## 2 Configuration Design and Problem Formulation  
### Variable-Sweep Configuration Design  
Due to the significant differences in physical properties between the two fluids, water and air, it is difficult to explore how to solve the problem of taking into account both aerodynamic and hydrodynamic shapes, as well as drag reduction during the water-entry process. So, how can the requirements of lift increase in the air and drag reduction underwater be met simultaneously? At present, the overall configuration of the HAUV mainly follows the traditional fixed-wing or multi-rotor design form, each with its own advantages and disadvantages. Creatures in nature provide inspiration to people [5]. As shown in Figure 1, the kingfisher constantly reconfigure its wings when plunge-diving [6], folds partially at the beginning of diving and completes the full folding of the wings before entering the water. A detailed description of the stages during which kingfishers dive into water to hunt can include three stages: aerial descent, impact entry water and underwater diving. The final stage of falling in the air and the initial stage of water immersion are shown in Figure 1, which are the complex stages. They not only need to protect themselves from damage of water impact force, but also ensure the accuracy of hunting. Therefore, kingfisher's wings and water-entry strategy are very important, which provides an important bionic reference for this research. Referring to the process of kingfisher, boobies and garnets contracting their wings and entering the water to prey [7], the idea of a variant structure of HAUV is to change the overall configuration actively based on the characteristics and navigation requirements of different media, meeting the requirements of reducing the impact of water on the wing during trans-media locomotion simultaneously. The morphing aircraft also disposes of the single-flight mode of the traditional aircraft, and it can change its shape configuration in an instant according to its flight state requirements to achieve the maneuverability required by different flight mission stages [8; 9]. [PERSON] et al. [10] of MIT Lincoln Laboratory in the United States fabricated the \"Project Gannet\" with a wing-folding mechanism and completed an experiment of the air to water trans-media process of splashing into water. [PERSON] et al. [11] adopted a method of variant sweepback wing in a wide range to overcome the challenges in structural design. However, the changes in inertia force, moment of inertia, position of center of mass, etc. brought by the process of variable sweep, as well as the changes in the center of buoyancy and added mass during the process of water entry, bring challenges to the control of HAUVs. The single-control strategy of \"controlled air flight process and non-controlled water entry process\" proposed by Air Force Engineering University is far from enough for the aircraft to ensure the stable navigation of the trans-media locomotion [12], and it is necessary to consider the controlled way to complete the water-entry process. Different shapes affect the implementation of HAUVs in different mission profiles from the aspects of structural strength, water entry and so on, such as the British Imperial College's imitation booby paddle propulsion [13], the fixed-wing HAUV eagle ray [14] flight-tested by the University of North Carolina in the United States, the Delta-Wing UAV [15] of Johns Hopkins University, the UAUV Manta ray [16] and Nezha [17] of Shanghai Jiaotong University and the flexible anamorphic amphibious vehicle represented by the bionic flying fish [18]. Above are multi-mode vehicles of the air to water transition. In contrast, it is more difficult to control the flexible deformed vehicle in the complex fluid  
Figure 1: The plunge-diving segments of a kingfisher [6]. environment, and the bird-like HAUV rapid direct entry process has higher maneuverability, which is more suitable for some emergency operations.