed employing NMPC for both altitude and attitude controllers, while taking some measures to reduce its dependency on an accurate model of the robot. Some studies endeavored to mitigate the problem by using learning algorithms (e.g., a Gaussian process or neural networks) that actively estimate the dynamics parameters of the robot and update the prediction model in real time [15, 16, 17, 18, 19, 20]. Although the resultant topologies improved the performance of the controller after learning the dynamical variations of the system, the methods have the potential to increase computation costs. Despite the fact that the aforementioned optimal control algorithms partially managed to improve the overall performance of controllers, they need powerful and fast processors to compute the online optimization problem. In order to avoid imposing high computing costs on the system, a number of research studies proposed using linear model predictive control (LMPC) [21, 22, 23]. The advantage of LMPC is its low computation cost, as compared with its nonlinear counterpart.