Unmanned Aerial Vehicles Glide-Path-Angle

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 00 (2014) 000–000 www.elsevier.com/locate/procedia

“APISAT2014”, 2014 Asia-Pacific International Symposium on Aerospace Technology, APISAT2014

Unmanned Aerial Vehicles Glide-Path-Angle-Tracking for Autonomous Carrier Landing Seokwon Leea, Hyunjin Choia, Youdan Kima, * , Sungwan Kimb, Seungkeun Kimc ,and Jinyoung Sukc a

Department of Mechanical & Aerospace Engineering, Seoul National University, Seoul, Korea b Department of Biomedical Engineering, Seoul National University, Seoul, Korea c Department of Aerospace Engineering, Chungnam National University, Daejeon, Republic of Korea

Abstract Carrier landing becomes one of the important issues for military application of UAV`s in the ocean. However, safe landing is hard to achieve because it is affected by ship motion and weather conditions, which make many difficulties in comparison with the ground landing system. To deal with this problem, an accurate & precise guidance and control system is required. This study proposes a guidance and control system of UAV using glide-path-angle-tracking approach for automatic carrier landing. The guidance loop generate flight path and heading angle commands which guarantee convergence of angular error between the relative angle of the UAV position and the glide slope angle with respect to the position of the carrier finally regulate the relative position error with respect to the three-dimensional position of the carrier deck. In the control loop, linearized UAV model is considered and command generator tracker is designed to track the guidance commands. To demonstrate the proposed guidance and control system, numerical simulations are performed in the MATLAB and X-Plane software environment. © 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA). Keywords: Automatic Carrier landing, Tracking guidance, UAV, Linear control

Nomenclature

d p, q, r

Distance between carrier and UAV. Body angular rates of UAV.

* Corresponding author. Tel.: +82-2-880-7398; fax: +82-2-888-0321. E-mail address: [email protected] 1877-7058 © 2014 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).

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Author name / Procedia Engineering 00 (2014) 000–000

rs , ra α, β φ ,θ ,ψ

Positions of carrier and UAV. Angle of attack, sideslip angles of UAV. Roll, pitch, and yaw angles of UAV.

δ th , δ e , δ a , δ r ηd , λd V , χ,γ

Throttle, elevator, aileron, and rudder. Horizontal, and vertical glide path angle. Velocity, heading and flight path angles of UAV.

1. Introduction Carrier landing of an UAV is more difficult than ground landing because a UAV should be controlled considering the motion of the carrier. The carrier has its own dynamics, which is sensitive to weather conditions such as wind and sea level. To accomplish the automatic carrier approach and landing successfully and safely, an automatic carrier landing system (ACLS) has been developed. ACLS consists of three subsystems: decision making process, guidance loop, and control loop, as shown in Figure 1. The decision making process is prerequisite to the guidance and control system. In the decision making process, the UAV determines appropriate policy whether or not the UAV is allowed to land based on various information. If weather conditions are severe or other circumstances are inappropriate, then the decision making process generates wave-off commands to avoid the failure of landing. Therefore, the decision making for the landing [1-4] requires accurate prediction & estimation of the carrier motion.[5-8]. After the decision making process, appropriate guidance commands are generated in the guidance process according to the decision policy. The guidance loop is also important because the UAV should be accurately guided for safe landing despite of poor condition. For the landing guidance, altitude and altitude rates were utilized to derive the glide slope command [8-9], or nonlinear path tracking guidance laws [10-11] have been suggested to derive the angle commands. Using the velocity and angle commands generated to track the glide slope, control loop or the inner loop system is required to track the guidance commands precisely and quickly. The overall system performance and the robustness with respect to uncertainties such as wind disturbance and un-modeled dynamics are determined by the control loop. Many research have been performed for ACLS, and most of the works were focused on control design. Given the flight path commands, flight path angle/ thrust controller was implemented by modifying pitch angle to track desired path angle with low angle of attack. To achieve the robustness under the wind and disturbances, H ∞ control theory was used in landing system [12,13] and nonlinear and adaptive control schemes were applied to automatic carrier landing systems. Denison [14] suggested ACLS using dynamic inversion, and Qidan et al. [15] designed approach power compensation system using sliding mode controller. Staeinberg and Page [16] designed six different control schemes for ACLS and evaluated the performances for the landing of F-18 aircraft model. In these studies, flight path angle command was converted to pitch angle commands. However, it is required to directly track the desired flight path in the ACLS. In this study, a guidance and control system of UAV using glide-path-angle-tracking approach is proposed for ACLS, which consists of guidance command generation and inner-loop controller design. In the guidance loop, the cruise speed of the UAV is chosen as the speed command, and heading angle and flight path angle commands are used to stabilize the tracking angle errors. The tracking angle errors reflect the relative angle of the UAV position and the glide slope angle with respect to the carrier position. Thus, glide path angle constraint can be satisfied by making the UAV track the guidance command. To design the controller, a linearized UAV model is considered, and Command Generator Tracker (CGT) is designed for the inner-loop UAV control systems. Finally, the tracking of glide path angle can be achieved by the proposed guidance law and controller. To demonstrate the effectiveness of the proposed guidance and controller, numerical simulations are performed. For the simulation scenario, the carrier moves to north, the UAV approaches behind the carrier while tracking the horizontal and vertical glide path angles, and sea level 4 [17] is assumed. Numerical simulations show that the UAV smoothly tracks the desired glide path angles and performs touch down safely on the carrier even though the carrier has translation motion. Section 2 describes the design of a guidance and control system. Section 2.1 presents the guidance generation, which consist of speed of the UAV, flight path angle, and heading angle command for tracking a desired glide path.


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In Section 2.2, Command generator tracker controllers are designed to track the desired guidance commands and the control systems are applied to a linear UAV model. Section 3 presents the results from the numerical simulations in the MATLAB and X-Plane software environment. Section 4 contains the conclusion of this work.

Fig. 1 . ACLS structure

2. Guidance and Control system design To design the guidance and control system for the ACLS, this study consider the following assumptions • •

Decision making process is prior to the guidance loop, and only landing policy is considered. Sea states are below 4 and weather condition is mild such that the UAV control system has the capability of disturbance rejection. All angles and positions of the carrier and the UAV are represented in local North-East-Down (NED) frames. Coriolis effect is negligible. ILS (Instrument Landing System) transfers the UAV position and glide slope data without delay.

• • •

There are two different ways to design a guidance and controller: One is to design a guidance and control simultaneously (integrated guidance and control, IGC) [11], the other one is to design a guidance and controller separately (separated guidance and control, SGC) [8-10]. In comparison to IGC system, SGC system does not consider aerodynamics in designing a guidance law, which makes guidance law simple. Also, if the guidance and controller are well-designed with time-scaled, then closed-loop stability is guaranteed by singular perturbation theory [18]. Therefore, the SGC system is well established technique, and it is easy to design a guidance law using this technique. In this study, guidance and control loop are designed separately.

2.1. Guidance commands generation In this section, guidance commands are generated to track the desired glide path which is attached to a carrier. To design a guidance law, the following assumptions are considered. • • •

Carrier and UAV are considered as point mass models. Control input is computed faster compared to guidance commands. Desired UAV speed is assumed to be constant prior to landing.

Desired speed, heading angle, and flight path angle of the UAV are regarded as the guidance commands, which are denoted as Vc , χ c , γ c , respectively. Let us define the horizontal angle η d , and vertical glide path angle λd .And, let us

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define horizontal and vertical angles of the UAV with respect to the carrier position η , and λ , respectively. Figure 2 shows the geometry of glide path guidance. Usually, glide slope is located behind the carrier, and carrier sends the ILS glide slope signal to the UAV. The desired horizontal and vertical glide paths are expressed as ηd χ carrier + η ILS = (1) λd = λILS where χ carrier denotes the carrier heading , and η ILS , and λILS are horizontal and vertical glide path angle with respect to carrier position, respectively. UAV positon ra can be expressed using the relative position and carrier positon as

ra = rs + ∆ where ∆ is relative position of the UAV with respect to the carrier, which is expressed as = ∆

[ d cos λ cosη

d cos λ sinη

−d sin λ ]

T

(2) (3)

Figure 2 Glide-path-angle description

The velocity of the UAV can be obtained by differentiating Eq.(2) as

V  Vs  Δ  Vs  dΔ1   Δ 2   Δ3

(4)

where

Δ1  cos  cos  cos  sin   sin  

T

Δ 2  d cos  sin  d cos  cos  0

T

(5)

Δ3  d sin  cos   d sin  sin   d cos  

T

Note that d ,η , and λ should be made to converge the desired glide path. If the desired velocity commands are generated to track the glide path, then the path error η − η , and λ − λ converge to zero as well as distance rate d d

d

to be negative. Because UAV usually keeps constant speed during the landing phase, d must be chosen considering the constant speed command. To make horizontal and vertical angles ( η , λ ) converge to the desired glide path angles ( η d , λd ), respectively, let us consider the following error dynamics. η = −kη (η − η d )

(6)


5

λ = −kλ (λ − λd )

(7)

where kη ,and kλ are positive guidance gains. For the desired speed command, Vc is set to be the norm of UAV velocity.

Vc  V

(8)

Using the velocity norm in Eq.(4), we have d 2  2(u cos  cos   v cos  sin   w sin  )d  (u 2  v 2  w2 ) Vref2  0 where T u v w  V   Δ   Δ s

2

3

(9) (10)

Now, d is determined by taking the negative roots of Eq.(9). Finally, heading and flight path angle commands are determined as  v  d cos  sin   , (11) c  tan 1   u  d cos  cos    ( w  d sin  )    c  sin 1    Vc

(12)

2.2. Controller design 2.2.1. Longitudinal controller To design the controller, a linearized 6-DOF UAV model is used. The longitudinal UAV model [19] can be expressed as (13) xlong Along xlong + Blong ulong = where xlong = [u α θ q ] are perturbed states from the trimmed state, and ulong = [δ th δ e ] are control inputs. Longitudinal system matrices are modeled as  0.0353 0.4547 −8.9246 −13.15  −0.0069 −1.0310 0.0118 0.96  Along =  ,  0 0 0 1     0.0082 −8.8842 0.0039 −2.57  (14)  1.1308 5.4386   0.0385 0.0632   Blong =   0 0     −0.1325 3.1175  Linearized flight path angle γ can be expressed in terms of longitudinal states α and θ as γ= θ − α (15) To track the desired flight path angle directly with speed hold, the error variable of flight path angle is defined as follows (16) eγ = γ − γ c T

T

Using the time scale separation assumption, the guidance command γ c is assumed to be constant which is regarded as trim point. Now, let us define a new state variable vector x = u α state vector x is obtained using similarity transformation as. = x Ax + Bu

eγ

T

q  . Then dynamic equation of new

(17)

6


where A, and B are new longitudinal system matrices. The new system matrices can be expressed as A = TAT −1

(18) B = TB For precise tracking, let us introduce the integral error of sγ = ∫ eγ dt . Considering the preceding term, new

longitudinal system matrices can be augmented as xaug =  x

sγ 

T

 A 04 X 1  = Aaug =  , Baug 0  0 0 1 0 To design the controller for the augmented system, performance output

(19)  B  (20)   02 X 1  ylong and output matrix are introduced as

T

ylong = δ u sγ  1 0 0 0 0  Clong =   0 0 0 0 1  To apply nonzero setpoint tracking [21], let us consider the augmented matrix F .  Aaug Baug  F =  Caug 02 X 2 

(21)

(22)

For the case that the dimension of output is equal to the dimension of input, set point xss and uss are obtained in the T

output commands yclong = uc sγ c  as

0   xss   N xy  −1  =  yc F     =  yc  uss   N uy  Finally, longitudinal control input can be obtained as ulong = ( Nuy + KN xy ) yclong − Kxaug

(23)

(24)

where, K is a LQR (Linear Quadratic Regulator) gain which minimizes the following performance index. J =

∫ {x ∞

0

aug

T

Qxaug + u T Ru} dt

(25)

where Q ∈  6 X 6 is positive semi-definite, and , R ∈  2 X 2 is positive definite.

2.2.2. Lateral controller To track the desired heading angle, coordinate turn is adopted in a UAV landing system [20]. The desired heading command (11) can be converted to the roll command as  V χ  (26) φc = tan −1  c c   g cos θ  To design the lateral controller, the following linearized lateral UAV model is considered. (27) = xlat Alat xlat + Blat ulat where xlat = [ β φ

p r ] , ulat = [δ a T

δ r ] , and lateral dynamics system matrices are modeled as T


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 −0.284 −0.16 −0.157 0.99   0 −0.05  0 1 Alat =  ,  2.97 −8.35 0.77  0   −0.49 −0.76  0  −3.45

(28)  0.039 −0.0017   0 0  Blat =  14.67 0.046    0.15  0.347 Note that the control objective of the lateral controller is to track the desired coordinate turn roll command while regulating the side slip angle. Therefore, the following performance output vector and output matrix are introduced to apply the command generator trackers.

ylat = [φ

β]

T

0 1 0 0  Clat =   1 0 0 0  Similar to the longitudinal controller, the control law can be obtained as ulat =− Kxlat + (Ωuy + K Ω xy ) yclat

(29)

(30)

(31)

where Ωuy and Ω xy are steady-state matrices in Eq. (23), yclat is desired output to track the roll and sideslip command, and K is a LQR gain. Note that (Ω 22 + K Ω12 ) yclat is the feed-forward term to play a role of tracking the desired commands, and − Kxlat plays a role of regulating the states. Overall control structure is shown in Figure 3.

Figure 3 Control structure of ACLS

3. Numerical simulations To demonstrate the performance of the proposed guidance and control system, numerical simulations are performed using MATLAB and X-Plane Software environment. Figure 4 shows the simulation environment. In the simulation, UAV and carrier are operated in X-plane simulation environment, and they are linked with Simulink block via UDP networks. In Simulink block, ILS data (distance, bearing, and vertical path, etc) and position of carrier are sent from the carrier, and UAV state information is sent from the UAV. Combining these data, guidance command and control inputs are generated, then the computed inputs are sent to X-plane via UDP. Simulation parameters are summarized in Table.1. Figure 5 shows the snap shot of landing scenario which is conducted in SIMULINK & X-Plane software environment. The UAV model in the simulation is MQ-9 reaper (predator B), which is operated in carrier landing system. Desired glide path can be obtained by using Eq.(1). Because the runway of carrier considered in this simulation is tilted at 9 degrees from ILS heading signal, the lateral heading command is switched at the beginning of the touch-down phase.

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Author name / Procedia Engineering 00 (2014) 000–000 Table 1. Simulation parameter Parameter

Symbol

Values

Carrier velocity

Vs

29knot (14.92m/s)

Guidance gain

kη , kλ

0.1

Carrier heading, ILS path

χ carrier ,η ILS , λILS

0°,3.5°,178°

Desired cruise speed

Vc

110knot(56.53 m/s)

Actuator limit

δ e ,δ a ,δ r ,δ e ,δ a ,δ r

20°, −20°

V0

107knot(55.04m/s)

max

Initial Speed

max

max

min

min

min

Figure 4 MATLAB simulation environment

Figure 5 snapshot of ACLS simulation (Head up view)


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Simulation results are obtained as follows. Figure 6 shows the trajectories of the carrier and the UAV in NED frame. In Fig. 6, black solid line and blue solid line denote the trajectories of the carrier and the UAV, respectively. In the beginning of the simulation, transient overshoot occurs in longitudinal motion, because the UAV uses full elevator and thrust by climbing the altitude. Then, the UAV declines the altitude and smoothly capture the glide path. In the lateral motion, the carrier slightly moves toward the west direction. To capture the drifted direction, the UAV also smoothly heads to the west during the approach phase and converges to the carrier runway. To analyze the tracking performance, the relative motion of the UAV with respect to the carrier is shown in Fig. 7. In the view of carrier frame, the UAV tries to capture the glide slope denoted by red solid line in Fig. 7 during the landing phase, but small drift error occurs. One of the possible factors causing the drift error is a measurement error. The carrier sends the ILS including as distance, vertical and horizontal path angle ( λ ,η ), and these data are sent to Simulink block with relatively low frequency than the UAV state data. For this low frequency, the UAV received the previous path angle, which results in drift errors. In the lateral relative motion, the horizontal path converges much faster than the vertical path. It is because the horizontal path error is quite small. Although horizontal heading is not directly fed -back to the closed -loop system, the UAV is made to follow the heading command by generating the coordinate turn command. Guidance commands and response are shown in Fig. 8 a), and control responses are shown in Fig. 8 b). The longitudinal and lateral output errors in the control loop are shown in Fig. 9. In the longitudinal motion, negative flight path angle commands are generated to descend toward glide path with constant speed. Figures 7 and 8 already show the same aspects, and the UAV tracks the desired flight path quite well. It is because the flight path error as well as integral error are considered simultaneously in the control design. To maintain the UAV speed constraint in the landing phase, thrust is turn on and elevator remains about 10 degrees. On the other hand, steady state error of velocity is shown. Because the flight path error components in Q matrix are more weighed than velocity components in LQR design. To improve the performance, integral of velocity error can be considered, or balanced LQR gain should be used. In the lateral motion, heading command is generated toward the west to capture the drifted carrier, and the UAV tracks the desired lateral heading and roll commands to guide the horizontal glide path. After 110 seconds, the landing phase is switched to the touch-down phase, and tilted runway heading is added to the heading command in this phase. To track the changed lateral command, aileron and rudder are used quickly. Finally, the UAV lands the carrier safely at about 118 seconds.

MQ-9 Trajectory in Relative Coordinate MQ-9 Trajectory in NED

0 -500 -1000

12000

-1500 11000

-2000

200 100 0 0 -200 -400 -600

-2500 Aircraft Path Ship Path Aircraft Ground Path

-3000 Altitude (m)

Altitude (m)

10000 9000 8000 7000

North (m)

East (m)

200 100 0 0 -50 -100 -150

-3500 -4000

Aircraft Path Aircraft Ground Path Ship Point Reference Glide Slope

North (m)

-4500

East (m)

Figure 6 Trajectory of UAV and carrier in NED frames

Figure 7 relative trajectory of UAV with respect to carrier

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Author name / Procedia Engineering 00 (2014) 000–000 VChiGamma

Control Inputs 1 Throttle (%)

60 V (m/s)

55 50 Command State

40

0

40

20

60

80

100

120

0 Elevator (deg)

45

140

0 χ (deg)

-5

40

20

80

60

100

Aileron (deg)

0

140

120

5

Rudder (deg)

γ (deg)

20

40

60

80

100

120

140

0

20

40

60

80

100

120

140

0

20

40

60

80

100

120

140

0

20

40

60

80

100

120

140

0 -20

0 -20

10

0 -5

0

20

20

-10 -15

0.5

0

20

40

60

80

100

120

20 0 -20

140

Time (s)

Time (s)

Figure 8 a). Guidance commands and responses (Left), b). Control response (Right)

Lateral Error 15

0

10 Roll error (deg)

Speed error (kts)

Longitudinal Error 5

-5 -10

5 0

-15

-5

-20

-10

0

20

40

60

80

100

120

140

0

20

40

60

0

20

40

60

80

100

120

140

80

100

120

140

6

10

LO error (deg)

GS error (deg)

4 5

0

2 0 -2

-5 -4 -10

0

20

40

60

80 Time (s)

100

120

140

-6

Time (s)

Figure 9 a) Longitudinal output error (Velocity, flight path angle), b) Lateral output error (roll angle, side slip angle)

4. Conclusion Guidance and control system of UAV for automatic carrier landing system was designed using glide-path-angletracking approach. Speed, heading angle, and flight path angle commands are generated to guide the UAV to follow the glideslope signal from the carrier. 3-DOF motion of the carrier was considered and guidance law was designed to smoothly capture the glide path angles. To track the desired flight path angle in the longitudinal motion, the proportional and integral feedback of the error was used in the control loop and CGT based controller. In the lateral system, desired heading command was tracked by the coordinate turn. To demonstrate the performance of the proposed ACLS, MATLAB and X-Plane based software environment was constructed, and numerical simulations using the software environment were performed. Simulation results showed that the proposed guidance & control algorithm worked fairly well. Wind disturbance and harsh attitude motion of the carrier will be considered for a future work.


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Acknowledgements This study was supported by Guidance/Control Study for Take-off and Landing on a ship program through the Agency for Defense Development (ADD) of KOREA (UD1130053JD)..

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