Research on water-exit and take-off process for Morphing Unmanned Submersible Aerial Vehicle

This paper presents a theoretic implementation method of Morphing Unmanned Submersible Aerial Vehicle (MUSAV), which can both submerge in the water and fly in the air. Two different shapes are put forward so that the vehicle can suit both submergence and flight, considering the tremendous differences between hydrodynamic configuration and aerodynamic configuration of a vehicle. The transition of the two shapes can be achieved by using morphing technology. The water-to-air process, including water-exit, morphing, take-off and steady flight, is analyzed. The hydrodynamic and aerodynamic model of the vehicle exiting the water surface obliquely and then taking off into the air has been founded. The control strategy after morphing is analyzed and the control method is given. Numerical method is used to validate the motion model of the water-exit process. Results of simulations show the validity of the proposed model and the feasibility of MUSAV in theory.


Introduction
With the science and technology development, more and more vehicles of different kinds with different functions have appeared. Among them, amphibious unmanned vehicle, which can combine the speed and range of an airborne platform with the stealth of an underwater vehicle, has attracted the attention of many researchers, and its motion performance in single medium (water or air) and switching status process while crossing the media are the main study contents.
In 1934, Boris Petrovich Ushakov, a student engineer at a Soviet military academy, considered assembling an integral vehicle with aircraft and submarine, and it took a few years to design (Paul, 2010). In the 1970s, in order to improve the survivability of the strategic nuclear weapons, the USA put forward a scheme of large submersible aircraft, which was used to launch strategic missiles. In 2006, Lockheed's Skunk Works developed a submarine-launched unmanned aerial vehicle, i.e. the Cormorant, which can both be on a reconnaissance mission and carry missiles to attack short range targets. And in 2008, the Defense Advanced Research Projects Agency started to develop a manned conceptual design of submersible aircraft, and it is used to strike enemy special operations off the coast (Rick and Jonathan, 2010;Kathryn, 2011). At the same time, France developed an unmanned submersible aerial vehicle named "Aelius". In 2013, Naval Research Laboratory in the US released details of the first-ever launch of an unmanned aerial vehicle from a submerged submarine.
Although many reports about such multirole vehicles are published, the relevant technologies are seldom aired in public. Numerical computing methods are used to study the forces (Chu et al., 2010) and movements (Cao et al., 2012) of vehicles vertically exit the water surface (Huang and Zeng, 2000). Experiments (Zhang et al., 2012) and numerical computing methods (Yang and Stem, 2007) are used to study the interaction between vehicles and the free surface (He et al., 2012). Li et al. (2010) used theoretical model method to calculate the development laws of the added mass when a sphere enters and exits from water. Xiao et al. (2010) studied the attitude control and trajectory simulation in the process of a mine out of water. Water-exit trajectory model of unpowered missile carrier was developed and validated by the carrier model tests on the sea by Yuan et al. (2003). Dynamic modeling and motion simulation for a winged hybrid-driven underwater glider are researched by Wang et al. (2011). Wave moment near water surface was calculated by Pan et al. (2011).
Most researches focus on the evolvement process of the complex multiphase flow, flow field structure, characters of fluid dynamics and the interaction between a vehicle or object and the free water surface. There is a lack of macroscopic researches on the forces and moments of a vehicle entering or exiting the water surface.
Conventional design of an aircraft conflicts with that of a submarine, and there are huge differences between the aerodynamic configuration and hydrodynamic configuration of one vehicle. Morphing technology (Rodriguez, 2007) is one of the effective ways to solve this problem.
On the basis of widely absorbing previous research achievements, a concept of MUSAV is proposed in this paper, which can both submerge in the water and fly in the air by changing the shape and adjusting the engine's work pattern. Firstly, the structure and appropriate implementation method of MUSAV are designed. Then, build two dynamic models of exiting water surface at low speed and taking off after changing its shape in the air, and analyze its motion control. At last, the motion state of MUSAV is simulated. The simulation results show that under certain initial conditions, MUSAV can submerge, and launch itself out of water at a fixed attitude angle, and then fly in the air by changing the shape and control.

Shapes of MUSAV
Because of the difference of physical properties between air and water, the morphing technology is adopted to meet the different requirements of being driven in different medium by keeping the vehicle in different shapes.

Shape in water
Peaked arch shape whose vertex angle is 30° is designed as the head of the vehicle. The tail is designed as a linear cutting tail. The contour of the vehicle in water is shown in Fig. 1.
In Fig. 1, (1) The radius of the vehicle changed with the length l, (2) 2.2 Shape in air Compared with the shape in water, the shape in air has a pair of additional wings (see Fig. 2). The area of a single wing is 1 m 2 . NASA GA(W)-1 high-lift airfoil and NASA standard roughness are adopted (Robert et al., 1979). It is assumed that the lift and drag act directly on the vehicle's center of the gravity.

Morphing process
The realizable way of MUSAV is studied with building the theoretical models. The structure design of morphing and the parameter variation caused by morphing have been simplified. There are statements and assumptions as follows: 1) Morphing process is a process in which the shape in water turns into the shape in air by unfolding the wing and adjusting the engine's work pattern.
(2) Morphing process is instantaneous and does not cause change of the parameter of the vehicle's mass and the gravity center.

Summary of water-to-air process
The whole water-to-air process of MUSAV can be divided into three stages, as shown in Fig. 3.
Stage 1: Water-exit process  HU Jun-hua et al. China Ocean Eng., 2017, Vol. 31, No. 2, P. 202-209 203 Before the water-exit process, the vehicle forms a waterexit condition with specific inclination degree and speed by attitude adjustment. Then, it can accomplish the water-exit process by means of the inertia under the water-exit condition. The vehicle keeps the water shape in the water-exit process.
Stage 2: Morphing and adjustment process After exiting out of the water surface, the MUSAV starts to change the shape in a short time, to unfold the wings and adjust the engine's work pattern, and rapidly comes up to relatively steady state.
Stage 3: Take-off process After morphing, the vehicle does not have enough ascensional force and descends continuously because of low speed. The speed should be increased by enhancing the thrust and using control strategy, so that the vehicle can get enough ascensional force to climb timely before dropping into the water.

Motion model of the water-exit process
In the water-exit process, the vehicle's velocity is low, so the effect of air can be ignored. The vehicle is merely under the effect of gravity G, buoyancy B and the fluid force H.
When the vehicle crosses the water surface, part of it is submerged below the water, which makes it difficult to analyze the fluid force H. In order to analyze the effect of fluid force, the summation of ideal fluid effect and viscous fluid effect has been taken.
(1) Ideal fluid effect According to the theory of momentum and moment of momentum, vector and moment of ideal force can be obtained: where H i is the ideal fluid force; M i is the moment; Q f and K f are the momentum and moment of momentum respectively, which can be obtained by the added mass approach (Fossen, 1994). ω and v are the angular velocity and displacement velocity, respectively. In the water-exit process, the variation of the added mass must be fully taken into account. The present research has considered the changing added mass in the process. In addition, the variation of the added mass's change rate is taken into consideration in this paper.
Based on Eqs.
(3), (4) and the definition of the added mass, the ideal fluid force equation can be drawn below: where H ix and H iy are the ideal fluid forces in the x and y directions, M iz is the moment, v x and v y are the velocity in the x and y directions, ω z is the angular velocity, and λ is the added mass. Profile analysis method is adopted to calculate the added mass (Логвиноовч, 1969).
where ρ v is the density of the vehicle, ρ v =1.2ρ w , L is the length of the vehicle, and x a is the length of the vehicle's front part out of the water surface, as shown in Fig. 4.
The added mass λ 11 of the slender body is very small, therefore λ 11 is assumed to be zero here. At the same time, is also zero. By differentiating on both sides of Eq.(6), the change rate of the added mass can be obtained: and dx a =v x dt.
(2) Viscous fluid effect Experimental and theoretical analyses have pointed out that the motion drag coefficient of underwater vehicle is closely related to the velocity, the Reynold number and the attack angle (Michael and Jerry, 1976).
Because the vehicle's water-exit speed is low and does not vary in a large scale, the effect of Reynold number's variation can be ignored here. One assumption is made that the drag coefficient can be expressed by the product of the zero attack angle drag coefficient function and the attack angle function independently.
Since the drag has nothing to do with the attack angle's signs (positive and negative), it is an even function of attack angle. Drag coefficient can be obtained from the equation below: where k is influence coefficient, and α is the attack angle. The drag coefficient of the zero attack angle can be assumed to have a liner relation with x a .
0) The zero attack angle drag coefficient and influence coefficient k can be obtained by the numerical calculation method.
The drag force is (10) The force caused by viscous fluid and the attack angle is where H μx is the drag caused by viscous fluid; H μy and M μz are the lift and pitch moment caused by the vehicle's attack angle; ρ w is the density of water; v is the vehicle's velocity; S is the wetted area of the vehicle. Based on the force analysis above, in the vehicle's body coordinate system, the water-exit process dynamic model is The assistant equation: After the calculation, the mass of the vehicle is 1248 kg. Buoyancy B: The location of the center of gravity: The buoyancy center is Distance between the mass center and the buoyancy center is The vehicle's wet area can be calculated by the integral method: (19) Based on the moment of inertia theorem of the disc shape and parallel axis formula, the vehicle's moment of inertia can be figured out by the integral method: The vehicle's volume is

Motion model of the take-off process
The vehicle is under the effect of gravity G, lift F 1 , drag of air F d , thrust P and control moment M z in the take-off process.
The mass does not change after morphing. The lift and drag of air can be worked out by the lift equation and drag equation, respectively.
The aerofoil is a high lift aerofoil, NASA GA(W)-1, and the regularity of the coefficient varying with the attack angle is shown in Fig. 6 (Li, 2007). The attack angle α∈(-10, 20.5).
The take-off process motion model is created in the absolute coordinate system. The vehicle's state includes the absolute coordinate, velocity, inclination angle, attack angle and rotation angular velocity. The state is  where J z is the vehicle's moment of the inertia. If the initial state is given, the model equation can be solved when the control thrust P and moment M z are inputted into the model.

Morphing and flight control
5.1 Analysis of the control strategy When the vehicle exits out of the water surface and makes morphing in a certain motion state, the control is required to achieve stable flight.
(1) Morphing occasion From the perspective of energy, after the vehicle exits out of the water, the main factors affecting the flight are the speed of the vehicle and the lift. The insufficient kinetic energy of the vehicle may lead to the vehicle dropping back into the water. Therefore, in order to take off successfully, the vehicle should make morphing as soon as possible to add the thrust, increase the speed, and augment the lift. The morphing moment has something to do with the mechanical structure and work mode switch of the engine, which is not considered here. In this paper, we assumed that the vehicle makes morphing at 0.5 s after it exits out of the water.
(2) Thrust In order to increase the lift as soon as possible after morphing, the speed should be increased in time. Therefore, the thrust must keep the largest state. In this paper, we assumed that the thrust remains the same during the whole process of the control.
(3) Control after morphing After morphing, the vehicle should be controlled to takeoff easily. The vehicle needs to keep in a pull-up state which means keeping in the state of an attack angle. The larger the attack angle in the limited scope is, the larger the lift will be.
But, the attack angle should not be too large, since the attack angle maybe larger than the critical attack angle, it has the risk of stall.
In view of the stall risk of the wing, the attack angle should be kept at 19° in this paper according to the characteristics of high lifting airfoil. In addition, it is assumed that the maximum moment of control is 1000 N•m.
The larger the maximum moment is, the more control over the attack angle will be, which will avoid stall.

Flight control
For the state transition Eq. (23), the control input is the moment M z =u; the control output is the attack angle α=C out ; and the ideal control output is the ideal attack angle . Try to obtain the relationship between the control output C out and control input u, Then, Assuming that , Eq. (26) can be rewritten as: The control law can be set as: where va is the auxiliary variable of the control law. Then The error . Design va in the form of feedback linearization.
where k 1 and k 2 are both positive real numbers. Therefore, Because k 1 and k 2 are positive real numbers, then t→∞, e→0.

Computer simulations
Simulation 1, verification of the motion model of the water-exit process. The initial condition: velocity is 10 m/s, inclination angle is 45°, and angular speed is 0 rad/s. The water-exit process of a vehicle with the same shape is simulated by CFD.
In Fig. 7, from the left to the right, and the top to the bottom, the interval between every two figures is 0.1 s, and the whole time of this simulation takes 1.02 s. The upper and saturated part is air, and the lower part and light color is water in Fig. 7.
With the above motion model, the water-exit process is obtained as shown in Fig. 8.
In Fig. 8, the heavy line is the location trajectory of the vehicle's mass center, the dotted line indicates the water surface. In contrast between Fig. 7 and Fig. 8, the results simulated by two different simulation methods are nearly the same. By comparing the variation of inclination angel Fig. 7. Simulation of the water-exit process by CFD. from these two methods, the result is shown in Fig. 9, and therefore, the verification of the model is guaranteed.
Simulation 2, the initial condition: the initial angle is 60°; the initial velocity is 20 m/s; the initial rotation angular velocity is 0 rad/s. And the morphing happened 0.5 s after the vehicle exits out of the water surface totally. Before morphing, there is no thrust. After morphing, the thrust increases to 30000 N at a constant rate in 2 s. The maximal available moment of the control is ±1000 N•m. The vehicle does not have maneuvers in the yaw direction.
The simulation of the vehicle's water-exit process, morphing process and take-off process in the vertical plane is shown in Figs. 10 and 11.
The pentagram in Fig. 10 and Fig. 11 is the position of the mass center of the vehicle when the vehicle exits out of the water surface totally, while the hexagram is that when the vehicle makes morphing. Fig. 10 is the simulation of the water-exit process and morphing process, which is part of the whole process simulated in Fig. 11. The wings of the vehicle are figured out in the drawing plane, so as to highlight the difference after morphing. Actually, the wing surface is vertical with the drawing plane.
The results of the attack angle and inclination angle, absolute velocity and velocities in each direction, height of the MUSAV, control moment in the whole water-to-air process can be seen in Figs. 12-15.
According to the simulation, we can obtain some special time points.
t=0.3225 s, the vehicle exits out of the water surface, and it is marked as a pentagon in these figures.
t=0.8225 s, the morphing has happened, and it is marked as a hexagon.
t=2.0337 s, the inclination angle becomes smaller than the attack angle, as shown in Fig. 12; the vertical velocity becomes smaller than 0, as shown in Fig. 13; and the height of the vehicle reaches a maximum about 11 m, and then begins to decrease, as shown in Fig. 14. t=4.5789 s, the inclination angle becomes larger than the attack angle again, as shown in Fig. 12; the vertical velocity becomes larger than 0 again, as shown in Fig. 13; and the height of the vehicle reaches the minimum about 4 m, and     HU Jun-hua et al. China Ocean Eng., 2017, Vol. 31, No. 2, P. 202-209 207 then begins to increase, as shown in Fig. 14.
The control moment into the system is shown in Fig. 15. After morphing, the moment is minus maximum -1000 N•m for a while. Then the moment becomes a positive value at t =1.4 s.
The attack angle stabilizes around 19° after a little overshoot at t =1.5 s, as shown in Fig. 12, which shows the validity of the motion model and the control strategy proposed in this paper.
Simulation 3, Simulations under water-exit angles of 50°, 60° and 70° with different water-exit velocity are carried out, which figure out the minimum thrust for the vehicle to take off after water-exit. That is to say, under the corresponding water-exit conditions, when the thrust is over the minimum one, the vehicle can exit water successfully.
In Fig. 16, three curves show the minimum thrust needed for the vehicle to exit water. The upper, middle and lower curves present the simulation result under initial water-exit angles of 50°, 60° and 70° respectively. The left part of every curve, which is straight and horizontal, implies that under certain conditions, the vehicle will stall for the attack angle exceeding the maximum value, no matter how much the vehicle's thrust reaches. According to the results of simulations, conclusions can be drawn as below. Firstly, there is a decrease trend of three curves, which indicates that, with the same initial water-exit angle, the larger the velocity is, the smaller the needed minimum thrust to take off will be. Secondly, it is implied from the distribution of three curves that, under the same water-exit velocity, the larger the initial water-exit angle is, the smaller the needed minimum thrust to take off will be. Moreover, when the velocity is small, the impact of the water-exit angle on the minimum thrust for the vehicle is more remarkable. Thirdly, the left part of the three curves, which is straight and horizontal, shows that, under the initial water-exit angle of 50°and 60°, when the velocity is 10 m/s, vehicle can not exit water and take off. Under the circumstance of water-exit angle of 70°, at the velocity of 15 m/s, the vehicle cannot exit water and take off. Analysis above shows that, the larger the waterexit angle is, the more difficult to control the attack angle will be.

Conclusion
A theoretic implementation method of MUSAV which is accomplished by using morphing technology is put forward in this paper. The shape in the water is similar to a torpedo. That means it suits submergence in the water. While the shape in the air is similar to a plane and it suits flight in the air. The transition between the two shapes can be accomplished by morphing technology. The dynamic models of the two shapes are set up and the control method is used to study the water-to-air process of the vehicle. The whole process is simulated. The results show that the theoretically implementation method is feasible and the MUSAV is the-   oretically practicable. The motion models are suitable for studying the MUSAV and the similar vehicle.