# Quadrotor UAV Dynamic Visual Servoing Based on Differential Flatness Theory
## 1 Introduction  
The navigation of unmanned aerial vehicles (UAVs) using a vision system has found much interest during the last few decades in several fields of its application, such as the military field and civil society [1, 2], traffic surveillance [3, 4], mapping and exploration [5, 6], and agriculture [7, 8]. Visual servoing methods use visual information to control a vehicle's pose relative to specific visual targets. They are divided into two main families [9]: 3D visual servoing, or position-based visual servoing (PBVS), and 2D visual servoing, or image-based visual servoing (IBVS). IBVS directly uses image feature errors in the image plane to derive control inputs. It regulates the vehicle without reconstructing the relativepose with respect to visual targets. It therefore does not need information on the geometry of the target a priori, as in the case of PBVS. Moreover, it is easy to calculate and more robust than PBVS. The IBVS technique is a control method that guarantees the convergence of the visual features of a target toward the desired values in the image, as stated in [9]. IBVS methods may face challenges, such as significant tracking inaccuracies or total tracking failure, in situations where the motion of the target changes over time or is not accurately anticipated [10]. Predictive visual control (PVC) tries to solve this problem by incorporating model predictive control constraints [11; 12]. These constraints include the field of view (FOV), actuator output limitations, and the workspace. In [13], a nonlinear predictive controller was effectively employed to produce the desired velocity for an underwater vehicle while adhering to visibility limitations. The same approach was investigated in [14] to develop a tracking controller for UAVs. The application of the model predictive control (MPC) scheme has been observed in the context of a mobile robot [15] and quadrotor [16]. In the aforementioned scenario, the model predictive control (MPC) was employed to ensure that the visual attribute of the target remains in the intended location within the image. In the context of navigation, the IBVS system has been observed to encounter occlusion issues leading to missing feature points. To address this, artificial patterns have been utilized to predict the missing feature points and maintain the proper functioning of the system. This approach has been documented in [17]. Nevertheless, the model predictive control (MPC) methodologies are restricted to immobile targets. Furthermore, a high-performance processing stage is necessary. Predictive control is a computational process that involves solving an optimization problem at every moment in real time. This is due to the fact that predictive control requires intensive calculations. This situation may result in a substantial computational load, particularly for complex or fast systems, as occurs in our scenario. For effective tracking control, it is crucial to have knowledge of the movement of a dynamic target. This information is frequently inaccessible and challenging to anticipate. Closed-loop control employs various image characteristics to maintain the target within the field of view (FOV), as stated in [18]. Various techniques have been developed for feature extraction and matching in image processing. These include RGB-based methods [19], scale-invariant feature transformation (SIFT) [20], and accelerated robust features (SURF) [21]. Notwithstanding, these techniques exhibit constraints with respect to object detection and the assessment of the camera's motion relative to the target. Quadrotors have been subjected to vision-based optimization techniques [22] for the purpose of tracking a moving target while avoiding obstacles. However, this is only possible if the target's position is predetermined. In [23], alternative model-based optimization techniques were employed to ensure reliable detection of an unmanned aerial vehicle (UAV), but the focus of the study was primarily on utilizing image features for indoor localization instead of target tracking.