Development of Multi-target Acquisition, Pointing and ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2868143, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS

1

Development of Multi-target Acquisition, Pointing and Tracking System for Airborne Laser Communication Qing Li, Lei Liu∗ , Xiaofei Ma, Si-Lu Chen, Hai Yun, and Shuo Tang

Abstract—Cluster unmanned aerial vehicles (UAVs) are widely demanded. To achieve high rate and large capacity communication with cluster UAVs, one of the key but still challenge task is to perform multi-target acquisition, pointing and tracking (APT) under complex airborne environment. To solve this problem, this paper gives one composite axis APT system for multitarget laser communication with cluster UAVs. The APT system consists of a gimbal mirror and piezoelectric fast steering mirrors (FSMs), which can achieve independent and synchronous control of multiple optical axes. The cascade control scheme is designed for the gimbal mirror and the H∞ controller is designed for the FSM. To further improve the control accuracy, the hysteresis compensator based on least square support vector machines (LSSVM) is proposed. The pruning error minimization method of LS-SVM is applied to reduce the computational cost. The simulation studies validate the control performance of the multi-target APT system. Finally, the experimental prototype is developed. The experimental results further validate the effectiveness of the proposed multi-target APT system. Index Terms—multi-target laser communication, acquisition, pointing and tracking system, least square support vector machines, fast steering mirror, composite axis control.

I. I NTRODUCTION

T

HE airborne multi-target laser communication with cluster UAVs holds the advantages of high mobility, good secret, and flexible layout, which plays an increasingly important role in modern warfare [1], [2], [3], [4]. As a key component of the laser communication, the multi-target APT system with high accuracy has been payed increasingly interest and attention. Most of the current airborne laser communication methods are developed primarily for point to point communication. The realization of multi-target laser communication is still a challenge task. A multi-mirror splicing structure based on the rotation paraboloid has been presented to achieve multitarget communication [5], [6]. Each mirror with a separate drive unit. The number of the mirror needs to be optimized to avoid large dimension and complicated structure. The designed Q. Li, L. Liu, H. Yun and S. Tang are with the Shaanxi Aerospace Flight Vehicle Design Key Laboratory, School of Astronautics, Northwestern Polytechnical University, Xi’an, 710072, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). S.L. Chen is with Zhejiang KeyLab of Robotics and Intelligent Equipment Manufacturing Technology, Ningbo Institute of Industrial Technology, Chinese Academy of Sciences, Ningbo, 315201, China (e-mail: [email protected]). X. Ma is with Xi’an Institute of Space Radio Technology, Xi’an, 710000, China (e-mail: [email protected]). Manuscript received Feb 26, 2018; revised Jun 29, 2018.

APT system can realize communication in a large range of space while the coupling relationship between optical paths is complicated. The designed method is not suitable for the long distance communication with the cluster UAVs due to the concentrated distribution of the UAVs. In this paper, the multitarget APT system is proposed aiming at the communication with cluster UAVs. The designed APT system share one main optical system and can enable multi-target communication. Both high accuracy and large field of view (FOV) are required in laser communication with cluster UAVs. The target uncertain region requires a large FOV of APT system to guarantee the acquisition probability [7], [8]. Considering the atmosphere influence, background light, communication distance, airborne vibration and other factors, the laser divergence angle must be small to obtain a high communication rate. The small divergence angle and the remote communication distance require more precise optical control [9], [10]. The singlestage APT system is not sufficient to meet the requirements of both large FOV and high accuracy. Thus, the composite axis control system is usually adopted [10], [11], [12], [13]. In this paper, the proposed novel multi-target composite axis control APT system consists of a coarse pointing assembly and multiple fine pointing assemblies. The gimbal mirror is used as the coarse pointing assembly and the FSMs are used as the fine pointing assemblies. The employment of the FSMs enables independent and high accurate control of multiple optical axes to realize multi-target communication. Further, accurate modeling and control are necessary to enhance the performance of the APT system. The fine assembly FSM is driven by piezoelectric actuators. The nonlinear hysteresis dynamics of piezoelectric actuators can severely limit the control accuracy of FSM. Various control strategies are studied to eliminate the hysteresis effect. Feedforward hysteresis compensator based on inverse hysteresis model is commonly employed for piezoelectric system with high accuracy requirement [14], [15]. Song[16] established the inverse classical Preisach model as a feedforward controller to cancel the hysteresis of the piezoceramic actuator system for microposition tracking control. The approximate inversion of the Preisach model is obtained using numerical method because it is not analytically invertible. Janaideh[17], [18] formulated the analytical inverse of the P-I model. The feedforward compensator based on the inverse model is applied to compensate for the hysteresis nonlinearities over different excitation frequencies in a piezoelectric actuator. Xiao[19] proposed hysteresis compensator to perform rate-dependent

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2868143, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS

hysteresis cancelation based on a novel modified inverse Bouc-Wen model. The particle swarm optimization method is adopted to identify the inverse Bouc-Wen model parameters. The challenge of such approaches is to accurately develop and identify the inverse hysteresis model which is difficult to be obtained. The modeling uncertainty and parameter sensitivity may generate serious compensation errors[20]. Thus, the inverse hysteresis modeling based on least square support vector machines (LS-SVM) is proposed in this paper to realize feedforward compensation. The LS-SVM has frequently emerged as a data-driven modeling method [21]. The model is learned without complex model and parameters. To reduce the computational cost, the pruning error minimization method of LS-SVM is implemented. Furthermore, the H∞ controller with input uncertainty is compounded in order to further compensate the control error. The main contribution of this paper is the development of multi-target APT system for laser communication with cluster UAVs. Further, the precise FSMs share one gimbal mirror. The modeling and control strategies, as well as the engineering prototype of the proposed multi-target APT system are validated by employing real-time experiments. This paper is organized as follows. Section II gives the design of the proposed APT system. Section III and Section IV provide the modeling and control methods, respectively. Section V presents the simulation studies. Section VI develops and validates the experimental prototype of the multi-target APT system. Finally, Section VII gives the discussion and conclusion of this paper. II. D ESIGN OF THE MULTI - TARGET APT SYSTEM As shown in Fig.1, the multi-target APT system for airborne laser beam communication is proposed in this paper. The multi-target APT system is aiming at the large capacity and high rate communicating with cluster UAVs at long distance. The communication distance of the proposed multi-target APT system is set to less than 150km because the maximum propagation distance of the optical signal is limited by the atmospheric channel effect. The proposed APT system combines a coarse pointing assembly and multiple fine pointing assemblies to achieve multi-target laser communication. The gimbal mirror is used as the coarse pointing assembly with a large field of view (FOV). The FSMs are adopted as fine pointing assemblies which meet the high accuracy and high bandwidth requirements. The implement of multiple FSMs makes it possible to achieve high accuracy and independent control of numbers of optical axes, so as to communicate with cluster UAVs. The multi-target APT system is designed to quickly acquire and accurately point the cluster UAVs under the condition of airborne vibration and relative motion. First, the gimbal mirror is used for scanning over a large area to determine the rough position of the cluster UAVs. Once the cluster UAVs have been detected by the wide FOV detector, the tracking and pointing are implemented by gimbal mirror to hold the targets within the FOV. The detectable range of the cluster UAVs is determined by the FOV of the coarse detector. Considering the

2

Coarse pointing subsystem Gimbaled mirror

Laser Splitter mirror

Wide FOV detector

Fine pointing subsystems FSM3

Dichroic mirror Laser2

Narrow FOV detector3

Splitter mirror Laser3

Splitter mirror

Dichroic mirror

Narrow FOV detector2

FSM2 Splitter mirror Laser1

Multi-target APT system

FSM1 Narrow FOV detector1

Fig. 1. Diagram of the proposed multi-target APT system. The diagram of 1-to-3 target APT system is given as an example. The system mainly consists of a coarse pointing subsystem and three fine pointing subsystems. The coarse pointing subsystem consists of gimbal mirror, lase and a wide FOV detector. The fine pointing subsystem consists of FSM, laser and a narrow FOV detector.

signal to noise ratio of the coarse detector and the distribution of the cluster UAVs, the detectable range of cluster UAVs for the proposed APT system is limited to 1060×1060m. In the meantime, the FSMs begin to scan within the FOV of the wide FOV detector to obtain the accurate position of each aerial vehicle in cluster. Finally, the FSMs are employed to point the cluster UAVs with high accuracy. Different FSMs are responsible for pointing different UAVs and hold them in the FOV of the corresponding narrow FOV detectors to establish stable laser communication. III. S YSTEM M ODELING The integrated modeling of the APT system is given in this section. The model of the gimbal mirror is derived according to the Newton-Euler approach [22]. The LuGre friction model is adopted to describe the nonlinear friction. The dynamics of the FSM combines the multi-field linear dynamics and the Bouc-Wen hysteresis. The inverse hysteresis model based on the LS-SVM is also proposed. A. Gimbal Mirror The gimbal mirror is driven by the torque motor. The definition of the corresponding coordinate frames of the gimbal mirror is illustrated in Fig.2. OxR yR zR , OxA yA zA and OxE yE zE are the inertial reference coordinate system, azimuth coordinate system and elevation coordinate system, respectively. ψ and θ represent the azimuth angle and the elevation angle, respectively. Only

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2868143, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS

yA yR yE

xR

O



Mirror

3



xE x A



Fast Steering Mirror

Voltage Amplifier Electric Dynamic of the Voltage Amplier

Hysteresis effect

Electric Dynamic of FSM

Mechanical Dynamics



Fig. 3. Composite dynamic model of the FSM.

Elevation motor Azimuth motor

zA zR

zE

Fig. 2. Coordinate frames of the the gimbal mirror.

the motion around xE axis and zA axis is considered, because the motor induced torque exclusively acting on the mounting shaft. The kinematics equation of the gimbal mirror is derived as 

IEx ω˙ Ex = TEx − TEx A
IAz + IEy sin2 θ + IEz cos2 θ ω˙ Az = TAz − TAz

(1) E

where I and T represent the moment of inertia and the applied torque around the corresponding axis, respectively. TEx A and TAz E are the coupling effect of the two axes and can be derived as 

TEx A = ωAz 2 sin θ cos θ (IEz − IEy ) TAz E = −2 (IEz − IEy ) ωEx ωAz sin θ cos θ

(3)

where Lm and Rm are inductance and resistance of the motor, respectively. kt is the motor torque constant and ke denotes back-emf constant. u, i are voltage and current of the motor, respectively. Tf is the friction torque. The total inertial J = IEx in the case of elevation axis, while in the case of azimuth axis J = IAz + IEy sin2 θ + IEz cos2 θ. As to ensure a stable and continuous communication, the gimbal mirror may work near zero velocity point. The dynamic friction around the zero velocity seriously restricts the control accuracy. In order to accurately describe the nonlinear friction near the zero velocity point, the induced friction torque Tf is modeled using the LuGre friction model as [23] Tf (t) = σ0 z (t) + σ1 z˙ (t) + σ2 ω (t)

where ωi and ξi denote the mode frequency and damping ratio of the poles of mode i, respectively. ω ¯ i and ξ¯i denote the mode frequency and damping ratio of the zeros of mode i, respectively. n is the mode number of the mechanical dynamics. 2) Hysteresis dynamics: The nonlinear hysteresis of FSM is described using the Bouc-Wen model as follows [26], [27] 

P

J ω˙ = T = Tm − Tf =kt i − Tf di + Rm i + ke ω u = Lm dt


Qn 2 ¯ ¯is + ω ¯ i2 ωn2 k i−1 s + 2ξi ω Qn 2 GL = 2 τ s + 1 (s2 + 2ξn ωn s + ωn2 ) i (s + 2ξi ωi s + ωi ) (5)

(2)

The electrical and mechanical equations of the gimbal mirror are written as 

1) Linear dynamics: Linear dynamics of FSM consists of the electric dynamics and the mechanical dynamics. The electric dynamics of the voltage amplifier is modeled as a classic second order system with natural frequency ωn and damping ratio ξn . The electric dynamics of FSM is described as an inertial element with time constant τ . Further, the high frequency mechanical dynamics of FSM is added to derive the linear non-hysteresis dynamics as

(4)

where ω is the relative velocity. σ0 , σ1 and σ2 are the stiffness, damping coefficient and viscous friction coefficient, respectively. z denotes the average deflection of the bristles. B. Fast Steering Mirror The multi-field composite dynamics of FSM is presented as shown in Fig.3. The composite model consists of the electric dynamics, mechanical dynamics as well as the hysteresis dynamics [24], [25].

y = du + h n−1 n h˙ = αu˙ − β |u| ˙ |h| h − γ u|h| ˙

(6)

where y is the system output, u is the voltage and h is the hysteresis output. The insensitive parameter n is set to 1 in this paper [28]. α, β and γ are model parameters. C. Inverse Hysteresis model based on LS-SVM In addition, the inverse hysteresis model of FSM based on LS-SVM is given to enhance the control accuracy of FSM. The inverse hysteresis model Hinv can be expressed as [29] u (t) = Hinv (x (t)) = ω T φ (x (t)) + b where w is the weight vector and w =

l P

(7)

αi φ(xi (t)). The

i=1

nonlinear mapping φ (·) denotes a map from the input space to a high dimensional space and b is the bias. x(t) is the input signal of the inverse hysteresis model and can be given as x(t) = [h(t), h(t − 1), ..., h(t − Nh ), u(t − 1), ..., u(t − Nh )] (8) where Nh is the maximum delay time, u and h are the control voltage and hysteresis output, respectively. The hysteresis output h is obtained based on the established linear dynamics of FSM. The linear dynamic effect is eliminated by the inverse linear model as shown in Fig.4. The final inverse hysteresis can be derived by solving the following equation        b b 0 0 1T K = = (9) α α θ 1→ Ω + γ −1 E

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u

H

h

GL

y

4

 h

GLinv

H inv

z1

w1

Fig. 4. Block diagram of the FSM. du

r

‐

K  s 

‐

wr

u

w2

wu

K FB

‐

GL

H

y

LuGre model

dt

d

Td

r

z2

‐ K  s 

Ki  s 

u

‐

i 1 Ls  R

kt

+

‐ ‐

1 Js

‐ 

1



s

Fig. 6. Control block diagram of the FSM.

Tf

Fig. 5. Control block diagram of the gimbaled mirror.

Moreover, the pruning error minimization method of LSSVM is applied to reduce the computational cost while ensuring the model accuracy. The pruning method is to select the support vector which will introduce the smallest approximation error for the next iteration after being omitted. The error caused by omitting the support vector xi is calculate as [30]   1 1 − (10) ∆e (i) = H(i) (xi ) − H (xi ) = αi γ kii where kii is the ith diagonal element of the inverse of matrix K. γ is the nonzero and finite regularization parameter. The pruning process is as follows: 1) The inverse of matrix K for the current training model is calculated, so as to obtain the corresponding ∆e(i) of the support vector xi . 2) The support vectors with small |∆e(i)| are deleted to update the training examples. 3) If the number of the examples is less than a given threshold, the process ends, otherwise, go for the next training iteration. 4) Compare the training model result and the real result, back to 1) if the error is still smaller than the given threshold, else end. The inverse hysteresis model based on LS-SVM is finally obtained after pruning process. IV. C ONTROLLER D ESIGN The control scheme of the APT system is presented in this section. The cascade controller combining with friction compensator is designed for the gimbal mirror. The composite controller comprising of the H∞ controller and the hysteresis compensator is designed for the FSM. A. Gimbal Mirror The gimbal mirror is used for stable pointing and tracking of the cluster UAVs, and hold them within the FOV. To guarantee the control performance under complex airborne disturbances, the cascade control scheme is presented as shown in Fig.5. The cascade control system consists of three control loops. The inner loop is designed for current control, the middle loop is velocity control and the outer control loop is set as position control.

Magnitude (dB)

ke

GL K FB

L1 Performance

p

c

bc

f (Hz) Robust stability

L2

Fig. 7. Illustration of loop shaping technique.

The current loop is designed as a PI controller to cancel out the electrical dynamic of the motor. The velocity loop is mainly used to resist angular velocity disturbance, and is designed as a PI controller. The position loop is designed as a PI control according to the internal model principle[31]. The bandwidth of the inner loop is chosen at least three times higher than the outer loop. Furthermore, to compensate the friction effect, a feedforward compensator is designed based on the established LuGre friction model. B. Fast steering Mirror The fine pointing FSM requires both high accuracy and high bandwidth. Considering the nonlinear hysteresis of the FSM, the composite controller synthesizes the LS-SVM based feedforward compensator and feedback H∞ controller is proposed as shown in Fig.6. The H∞ controller is employed to enhance the control accuracy and bandwidth. The H∞ controller is designed depending on the non-hysteretic dynamics GL while the hysteresis dynamics is regarded as a bounded uncertainty. The loop shaping technique is used to design the H∞ controller according to control bandwidth. The performance and stability requirements are satisfied by specifying L1 and L2 . The frequency ωp and ωbc are designed according to the requirements of the system performance and robust stability. ωbc represents the boundary frequency which guarantee robust stability of the system under modeling error and measurement noise. ωp can be represented as[32] ωp = κωd

(11)

where ωd is the bandwidth of the disturbance, κ denotes the disturbance rejection performance and should be set as large as possible to suppress more disturbance. The relevant parameters can be obtained based on the characteristic of the specific system.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2868143, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS

5

50

Magnitude (dB)

Bode Diagram

0 -50 -100 -150

The weighting function wu denotes the model uncertainty due to hysteresis nonlinearity. wu is chosen according to the hysteresis output of FSM. ∆u is an unit complex dynamic uncertainty with norm k∆u k < 1. Reference weighting function wr is set to 1. After the weighting functions are selected, the H∞ controller is solved using D-K iteration. The feedforward controller is designed to compensate the nonlinear hysteresis using the inverse hysteresis model based on LS-SVM. The detailed solution process of the inverse hysteresis model is described in SectionIII-C.

Phase (deg)

(12)

-180 -360 -540 101

Bode Diagram

0 -50 -100 -150 -200 0

-200 0

ω1 ω≤ωp = L1 ω2 |ω≥ωbc = 1/L2

Phase (deg)



50

Magnitude (dB)

The performance weighting function w1 and the control weighting function w2 are designed to satisfy the boundary constrains L1 and L2 in Fig.7. The relationship is given by

102

103

104

-180 -360 -540 101

102

103

Frequency (Hz)

Frequency (Hz)

Frequency (Hz)

Frequency (Hz)

(a) PI controller

104

(b) Composite controller

Fig. 8. Stability margin of the FSM. 140 PI control Composite control

120 100 80

V. S IMULATION S TUDIES 60

A. Simulation Parameters Simulation parameters are selected according to typical motors and FSMs. The parameters of the gimbal mirror mentioned in Eq. 3 are set as L = 0.01H, R = 8.05Ω, kt = 0.39N·m/A, ke = 40.8V/KRPM, IEx = IEy = 0.0235kg·m2 , IEz = 0.0447kg·m2 , and IAz = 0.181kg·m2 . The parameters of the LuGre friction model are set as σ0 = 328, σ1 = 2.97, σ2 = 0.0135N·m/rad/s, ωs = 0.05rad/s, Tc = 0.03N·m, Ts = 0.0664N·m. The cascade controllers for gimbal mirror are designed as Ki = 114.59 (1 + 4902/s) , Kω = 53.05 (1 + 452.49/s) , Kθ = 10.42 (1 + 1.68/s). The linear dynamics model of FSM in Eq.5 is given as follow GL =

2

(600π) 20 · · 1 s+1) (s2 +2×0.4×600πs+(600π)2 ) ( 2996

40 20 0 0

0.005

0.01

0.015

0.02

Time (s)

Fig. 9. Step response of the FSM.

in Fig.9. The rising time of the PI controller and the composite controller are 0.0013s and 0.0009s, respectively. It can be seen that the proposed composite controller shows better stability and faster response compared with the PI controller.

(800π)2

s2 +2×0.2×800πs+(800π)2

(

)

The parameters of the Bouc-Wen hysteresis model are set with d = 1.408, α = −0.475, β = 0.023, and γ = −0.0025. According to the dynamics of FSM, the weighting functions of the H∞ controller are describe as w1 = w2 =

1000 s+0.0001 ,wr = 1,wu 2 s+50π 0.0001 · s+500π

= 0.05

Moreover, the feedforward compensator is obtained using the inverse hysteresis model based on LS-SVM. The PI controller of FSM is also designed for comparison, and KP I = 0.0052 + 23/s. The parameters of the PI controller are selected by using the Ziegler-Nichols tuning method [33]. B. Simulation of FSM The performance of the PI controller and the proposed composite controller is evaluated at first. Fig.8 shows the stability margins analysis of the two kind of controllers. For the PI controller, the amplitude margins is 1.9dB, and the phase margins is 52◦ . For the proposed composite controller, the amplitude margins is 4.4dB, and the phase margins is 50◦ . The step responses of the FSM are illustrated

C. Simulation of multi-target APT system The scanning and pointing simulation studies are carried out to validate the proposed multi-target APT system. The attitude adjustment at low frequencies and the airborne vibration at high frequencies are considered. The coupling effect between the FSMs is taken into account. 1) Micro-scanning Simulation: The scanning simulation is carried out at first assuming that the cluster UAVs have been detected by gimbal mirror. The FSMs are employed to scan within the FOV of the gimbal mirror. The scanning reference of FSMs is designed as shown in Fig.10. The simulation result is shown in Fig.11. Both the composite controller and the PI controller for FSM are given for comparison. The scanning error is 1.75µrad by using PI controller and 0.29µrad by using composite controller. 2) Pointing Simulation: After the scanning process, the APT system begins to point the targets with high accuracy so as to establish the communication links. The relative movement of the communication targets is assumed as a sinusoidal signal with frequency of 0.5Hz and with amplitude of 300µrad. The simulation result of the APT system is shown in Fig.12. It can be seen from Fig.12 that the pointing error is 1.53µrad by using PI controller and 0.37µrad by using composite

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2868143, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS

6

Image transmission

200

Gimbal mirror Convex lens

150 100

Encoder Drivers Control signal

50

CCD 0

Control commands

Eddy-current sensor

Filter Reflector

-50

Lasers

-100 -150

Splitter mirror SGS sensor information

FSM

-200 -200

-100

0

100

Voltage

200

Voltage Lasers

Fig. 10. Scanning reference of the FSM.

Filter

FSM

Voltage Control dSPACE real-time control system amplifier signal

SGS sensor information

4 PI control Composite control

3

Fig. 13. Schematic diagram of the multi-target APT system. The APT system is designed for 1-to-2 target acquisition, pointing and tracking. The APT system consists of the optical subsystem, the sensing and control subsystem. The optical subsystem mainly consists of a gimbal, two FSMs, lasers, splitter mirror and convex lens. The sensing and control subsystem mainly consists of eddy-current sensor, CCD, real-time controller dSPACE, drivers of gimbal mirror, voltage amplifier of FSMs and host computer.

2 1 0 -1

VI. E XPERIMENTAL S TUDIES

-2

A. Experimental prototype development

-3 0

0.5

1

1.5

2

2.5

Time (s)

Fig. 11. Scanning error of the FSM.

PI control Composite control

3 2 1 0 -1 -2 0

1

2

3

4

5

Time (s)

Fig. 12. Pointing error of the FSM.

TABLE I C ONTROL ERROR OF THE APT SYSTEM (RMS)

Scanning simulation Pointing simulation

PI controller

Composite controller

1.75µrad 1.53µrad

0.29µrad 0.37µrad

controller. The simulation results are summarized in Table I. The simulation studies demonstrate the effectiveness of the proposed multi-target APT system. The control accuracy of the proposed composite controller is increased by 75.8% compared to the PI controller.

To validate the proposed multi-target APT system, this paper develops an experimental prototype. The schematic diagram of the experimental prototype of multi-target APT system is shown in Fig.13. The gimbal mirror is used for coarse acquisition, pointing and tracking. In addition, the disturbances caused by airborne vibration and relative motion is added to the gimbal mirror input to simulate the working environment of the APT system. The FSMs are employed for fine acquisition, pointing and tracking. The independent control of two optical axis can be realized by employing two lasers and two FSMs. The convex lens is used to eliminate the effect of translation motion and convert the deflection of the optical axis into the visual movement of the laser spot on CCD target surface. The splitter mirror is adopted to constitute a coaxial optical system. The gimbal mirror is controlled by the drivers, the control commands is sent using host computer. The motion information of gimbal mirror is measured by eddy-current sensor, collected by dSPACE and transmitted to FSMs for further control. The FSMs are controlled by dSPACE. The image information of the laser spot is collected by a CCD camera, which is used to evaluate the control accuracy of the developed APT system. According to the schematic diagram, the experimental prototype of multi-target APT system is developed as shown in Fig.14. All optical components are mounted on the Newport optical platform. The details of the optical system are shown in Fig.15. The azimuth axis of gimbal mirror and FSMs are perpendicular to the optical platform. The model of the FSMs is S-330.2SL with an closed loop deflection angle sets to 2mrad. The gimbal mirror is driven by torque motor with an accuracy of 25µrad. The dSPACE MicroLabBox is adopted as real-time controller,

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2868143, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS

7

Convex lens CCD

CCD target surface

Eddy current sensor



Mirror drivers

x

FSM voltage amplifier

Optical system

Focal length  dSPACE

Fig. 17. Geometric relationship of the imaging system.

Host computer

Fig. 14. Experimental prototype of multi-target APT system. The system consists the optical subsystem, the sensing and control subsystem as the schematic diagram in Fig.13.

Splitter mirror

FSM

x φχ 2χϑ cos δ = = (13) σ σ σ where χ is the focal length of convex lens and σ is the pixel size. φ is the divergence angle of the laser beam. ϑ is the azimuth (elevation) angle of the gimbal mirror and the FSM. δ is the angle between the azimuth (elevation) axis and the incident light. The precise geometrical relationship requires further calibration due to installation errors. ε=

Gimbal mirror FSM

Laser

B. Composite controller of FSM In order to verify the proposed composite controller of the FSM, the comparison between the composite controller and the PI controller is carried out. First, the linear dynamics of the FSM is identified as follows

Laser 4.1578×1020 ×(s2 +251.1s+4.145×106 ) (s+3594)(s2 +1222s+4.536×106 ) 1 2 (s +14050s+1.664×108 )(s2 +24650s+6.768×108 )

Convex lens

GL =

Fig. 15. Details of the optical system.

Laser spots

The parameters of the Bouc-Wen hysteresis dynamics are identified as d = 1.193, α = −0.384, β = 0.0275, and γ = −0.0038. The controllers are designed by using the identified dynamics. The PI controller is set to KP I = 0.0047 + 20.8/s using Z-N tuning method. The parameters of the composite controller are designed where the weighting function of the H∞ controller are set to w1 = w2 =

Fig. 16. Laser spots on the CCD target surface. The positions of the two laser spots coincide on the CCD target surface due to coaxial optical design.

and the sampling rate of the system is 10kHz. The pixel size of the CCD camera is 3.45µm. The focal length of the convex lens is 0.5m. Self-calibration of the optical axis is carried out before the experiments. The laser spots on the CCD target surface are shown in Fig.16, the spots diameter is 37 pixels. The optical axis rotation can be converted to visual movement of the laser spot on CCD target surface by geometric relation conversion as shown in Fig.17. The relationship between the rotation angle and the number of pixels moved on the CCD in case of small angle motion is written as

1000 wr = 1, wu = s+0.001 ,  2 s+100π 0.0001 · s+1000π

0.05

The cascade controllers for gimbal mirror are designed as Ki = 2.452 + 824.01/s, Kω = 0.132 + 15/s, Kθ = 22.3 + 1.316/s. Fig.18 shows the experimental results under different reference signals. The comparisons of the experimental results are given in Table II. The results indicate that the control accuracy of the composite controller is increased by more than 32.9% compared to the PI controller in experiment. It can be seen form the response under square signal that the rising time of FSM is 0.0046s while using the PI controller, but is 0.0015s while using the proposed composite controller. The composite controller exhibits higher accuracy and faster response. In the following experiments, the composite control method for FSM is employed to validate the designed multitarget APT system.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2868143, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS

8

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Fig. 19. Control error of the FSM in micro-scanning experiment.

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Fig. 18. Control error of the FSM under different signals.

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TABLE II C ONTROL ERROR OF FSM (RMS)

Sinusoidal signal(100µrad/5Hz) Square signal(100µrad/2Hz) Triangular signal(100µrad/2Hz) Random signal(≤100µrad/0-10Hz)

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6.68µrad 17.69µrad 2.40µrad 6.62µrad

1.70µrad 11.87µrad 0.52µrad 2.21µrad

Fig. 20. Motion trajectory of laser spot in micro-scanning experiment.

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The micro-scanning and pointing experiments for 1-to-1 target communication are given at first. Only one FSM is employed in the experiments. Then, the experiment for 1-to-2 target communication is carried out. Two FSMs are employed to verify the effectiveness of the proposed multi-target APT system. 1) Micro-scanning Experiment: The micro-scanning experiment using the FSM is carried out at first. The FSM needs to scan according to the reference trajectory while compensating the optical axis jitter. Fig.19 shows that the azimuth and elevation errors (RMS) of FSM are 0.76µrad and 0.42µrad, respectively. Fig.20 illustrates the comparison of the motion trajectory of the laser spot on CCD target surface. The scanning error of the APT system is 7.76µrad. 2) Pointing Experiment: The pointing experiment is carried out. The FSM is used to compensate the jitter of the optical axis in order to accurately point to the target. The input signal and the control error of FSM are shown in Fig.21. The azimuth and elevation errors (RMS) of FSM are 1.76µrad and 1.25µrad, respectively. The motion trajectory of the laser spot is shown in Fig.22. The jitter range of the laser spot is limited less than 10.71µrad.

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Fig. 22. Motion trajectory of the laser spot in pointing experiment.

3) Multi-target Experiment: In this section, two FSMs are used for micro-scanning. The reference trajectories of FSMs

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2868143, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS

9

Real trajectory Reference trajectory

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axis, image processing error and installation error of the APT system.

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Fig. 23. Motion trajectory of one laser spot in multi-target experiment. TABLE III C ONTROL ACCURACY OF THE APT

SYSTEM

Control error (RMS) Scanning experiment Pointing experiment Multi-target experiment

7.76µrad 10.71µrad 7.82µrad

and the disturbance condition are the same as that in Section VI-C1. Fig.23 shows the comparison of the motion trajectory of one of the laser spots on CCD target surface. The scanning error is 7.82µrad. The experimental results are summarized in Table III. VII. D ISCUSSION AND C ONCLUSION A. Discussion In the simulation studies, by using the proposed composite controller, the response rate is increased by 44% and the control accuracy is improved by 75.8% compared to the PI controller. When adopting the composite controller, the scanning and pointing errors are 0.29µrad and 0.37µrad, respectively. The simulation results demonstrate the effectiveness of the designed multi-target APT system. In the experimental studies, the control accuracy of the proposed composite controller is increased by more than 32.9% compared to the PI controller. The scanning and pointing experimental results demonstrate the control accuracy and multitarget processing capability of the developed experimental prototype of multi-target APT system. The control accuracy of the multi-target APT system is better than 10.71µrad considering complex disturbances. It can be seen from the comparison of the results in Fig.20 and Fig.23 that the control accuracy is attenuated by 0.77% when considering the coupling effect of FSMs. The multi-target scanning and pointing ability of the APT system with small coupling effect makes its practical application possible. As a key component of the multi-target APT system, the improvement of the control accuracy of FSM is fundamental to improve the control accuracy of the APT system. To further improve the control accuracy of the multi-target APT system, it is necessary to reduce the self-calibration error of the optical

To realize laser communication with cluster UAVs at long distance, the multi-target APT system is investigated in this paper. The combination of a gimbal mirror and FSMs is employed to realize synchronous communication with cluster UAVs. The composite control method comprising of the H∞ controller and the hysteresis compensator based on LS-SVM is proposed for fine scanning and pointing. The experimental prototype of multi-target APT is designed and the experiments are carried out to verify the proposed multi-target communication strategy. ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (51675430, 11402044 and U1537213). R EFERENCES [1] J. Mikolajczyk, Z. Bielecki, et al., “Analysis of free-space optics development,” Metrology and Measurement Systems, vol. 24, no. 4, pp. 653-674, 2017. [2] A.K. Majumdar, ”Advanced Free Space Optics (FSO): A Systems Approach,” Springer, vol. 186, 2014. [3] S.S. Muhammad, T. Plank, E. Leitgeb, et al., “Challenges in establishing free space optical communications between flying vehicles,” Communication Systems, Networks and Digital Signal Processing, 6th International Symposium on. IEEE, pp. 82-86, 2008. [4] E. Leitgeb, K. Zettl, S.S. Muhammad, et al. “Investigation in free space optical communication links between unmanned aerial vehicles (UAVs),” Transparent Optical Networks, ICTON’07. 9th International Conference on. IEEE, vol. 3, pp. 152-155, 2007. [5] Q. Fu, X. Liu, H. Jiang, et al., “The network and transmission of based on the principle of laser multipoint communication,” International Symposium on Optoelectronic Technology and Application 2014: Infrared Technology and Applications International Society for Optics and Photonics, 2014, vol. 9300. [6] T. Zhang, S. Mao, Q. Fu, et al., “Networking optical antenna of space laser communication,” Journal of Laser Applications, vol. 29, no.1, p. 012013, 2017. [7] T.H. Ho, S. Trisno, I.I. Smolyaninov, et al., “Studies of pointing, acquisition, and tracking of agile optical wireless transceivers for free-space optical communication networks,” In Optics in Atmospheric Propagation and Adaptive Systems VI, International Society for Optics and Photonics, vol. 5237, pp. 147-159, 2004. [8] Y. Kaymak, R. Rojas-Cessa, J. Feng, et al., “A survey on acquisition, tracking, and pointing mechanisms for mobile free-space optical communications,” IEEE Communications Surveys and Tutorials, vol. 20, no. 2, pp. 1104-1123, 2018. [9] J.C. Juarez, A. Dwivedi, A.R. Hammons, et al., “Free-space optical communications for next-generation military networks,” IEEE Commun. Mag., vol. 44, no. 11, 2006. [10] C. Lv, S. Tong, Y. Song, “Optimization design and demonstration of compound-axis APT in airborne laser communication,” In Photonics and Optoelectronics (SOPO), 2012 Symposium on. IEEE, pp. 1-4, 2012. [11] E.D. Miller, R.A. de Callafon, “Dual-stage servo control for an optical pointing system,” ASME 2013 Conference on Information Storage and Processing Systems. American Society of Mechanical Engineers, pp. V001T03A006-V001T03A006, 2013. [12] J.M. Hilkert, “A comparison of inertial line-of-sight stabilization techniques using mirrors,”In Acquisition, Tracking, and Pointing XVIII, International Society for Optics and Photonics, Orlando, FL, USA, vol. 5430, pp. 13-23, 2004. [13] M. Borrello, T. Enterprises, “A multi stage pointing acquisition and tracking (PAT) control system approach for air to air laser communications,” In American Control Conference, Proceedings of the 2005. IEEE, pp. 3975-3980.

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Qing Li received the B.Eng. degree in 2015 and the M.Eng. degree in 2017 from the School of Astronautics, Northwestern Polytechnical University, Xi’an, China, where she is currently working toward the Ph.D. degree. Her research interests include modeling, identification and control of precision motion systems, and electro-optical system control.

Lei Liu received the B.Eng. and Ph.D. degrees from Harbin Institute of Technology, China, in 2005 and 2011, respectively. In 2012, he received the second Ph.D. degree at the National University of Singapore. He is currently an Associate Professor with the School of Astronautics, Northwestern Polytechnical University, Xi’an, China. His research interests include modeling, identification and control of precision motion systems, spacecraft dynamics and control, active vibration isolation, and electrooptical system control. Xiaofei Ma received the B.Eng. degree from Northeastern University, Shenyang, China, in 2000, and the Ph.D. degrees from China Academy of Space Technology, Xi’an, China, in 2011. He is currently a Researcher and Associate Director with Xi’an Institute of Space Radio Technology, China. His research interests include satellite antenna and space mechanical engineering.

Si-Lu Chen (S’07-M’11) received his B.Eng. and Ph.D. degrees, both from the National University of Singapore (NUS), in 2005 and 2010 respectively. From 2010 to 2011, he was with Manufacturing Integration Technology Ltd, a Singapore-based semiconductor machine designer, as a senior engineer on motion control. From 2011 to 2017, he was a scientist in Mechatronics group, Singapore Institute of Manufacturing Technology (SIMTech), Agency for Science Technology and Research (A*STAR). During this period, he also acted as co-PI of the SIMTech-NUS Joint Lab on Precision Motion Systems, adjunct assistant professor of NUS, and PhD co-advisor for A*STAR Graduate School. Since 2017, he has been with Ningbo Institute of Industrial Technology, Chinese Academy of Sciences, as a professor. His current research interests include design and optimization of high-speed motion control systems, and beyondrigid-body control for compliant light-weight systems. He is currently serving as technical reviewers for IEEE/ASME Transactions of Mechatronics, IFAC Journal of Mechatronics, and ISA Transactions. Hai Yun received the B.Eng. degree in 2017 from the School of Astronautics, Northwestern Polytechnical University, Xi’an, China, where he is currently working toward the M.Eng. degree. His research interests include modeling, identification and control of precision motion systems, and active vibration isolation.

Shuo Tang received the B.Eng. and Ph.D. degrees from Northwestern Polytechnical University, Xi’an, China, in 1985 and 1988, respectively. He is currently a Professor and Director of Shaanxi Aerospace Flight Vehicle Design Key Laboratory with the School of Astronautics, Northwestern Polytechnical University, Xi’an, China. His research interests include aerospace design, flight dynamics and control, flight simulation and virtual prototyping technology, hypersonic dynamics and integrated design, spacecraft guidance and control technology.

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