Aerospace Science and Technology 53 (2016) 241–251
Contents lists available at ScienceDirect
Aerospace Science and Technology
www.elsevier.com/locate/aescte
Energy-optimal path planning for Solar-powered UAV with tracking
moving ground target
Yu Huang, Honglun Wang ∗, Peng Yao
School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China
a r t i c l e i n f o a b s t r a c t
Article history:Received 14 January 2016Received in revised form 3 March 2016Accepted 29 March 2016Available online 1 April 2016
Keywords:Solar-powered Unmanned Air Vehicle (SUAV)Energy-optimal routeIntegrated modelTracking targetReceding horizon control (RHC)
This paper presents the novel use of receding horizon control (RHC) with particle swarm optimization (PSO) to generate the energy-optimal trajectories for Solar-powered Unmanned Air Vehicle (SUAV) with the mission of target tracking. Firstly, an integrated model is presented that accounts for the couplings, such as kinematics, energetics and mission. The model can formulate the relationship between the aircraft’s position or attitude and the solar time or angle at anytime and anywhere in the world. Next, the mission of tracking moving ground target is studied in this paper, which is unique relative to past work about the SUAV. At the same time, to collect more energy and track the moving ground target, the optimization method of RHC with PSO is used here. To evaluate optimization performance, some performance indexes are put forward, and the definitions of them are given. Finally, several numerical simulations demonstrate that this method is feasible and flexible to generate the energy-optimal route for solar-powered UAV online with tracking ground moving target. The analysis of simulations results indicates that it’s possible to carry out the task of tracking maneuvering target for a longer time for SUAV.
In recent years, researchers have increasingly focused on im-proving the endurance performance for the HAVE/UAV (High Alti-tude Very-long Endurance/Unmanned Air Vehicle). And Solar-pow-ered UAV (SUAV), e.g. Sky Sailor and Helios, has proved to be an effective solution with high energy utilization efficiency. In Ref. [1], a solar-powered helicopter prototype is designed and developed. It was equipped with solar cell on top of its wings, and the con-sumed energy by the aircraft can be derived from the solar cell and battery. In [2–9], the application of optimization techniques plays a decisive role in increasing the required energy utilization efficiency for SUAV. However, there are still some big challenges. For example, a suitable mathematical model is difficult to obtain, which can show the relationship between the attitudes of aircraft and the solar radiation intensity at any time and any place. In addition, it is challenging to generate the energy-optimal target-tracking trajectories, as there are some complex couplings among SUAV aerodynamic model, the solar energy harvesting and the mis-sion constraints.
There has been great progress in the recent studies on the solar powered aircraft. In Ref. [10], the research progress about photo-
voltaic cells, rechargeable batteries, maximum power point track-ing and so on for aircraft has been reviewed, and some guidance principles for designers in the design of UAVs are also provided. A review of the general history and existing literature on the anal-ysis and design of solar-powered vehicles and trajectory planning is provided in [4,5,8,9,11–19]. In [20], implications of longitude and latitude on the size of solar-powered UAV have been studied. It is concluded that solar-powered UAVs can be utilized more effec-tively in the places closer to the equator, where smaller and lighter solar-powered UAV can be designed. Spangelo et al. [5] put forward a method to plan a smoother and energy-optimal path in a three-dimensional space. In [21], an active power management method for path planning has been investigated. The usefulness, advan-tages, and disadvantages of this method over a passive method are analyzed. To fulfill the power requirement with weight con-straint of rechargeable batteries, the method of energy stored by gravitational potential for solar-powered aircraft has been put for-ward in [22,23]. And the equivalence of gravitational potential and rechargeable battery for aircraft on energy storage has also been analyzed.
However, for the definition of energy collection model, the pre-vious studies usually assumed that the solar position and radiation is invariable and known. Consequently these models may not cor-rectly reflect the genuine relationship between solar and SUAV dur-ing the long-time flight. In addition, the SUAV must be designed
242 Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251
Fig. 1. Overall view about sun and aircraft.
based on executing the variety of required missions, and the typ-ical tasks include the intelligence, surveillance and reconnaissance missions. But in most of literatures such as [3,16,22,23], the op-timal path planning of solar aircraft is only based on the simple mission such as flying from the start position to the final position. The energy-optimal path is planned off-line in known static envi-ronments, and it may be inapplicable to the dynamic tasks e.g. the target tacking. To the best of our knowledge, the receding hori-zon control (RHC) has been used and proved to be an efficient on-line optimization method in a dynamic environment, which is based on the simple idea of repetitive solution of an optimal con-trol problem and state updating after the first input of the optimal command sequence [24,25].
Based on the above analysis, to achieve the mission of tracking moving ground target for the SUAV for a long time, an integrated model is presented and the energy-optimal path planning with RHC with PSO solver is studied. The simulation results show that it’s possible to carry out the task of tracking target for a longer time for SUAV, with the advantages of simple principle, high com-putation efficiency and good real-time performance. This paper has the following contributions.
First, by analyzing the relationship between the aircraft’s at-titude and the solar angle, an integrative model is presented, by which the radiation on the SUAV’s surface can be calculated at any-time and anywhere in the world.
Second, the method of RHC with PSO solver is utilized here, to plan the on-line energy-optimal trajectory of SUAV for tracking ground moving target.
Finally, an important conclusion has been drawn that it’s pos-sible to carry out the task of tracking target for a longer time for SUAV with the right conditions, e.g. the sufficient solar radiation and the reasonable speed of target.
2. Problem formulation
In this section, the model and multiple constraints of SUAV are presented. The integrated model of the aircraft kinematics and en-ergetics, the constraints consisting of maneuvering patterns, and the airborne electric-optical pod model are formulated, by refer-ring to literatures [3,23,26–31].
Fig. 1 shows the overall view, including the composition of sun, earth, target and aircraft. All their information about posi-tion and attitude is expressed in the navigation frame (P-NED in Fig. 1) which has its origin at the location of the navigation sys-tem, point P , and axes aligned with the directions of north, east
and the local vertical (down). The computational rules of solar an-gle are referred in [31], and the definitions of axes and notation are used the same with Ref. [30].
2.1. Modeling
2.1.1. Aircraft kinematic modelIn this paper, the wind axes system is used for SUAV. To sim-
plify the problem, the aircraft is assumed to fly in still air at a constant altitude with the bank-to-turn control scheme, and the path angle is zero. Hence, aircraft kinematic model is as follows:
dx
dt= V cosψ (1)
dy
dt= V sinψ (2)
dψ
dt= g tanφ
V(3)
where x is the value of N-axis, y value of E-axis, V is the speed of aircraft, ψ the yaw angle, α the angle of attack, g the constant of gravity, and φ is the bank angle.
2.1.2. Solar radiation modelSolar thermal energy can be converted into the electric energy
of UAVs by photovoltaic cell. Solar irradiance, I (W/m2), is the rate at which radiant energy is incident on a unit surface. The sun’s radiation is subject to many absorbing, diffusing, and reflecting effects within the earth’s atmosphere. The extraterrestrial solar ra-diation perpendicular to the horizontal surface may be calculated by the following approximate relationship:
I = I0
(1 + 0.034 cos
2πnday
365.25
)2
(4)
where I0 is the solar constant, and nday is the number of days (start from January 1 as 1).
In this work, the terrestrial solar radiation is calculated with ASHRAE Clear Sky Model in [31]. This is a simple statistic model which is developed based on a large number of simulations us-ing sophisticated spectral simulations and validating with ground based measurements, which is widely used in the world. This model is reasonable that the radiation on the wing’s is calculated, when the SUAV flies in the stratosphere with almost completely cloudless sky. The model is described as follows:
Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251 243
Ih = Ib sinαe + Id (5)
Ib = Ie−τbmbr (6)
Id = Ie−τdmdr (7)
b = 1.219 − 0.043τb − 0.151τd − 0.204τbτd (8)
d = 0.202 + 0.852τb − 0.007τd − 0.357τbτd (9)
mr = 1
sinαe(10)
where
Ih: solar radiation on a horizontal surface;Ib: beam normal irradiance per unit area normal to the sun rays;Id: diffuse horizontal irradiance per unit area on a horizontal sur-
face;mr : air mass ratio;τb, τd: beam and diffuse optical depths, the values of which can
be got by looking up table and interpolation;b,d: beam and diffuse air mass exponents;αe: the elevation angle of the sun.
In practical applications, a rough estimate has been used for calculating the average value of solar radiation on the surface earth. Assuming that the radiation is equal in all directions, the flux of the radiation will be the same. If IT is the total solar radia-tion output at a distance l from the sun’s center, the radiation flux per unit area at a distance l is represented by Q (l), then the total radiation is equal to 4π l2 Q (l). Hence we can obtain:
Q (l) = IT
4π l2(11)
Pe = Q (l) × Se
Sb(12)
Se = πr2 (13)
Sb = 4πr2 (14)
According to Eqs. (11)–(14), we can infer:
Pe = IT
16π l2(15)
where Se is the sectional area; Sb is the area of earth’s surface; r is the radius of the earth; Pe is the average radiation on the earth’s surface (about 340 W/m2).
It should be noticed that, all these calculations assume that the earth is perfectly spherical without any atmosphere and revolves on a circular orbit without eccentricity.
In this paper, the solar radiation calculation rules are used as follows. The average radiation on the UAV’s surface is subject to the attitude angles of SUAV, solar azimuth and zenith angle.
According to literature [31], solar azimuth and zenith angle at any time of a day are described as follows:
where αs is the azimuth angle of the sun; αe represents the eleva-tion angle of the sun; nlat is the latitude; δ is the declination angle of sun; ω(t) is the hour of sun, and tlocal is the current hour of the day.
Fig. 2. Solar angle and attitude of aircraft in the navigation frame.
We assume that the wing configuration is flat and the dihedral angle is zero. The pitch angle is small when the solar aircraft flies in still air at a constant altitude in this paper, and the effect of energy collection power on the UAV’s surface due to pitch angle is negligible. Therefore, the incidence angle of the sun rays upon the solar cells satisfies with the expression as follows.
In Fig. 2, o′bx′
b is the shadow of obxb in the horizontal plane of earth. o′
b N ′E ′ is translated from P-NED. ψa is the tilt angle of air-craft. i is the incident angle of the solar radiation for the wing’s surface (angle between sun rays and the normal to the wing’s sur-face). We can obtain:
where ρr is the ground reflectance factor. The radiation on the UAV’s surface, Puav, is calculated as follows:
Puav ={
P s(λ) the accurate calculation
Pe cos(λ) the rough estimate(23)
2.1.3. Energy harvesting modelThe solar cells are mounted on the top side of the wings of
aircraft and gain solar energy from the sun shining on the cells. The power produced by the photovoltaic panel is:
P in = ηsolSPuav (24)
where S is the total surface area of the wing, ηsol is the efficiency of the solar, and P in is the total power. The value of ηsol can be adjusted in accordance with the ratio of full wing’s surface covered by solar cells.
In a daytime interval [t0, t f ], the energy collected by the air-craft is:
E in(i) =t f∫
t0
P indt (25)
2.1.4. Energy consumption modelConsumption of aircraft mainly contains standard lift, drag and
propulsion models assuming quasi-static equilibrium flight [3]. Consumption of propulsion, Pout(V , φ), is defined:
244 Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251
Pout(V , φ) = TV
ηprop(26)
T = D (27)
D = 1
2ρV 2SCD (28)
C D = C D0 + KC2L (29)
K = 1
επ Ra(30)
Because of aircraft flying in still air at a constant altitude, we can infer L cos φ = mg and L = ρV 2SCL/2. Hence CL satisfies:
CL = 2 mg
ρV 2 S cosφ(31)
T is the thrust of the aircraft, ηprop is the efficiency of the pro-peller, D is the drag of the aircraft, C D is the parasitic drag, K is the aerodynamic coefficient, Ra is the aspect ratio of the wing, ε is the Oswald efficiency factor, L is the lift of the aircraft, and CL is the coefficient of lift.
In a daytime interval [t0, t f ], energy consumption of aircraft is
Eout(t0, t f ) =t f∫
t0
Pout(V , φ)dt (32)
2.1.5. Airborne electric-optical pod modelThe airborne electric-optical pod model is used to localize and
trace target with electric-optical sensor. When the attitudes of air-craft are varying, the view angle of electric-optical sensor remains unchanged.
Aircraft’s position (xb, yb, zb) and target’s position (xc, yc, zc)
in earth coordinate system are shown in Fig. 3. In this work, the electric-optical sensor is assumed to be installed in the center of gravity of UAV, and aircraft’s position (xb, yb, zb) is the center of UAV’s gravity. The coordinate point (xo, yo, zo) is the planar pro-jection of the aircraft’s position in earth coordinate system. Then, the projection (xo, yo, zo) is satisfied with equations (33)–(35)
xo = xb (33)
yo = yb (34)
zo = zc (35)
And the distance between UAV and moving target is described as follows:
ltarget =√
(xb − xc)2 + (yb − yc)2 + (zb − zc)2 (36)
The field of view ϑ is described as follows:
ϑ = arccosH
ltarget(37)
H = zb − zc (38)
2.2. Multiple constraints
2.2.1. Surveillance taskTo achieve the mission of tracking moving ground target, the
distance ltarget and the angle of view ϑ should be satisfied with the following constraint equations:
ltarget ≤ Lmax (39)
ϑ ≤ ϑmax (40)
where Lmax is the maximum detectable range of airborne electric-optical pod; the value of ϑmax represents the maximum angle of view of electro-optical pod on aircraft.
Fig. 3. Aircraft tracking moving ground target in the navigation frame.
2.2.2. Dynamic constraintTo maintain the stability of vehicle, the two control inputs of
aircraft including the velocity and the bank angle, should satisfy the following constraints:
Vmin ≤ V ≤ Vmax (41)
|φ| ≤ φmax (42)
where Vmin is the minimum level flight speed, Vmax the maximum level flight speed and φmax the maximum roll angle. In general, they are determined by the flight vehicle performance. However, referring to literature [3], Vmin can be set to Vminpower so that air-craft flies at the minimum power.
Vminpower = 4
√4K (mg)2
3C D0ρ2 cos2(φ)
(43)
3. RHC with PSO for energy-optimal route planning
3.1. PSO
Particle Swarm Optimization (PSO) was first intended for simu-lating social behavior, as a stylized representation of the movement of organisms in a bird flock or fish school. The algorithm has the advantage of simple principle and it can be observed to be per-forming optimization [32].
PSO is a metaheuristic method as it makes few or no assump-tions about the problem being optimized and can search very large spaces of candidate solutions. More specifically, PSO does not use the gradient of the problem being optimized, which means it is not required by PSO that the optimization problem be differentiable as is required by classic optimization methods such as gradient descent and quasi-Newton methods. PSO can therefore be used on optimization problems that are partially irregular, noisy, and changeable over time, etc.
It is demonstrated that PSO can find better results in a faster, cheaper way compared with other methods [24]. In this work, PSO is used for searching optimum value in given space at every step. The PSO algorithm is described as
v j+1(k,n) = w v j(k,n) + c1r1(0,1)(
p jpest(k,n) − x j(k,n)
)+ c2r2(0,1)
(g j
pest(k,n) − x j(k,n))
(44)
x j+1(k,n) = x j(k,n) + v j(k,n) (45)
k = 1,2, . . . , Np
n = 1,2, . . . , Dnum
Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251 245
Subject to
a j ≤ x j(k,n) ≤ b j (46)∣∣v j(k,n)∣∣ ≤ |b j − a j| (47)
Dnum = NvarN (48)
where Np represents the number of particle population, the value of which should be chosen by considering complexities and diver-sities of optimization problem, and computational time at same time. The bigger Np is, the longer time PSO costs. Dnum repre-sents the search space dimension. Nvar represents the number of control variables in RHC about aircraft kinematic model. N is the length of future control sequence in RHC. r1(0, 1) and r2(0, 1) are two independent random numbers within the range [0, 1]; c1 and c2 are two learning factors; a j and b j are the upper bound and lower bound of particle position. In this paper, each particle repre-sents a possible solution to the constrained optimization problem and results in a specific value of the objective function.
3.2. RHC
The RHC method based on PSO is adopted in this paper. RHC is an optimizing control algorithm within limited time domain, where the future state of the controlled plant could be predicted using the prediction model and optimized in receding horizons [6]. It has been proved to be more successfully optimized online in a dynamic environment, which is based on the simple idea of repet-itive solution of an optimal control problem and state updating after the first input of the optimal command sequence [24]. The main idea of RHC is the online receding/moving optimization. It breaks the global control problem into several local optimization problems of smaller sizes, which can significantly decrease the computing complexity and computational expense. Based on the updated information, the UAV will optimize the local paths with the regular horizon by PSO. Then the results are executed. The above steps repeat until the mission ends.
The process of RHC method is as follows. At time k, suppose that u[k : k + N − 1] = [u(k), · · · , u(k + N − 1)] is the future control sequence of length N , x(k) is the state vector, and J (x(k), u[k :k + N − 1]) is the objective function by evaluating the effects of the future control sequence. The optimal control sequence u∗[k :k + N − 1] is obtained by minimizing the objective function:
minu
J = J(x(k), u[k : k + N − 1]) (49)
Given the accuracy of the prediction, only the first term i.e. u∗(k) is executed, and the other terms i.e. u∗[k + 1 : k + N − 1]are taken as the initial guess of control inputs for the next step. During the execution, the new control sequence for the next step is planned. And the planning time should be less than the execu-tion time.
For the definition of total objective function, the control ob-jective function Jc and the reconnaissance object function J r are considered at the same time:
J(x(k), u[k : k + N − 1]) = Jc + J r (50)
3.2.1. Control objective functionThe control object is to obtain the total energy as much as pos-
sible. However, considering Eq. (49), the value of the total energy must be multiplied by −1 as follows
Jc = −ζ1
k+N−1∑i=k+1
�t × (P(i)in − P(i)out
)(51)
where, ζ1 is the weight coefficient, the value of which will be set depending on the actual problem. �t the time step; P(i)in and
P(i)out are the aircraft’s energy harvesting power and energy con-sumption power, which are defined by Eq. (24) and Eq. (26).
3.2.2. Reconnaissance objective functionThe reconnaissance objective function will be chosen according
to requirement of reconnaissance task. The reconnaissance objec-tive function is formulated as follows:
J r ={
ζ2∑k+N−1
i=k+1 li if ϑi ≤ ϑmax
ζ2∑k+N−1
i=k+1 (li
Lmax)2li otherwise
(52)
where li is the distance between UAV and moving target at the time i, and it is defined by Eq. (36), ϑi is the angle of view at the time i, ζ2 is the weight coefficient of object function.
3.3. RHC with PSO implementation procedure
The detailed implementation procedure of RHC with PSO for Energy-Optimal path planning can be described as follows.
Step 1: According to the environmental and the optimization problem models in Section 2, initialize the beginning, final infor-mation and reconnaissance information.
Step 2: Initialize parameters of PSO algorithm, such as search space dimension D , the population size Np and the maximum number of the iterations Nit , and set the beginning values of x(k)
and v(k) about each particle.Step 3: Initialize parameters of RHC algorithm, such as the
length of future control sequence N , the objective function.Step 4: Initialize the position and velocity of each particle, and
compare the fitness of each particle to find the current best control command.
Step 5: Update particle velocity and position using Eqs. (44)–(45), and choose the optimal control sequences at the current it-eration j by comparing the fitness of each group particle. Repeat this step until j reaches the maximum iteration.
Step 6: Calculate the optimal trajectory with the first term of the optimal control sequences using Eqs. (1)–(3).
Step 7: If the mission does not end, go to step 4.The above steps can be summarized as pseudo code (see Ta-
ble 1).
4. Simulation and results
In this section, the parameters of aircraft and battery pack are listed in Table 2 from [23,27]. At first, the simulation results about energy harvesting model with specific attitude of UAVs have been given in Beijing (39.93◦N, 116.28◦E) throughout the year. Then, we present the simulation results of energy-optimal path plan-ning with tracking moving ground object on January 21 using the method of RHC with PSO. More ever, the total collection energy and the tracking success ratio are introduced to evaluate the opti-mization results. (See Table 2.)
4.1. Numerical simulation of energy collection model
According to Eqs. (4)–(24), the simulations of instantaneous power produced by solar cell form solar radiation on the SUAV’s wing on Jan 21, Apr 21, Jul 21 and Oct 21 in Beijing are shown in Fig. 4, which are chosen in different seasons.
As shown in Fig. 4, the instantaneous power at any time on Jul 21 in the summer season is the biggest compared with that of other days solar radiation, and in general, the power reaches the maximum value at noon in every day.
246 Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251
Table 1Proposed algorithm.
1 //Initialization2 Set the parameters of the aircraft model: ηprop,ρ, S, C D0 ,g,m, ε, K , AR3 Set the parameters of the solar radiation model: I0, τb, τd
4 Set the parameters of the algorithm: Nvar, N, N p , Nit , c1, c2, w5 Set the initial sates of the vehicle: nlat,nlon,nday, tlocal, V 0,ψ0, φ0, zb06 Set the initial sates of the objection: xc0, yc0, zc0
7 Set the end condition: T f
//Main loop8 While tlocal ≤ T f (not reaching the stop criteria) do9 Generate the solar radiation using Eqs. (4)–(10), Eqs. (16)–(23)
10 for Nit iterations11 Generate the population with Np random particles with constraint Eqs. (41), (42)12 Update particle velocity and position using Eqs. (44), (45)13 Calculate the objection function using Eqs. (49)–(52)14 Determine the personal best position and global best position15 end for16 Generate the optimal control sequences according to global best position17 Calculate the optimal trajectory with the first term of the optimal control sequences using Eqs. (1)–(3)18 Update the initial sates of UAV with the optimal trajectory19 tlocal = tlocal + �t20 end while
Fig. 4. The instantaneous power on different day throughout the year.
4.2. Energy-optimal path planning
In this section, the simulations consist of three parts: a brief comparison of path planning with/without energy optimization, the influence of main parameters on the optimization method and the optimization results with different target velocities. To math-ematically analyze and adjust optimal design, some performance indexes will be introduced. In this paper, the total energy of SUAV at the end of flight and the tracking success ratio are defined.
The total energy, Etotal , is the difference between the collected energy and energy consumption. The optimization strategy will be better if the total energy is bigger. It can be described as
Etotal = E in(λ) − Eout(t0, t f ) (53)
The tracking success ratio, σ , is defined as the time meeting the requirements of mission to the total time ratio. The optimization strategy will be better if the tracking success ratio is bigger. It can be described as
σ = ntask�t
t f − t0(54)
where, ntask is the number of waypoints meeting the relation of Eqs. (39), (40), �t is the time interval in two adjacent waypoints.
In these simulations, the equation of motion of the moving ground target is described as
Table 2Aircraft model parameters [23,27].
Parameters Notation Value Unit
Wing area S 0.1566 m2
Mass m 1.2 kgWingspan b 0.711 mOswald efficiency factor ε 0.992Parasitic drag CD0 0.011Propeller efficiency ηprop 0.7Efficiency of the solar cell ηsol 0.22Air density ρ 1.29 kg/m3
Battery capacity C ±30 W
x = A√2
t + B(2 × rank(0,1) − 1
)(55)
y = A√2
t + B(2 × rank(0,1) − 1
)(56)
where, x and y are components of N axis and E axis respectively in the navigation frame (P-NED) whose origin is set in Beijing. Arepresents the speed of ground object. B(2 × rank(0, 1) − 1) repre-sents the error of target position.
4.2.1. Path planning with/without solar energy optimizationIn this case, a brief comparison of path planning with/without
solar energy optimization is presented. The simulation parameters are set by Table 3. To make SUAV path planning, we have an intu-
Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251 247
Table 3Simulation parameters.
Place: Beijing Date: January 21 Begin time: 12:30 pm End time: 12:35 pm
Parameters Notation No optimized Optimized
The number of particle population Np 60 60The number of the iterations Nit 20 20The length of future control sequence N 5 5The number of control variables Nvar 2 2The weight coefficient of control object function ζ1 0 5The weight coefficient of reconnaissance objective function ζ2 1 1The flight altitude z 300 m 300 mThe maximum roll angle φmax 20◦ 20◦The speed of UAV with the minimum power V minpower 15 m/s 15 m/sThe maximum level flight speed V max 30 m/s 30 m/sThe time step �t 1 s 1 sThe maximum detectable range Lmax 360 m 360 mThe maximum angle of view ϑmax 70◦ 70◦The object’s speed A 5 5The error of object’s position B 5 5
Fig. 5. Tracking moving ground object without energy optimization.
Fig. 6. Tracking moving ground object with energy optimization.
Fig. 7. The energy harvesting curve with time.
248 Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251
Fig. 8. The tracking success ratio curve with time.
Fig. 9. Tracking path with the different value of N .
Fig. 10. The energy harvesting curve with different N .
itive feeling for energy collection, and the instantaneous power is defined as follows:
Pi = P in − Pout(V , φ) (57)
If P in ≥ Pout(V , φ), the waypoint of SUAV is plotted in simula-tion figure with the form of plus. If P in < Pout(V , φ), the waypoint of SUAV is plotted in simulation figure with the form of the filled circle. Where, Pi represents the total UAV’s power at ith time. If Pi is negative, the total collection energy stored in rechargeable batteries on the solar airplane will decrease.
Fig. 5 and Fig. 6 illustrate the trajectories of moving target and solar aircraft. It’s very easy to see that the sum of positive instan-taneous power in Fig. 6 is more than the other. From Fig. 7, the total energy with energy optimization is more than doubled the amount without energy optimization. However, their tracking suc-cess ratios are very close, as shown in Fig. 8.
4.2.2. The effect of main parameters on the optimization designIn this section, we mainly analyze the length of future control
sequence N that represents the fixed future time interval and the
Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251 249
Fig. 11. The tracking success ratio curve with different N .
Fig. 12. Tracking path with different detectable range.
Fig. 13. The energy harvesting curve with different detectable range.
maximum detectable range. In the following simulations, the sim-
ulation parameters are the same with Table 3 with the exception of N and Lmax.
The optimized paths with different N are given in Fig. 9, and their corresponding performances are shown in Fig. 10 and Fig. 11. By analyzing Fig. 10 and Fig. 11, N = 3 is a reasonable choice, com-
paring with other values. In a general way, the value of N can
be decided by cut and try methods for practical matters, which is nearly optimum.
Figs. 12–14 are the simulation results by RHC with PSO with different detectable ranges. In this paper, we assume that the angle of view is big enough so that it has no influence upon the total collection energy and tracking success ratio. By analyzing Fig. 13and Fig. 14, the total energy and the tracking success ratio will be better if the value of maximum detectable range is bigger.
250 Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251
Fig. 14. The tracking success ratio curve with different detectable range.
Fig. 15. Tracking path with different object velocities.
Fig. 16. The energy harvesting curve with different object velocities.
4.2.3. The optimization results with different target velocitiesIn this case, the simulation parameters are the same with Ta-
ble 3 except the target speed. By analyzing Figs. 15–17, it shows that the aircraft has to do large maneuver to keep the solar aircraft with preferable tracking success ratio and satisfied total energy, if the moving object’s velocity is low. If the target moves too fast (e.g. 21 m/s), the total energy will be negative, which shows that the task executed for a long time is not feasible. And more, it is easy to understand that the smaller the speed of aircraft is, the
less the energy consumption is, and the more the total energy will be in the given time interval with the same collection energy.
5. Conclusions
The design of energy-optimal trajectory contributes to increas-ing endurance for the solar aircraft. By the presented method, it is possible to carry out the task of tracking target for a long time for SUAV.
Y. Huang et al. / Aerospace Science and Technology 53 (2016) 241–251 251
Fig. 17. The tracking success ratio with different object velocities.
1) In this paper, we present a simple energy integrated model in two-dimensional space to calculate the instantaneous power at any time in any place.
2) The generation of waypoint for solar aircraft to track moving ground target is carried out by using the constrained RHC with PSO algorithm.
3) Based on the energy integrated model and the control design, the effect of main parameters (the size of the sliding window, the detectable range and the target velocity) on optimization results are discussed.
Future work will focus on the research about energy-optimal path planning in three-dimensional space with uncertainty in com-plex environment.
Conflict of interest statement
The authors declared that they do not have any conflicts of in-terest to this work.
Acknowledgements
The authors would like to thank the editors and reviews for their critical review of the manuscript. This research has been sup-ported by the Changjiang Scholars and Innovative Research Team in University under Grant IRT 13004, in part by Aeronautical Sci-ence Foundation of China under Grant 2014ZA51002, and in part by the National Natural Science Foundation of China #61175084.
Appendix A. Supplementary material
Supplementary material related to this article can be found on-line at http://dx.doi.org/10.1016/j.ast.2016.03.024.
References
[1] M.H. Shaheed, et al., Flying by the Sun only: the Solarcopter prototype, Aerosp. Sci. Technol. 45 (2015) 209–214.
[2] S. Hosseini, R. Dai, M. Mesbahi, Optimal path planning and power allocation for a long endurance solar-powered UAV, in: 2013 American Control Conference (ACC), 2013, pp. 2588–2593.
[3] A.T. Klesh, P.T. Kabamba, Solar-powered aircraft: energy-optimal path planning and perpetual endurance, J. Guid. Control Dyn. 32 (4) (2009) 1320–1329.
[4] J.K. Shiau, et al., Design of a solar power management system for an experi-mental UAV, IEEE Trans. Aerosp. Electron. Syst. 45 (4) (2009) 1350–1360.
[5] S.C. Spangelo, E.G. Gilbert, Power optimization of solar-powered aircraft with specified closed ground tracks, J. Aircr. 50 (1) (2013) 232–238.
[6] X.-M. Tang, P. Chen, B. Li, Optimal air route flight conflict resolution based on receding horizon control, Aerosp. Sci. Technol. (2015).
[7] W. Harasani, et al., Initial conceptual design and wing aerodynamic analysis of a solar power-based UAV, Aeronaut. J. 118 (1203) (2014) 540–554.
[8] X.Z. Gao, et al., Parameters determination for concept design of solar-powered, high-altitude long-endurance UAV, Aircr. Eng. Aerosp. Technol. 85 (4) (2013) 293–303.
[9] E. Cestino, Design of solar high altitude long endurance aircraft for multi pay-load & operations, Aerosp. Sci. Technol. 10 (6) (2006) 541–550.
[10] X.-Z. Gao, et al., Reviews of methods to extract and store energy for solar-powered aircraft, Renew. Sustain. Energy Rev. 44 (2015) 96–108.
[11] P. Panagiotou, et al., Aerodynamic design of a MALE UAV, Aerosp. Sci. Technol. (2016).
[12] J.K. Shiau, D.M. Ma, Development of an experimental solar-powered unmanned aerial vehicle, J. Chin. Inst. Eng. 38 (6) (2015) 701–713.
[13] A. Malaver, et al., Development and integration of a solar powered unmanned aerial vehicle and a wireless sensor network to monitor Greenhouse gases, Sen-sors 15 (2) (2015) 4072–4096.
[14] E. Troncoso, N. Lapena-Rey, O. Valero, Off-grid test results of a solar-powered hydrogen refuelling station for fuel cell powered Unmanned Aerial Vehicles, Int. J. Hydrog. Energy 39 (21) (2014) 11267–11278.
[15] J.K. Shiau, et al., Optimal sizing and cruise speed determination for a solar-powered airplane, J. Aircr. 47 (2) (2010) 622–629.
[16] J. Meyer, et al., Design considerations for a low altitude long endurance solar powered unmanned aerial vehicle, in: 8th IEEE Africon Conference, September 2007, IEEE, 2007, pp. 507–512.
[17] B. Lee, et al., The flight test and power simulations of an UAV powered by solar cells, a fuel cell and batteries, J. Mech. Sci. Technol. 28 (1) (2014) 399–405.
[18] X.F. Zhu, et al., How high can solar-powered airplanes fly, J. Aircr. 51 (5) (2014) 1653–1659.
[19] G. Marques Hobold, R.K. Agarwal, A methodology for predicting solar power incidence on airfoils and their optimization for solar-powered airplanes, Proc. Inst. Mech. Eng., Part G, J. Aerosp. Eng. 229 (7) (2014) 1267–1279.
[20] P. Rajendran, H. Smith, Implications of longitude and latitude on the size of solar-powered UAV, Energy Convers. Manag. 98 (2015) 107–114.
[21] B. Lee, et al., Active power management system for an unmanned aerial vehicle powered by solar cells, a fuel cell, and batteries, IEEE Trans. Aerosp. Electron. Syst. 50 (4) (2014) 3167–3177.
[22] X.Z. Gao, et al., The equivalence of gravitational potential and rechargeable bat-tery for high-altitude long-endurance solar-powered aircraft on energy storage, Energy Convers. Manag. 76 (2013) 986–995.
[23] A. Klesh, P. Kabamba, Energy-optimal path planning for solar-powered aircraft in level flight, in: AIAA Guidance, Navigation and Control Conference and Ex-hibit, 2007.
[24] H. Duan, Y. Zhang, S. Liu, Multiple UAVs/UGVs heterogeneous coordinated tech-nique based on Receding Horizon Control (RHC) and velocity vector control, Sci. China, Technol. Sci. 54 (4) (2011) 869–876.
[25] P. Yao, H. Wang, Z. Su, Real-time path planning of unmanned aerial vehicle for target tracking and obstacle avoidance in complex dynamic environment, Aerosp. Sci. Technol. 47 (2015) 269–279.
[26] D.M. Ma, et al., Optimal level turn of solar-powered unmanned aerial vehicle flying in atmosphere, J. Guid. Control Dyn. 33 (5) (2010) 1347–1356.
[27] S. Hosseinisianaki, M. Mesbahi, Energy aware aerial surveillance for a long en-durance solar-powered UAV, in: AIAA Guidance, Navigation, and Control, GNC, Conference, 2013.
[28] Q. Dai, X. Fang, A simple model to predict solar radiation under clear sky con-ditions, Adv. Space Res. 53 (8) (2014) 1239–1245.
[29] S. Pattarapanitchai, S. Janjai, A semi-empirical model for estimating diffuse so-lar irradiance under a clear sky condition for a tropical environment, Proc. Eng. 32 (2012) 421–426.
[30] D. McLean, Automatic Flight Control Systems, Prentice Hall International (UK) Ltd., 1990.
[31] D.Y. Goswami, Principles of Solar Engineering, third edition, CRC Press, 2015.[32] J. Zhao, R. Zhou, Particle swarm optimization applied to hypersonic reentry
trajectories, Chin. J. Aeronaut. 28 (3) (2015) 822–831.
