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Application research of high-precision laser beam pointing technology in airborne aiming pod
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Application research of high-precision laser beam pointing technology in airborne aiming pod
T
⁎
Meilin Xiea,b, , Peng Liua,b, Caiwen Maa, Wei Haoa, Furui Zhanga,b, Wei Huanga, Xuezheng Liana a b
Xi’an Institute of Optics and Precision Mechanics of CAS, Xi’an, 710119, China University of Chinese Academy of Sciences, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Airborne aiming pod Composite axis Laser beam pointing technology Atmospheric turbulence
Airborne aiming pod is mainly used for searching, capturing and tracking the target indicated by the laser, and then dropping the laser-guided weapons precisely to complete the close-range support attack or dual-aircraft cooperative instruction/attack. High-precision laser beam pointing technology is the core of the airborne aiming pod, and the accuracy of it is fatal for the realization of the final tactical index. In this paper, the factors affecting the beam pointing accuracy based on the research of airborne aiming pod platform are analyzed. At first, the composition of the pod system and the motion coupling of the composite axis pod are introduced; and then the beam pointing algorithm under the external guidance combined with aircraft disturbance and the effects of atmospheric turbulence and atmospheric attenuation on beam quality, including optical axis drift, beam spread and intensity distribution variation are discussed. Finally, the performance of the pod servo system is simulated and verified in Simulink. The simulation result of the real flight situation with disturbance moment shows that the pointing accuracy of the airborne aiming pod can reach 0.0075 degrees. The data analyzed in this paper can provide technical reference for other aiming photoelectric platforms.
1. Introduction Airborne aiming pod is mainly used to provide target indication function for various laser guided weapons. The basic principle of the airborne aiming pod is that the laser indicator emits a beam to illuminate the target, and the laser receiving device mounted on the missile body receives the irradiated signal or the reflected signal of the target, and then calculates the degree of the missile body deviating from the irradiated or reflected laser beam, and continuously adjusts the flight trajectory so that the missile body moves along the irradiated laser until it hits the target. Airborne targeting pod will play a greater role in the future wars. According to the characteristics of modern warfare, the ways to improve the photoelectric targeting pod are as follows: firstly, the resolution of day and night forward-looking infrared sensors, television cameras and the effective detection distance under various adverse weather conditions should be continuously improved; secondly, the maximum action distance of laser indicators should be increased to enable aircraft to launch attacks from high altitude or outside enemy defense areas; thirdly, the pod should be equipped with more advanced target recognition. The system and data link should be separated to enhance the cooperative combat capability and improve the combat response speed [1]. It can be seen from the above that the operating distance and pointing accuracy of laser indication is one of the key technical ⁎
Corresponding author at: Xi’an Institute of Optics and Precision Mechanics of CAS, Xi’an, 710119, China. E-mail address: [email protected] (M. Xie).
https://doi.org/10.1016/j.ijleo.2019.02.152 Received 23 January 2019; Accepted 26 February 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
M. Xie, et al.
Fig. 1. Composition of Airborne Aiming Pod.
indexes of aiming pod. The main factors affecting the high accuracy of beam pointing include the real-time and accuracy of the pointing algorithm, the optical axis drift caused by atmospheric turbulence and beam expansion, the change of light intensity distribution caused by atmospheric turbulence and atmospheric attenuation, and the performance of pod servo system [2,3]. In view of the above problems, this paper makes a comprehensive and quantitative analysis of many factors affecting the beam pointing accuracy. The method proposed in this paper can be quickly transplanted to other photoelectric platforms on moving bases, and the analysis data are instructive to other laser indication systems. 2. Composition and motion coupling of the airborne aiming pod system 2.1. Composition of the airborne aiming pod system As shown in Fig. 1, the airborne aiming pod is designed in the form of two axes and four frames. The load of it is mainly a three axes fiber optic gyroscope, a laser illumination and indication system, a visible zoom TV and an infrared TV. The airborne aiming pod realizes high precision stabilization and pointing through two-stage shafting. The platform has two degrees of freedom, namely, azimuth and pitch. There are two frames for each degree of freedom, and their names are the exterior frame (A), the exterior pitch frame (E), the interior pitch frame (e) and the interior azimuth frame (a). Consequently, the structure of this platform is also called the A-E-e-a structure. The outer frames are driven by DC motor through reducer, and the inner frames are driven by DC torque motor directly. In order to overcome the problem that the accuracy of the airborne aiming pod decreases when it operates in a wide range, this paper adopts the design of the inner frames which are always stable while the outer frames follow the inner frames. The details are as follows. When the carrier of the airborne aiming pod moves, the interference angle motion generated by the carrier is coupled to the load axis step by step, which affects the stability of the load axis. The gyroscopes installed on the inner frames send the measured coupling interference rates in azimuth and pitch axes to the interior pitch frame (e) and the interior azimuth frame (a) motors respectively. Then the two motors generate angular motion with equal disturbance speed in the opposite direction to counteract disturbance speed and ensure stable direction of load sight axis [4,5]. While the angle sensors installed on the axes of the interior pitch frame (e) and the interior azimuth frame (a) send the angle deviation signals of the two inner frames relative to the outer frames to the servo motors on the two outer frames respectively through the control loop to control the outer frames and the outer pitch frame to follow the inner frames. Then, the airborne aiming pod can track the target directly below and near the carrier. 2.2. Solution of motion coupling relation Multiple aiming pods isolate the interference motion by four pods. As shown in Fig. 2, the isolation principle of multiple systems to carrier interference motion is simply analyzed. Where the OXb Yb Zb denotes the carrier coordinate system; the OXA YA ZA denotes the outer azimuth coordinate system which rotates θA around the outer azimuth axis ZA , relative to the carrier coordinate system; the OXE YE ZE denotes the outer pitch coordinate system which rotates θE around the outer pitch axis YE , relative to the outer azimuth coordinate system; the OXe Ye Ze denotes the inner pitch coordinate system which rotates θe around the outer pitch axis Ye , relative to the outer pitch coordinate system; the OXa Ya Za denotes the inner azimuth 776
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
M. Xie, et al.
Fig. 2. A-E-e-a coordinate rotation.
coordinate system which rotates θa around the inner azimuth axis Za , relative to the inner pitch coordinate system [6–8]. According to the Fig.2, the angular velocity expressions of the motion of each frame are calculated as follows.
• the exterior frame (A): 0 cos θA sin θA 0 ⎞ ωbx ω ⎛ ⎞ ⎛ ⎞ ⎛ AX ⎞ ⎛ ωA = ⎜ ωAY ⎟ = ⎜− sin θA cos θA 0 ⎟ ⎜ ωby ⎟ + ⎜ 0 ⎟ ⎜ ⎟ ⎝ ωAZ ⎠ ⎝ 0 0 1 ⎠ ⎝ ωbz ⎠ ⎝ θ˙AZ ⎠
(1)
Where ωbx , ωby , ωbz denote the disturbance of the carrier, θ˙AZ denotes the angular velocity of the exterior frame driven by its motor
• the exterior pitch frame (E): 0 ⎞ cos θE 0 − sin θE ⎞ ωAX ω ⎛ EX ⎞ ⎛ ⎛ ⎞ ⎛ ωE = ⎜ ωEY ⎟ = ⎜ 0 1 0 ⎟ ⎜ ωAY ⎟ + ⎜ θ˙ EY ⎟ ⎜ ⎟ ⎝ ωEZ ⎠ ⎝ sin θE 0 cos θE ⎠ ⎝ ωAZ ⎠ ⎝ 0 ⎠
(2)
Where ωAX , ωAY , ωAZ denote the disturbance of the exterior frame (A), θ˙ EY denotes the angular velocity of the exterior pitch frame driven by its motor
• the interior pitch frame (e): 0 ω cos θe 0 − sin θe ⎞ ωEX ⎛ eX ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ωe = ⎜ ωeY ⎟ = ⎜ 0 1 0 ⎟ ⎜ ωEY ⎟ + ⎜ θ˙eY ⎟ ⎜ ⎟ ⎟ ⎜ ⎝ ωeZ ⎠ ⎝ sin θe 0 cos θe ⎠ ⎝ ωEZ ⎠ ⎝ 0 ⎠
(3)
Where ωEX , ωEY , ωEZ denote the disturbance of the exterior pitch frame (E), θ˙eY denotes the angular velocity of the interior pitch frame driven by its motor.
• the interior azimuth frame (a): 0 ω cos θa sin θa 0 ⎞ ωeX ⎞ ⎛ ⎞ ⎛ ⎛ aX ⎞ ⎛ ωa = ⎜ ωaY ⎟ = ⎜− sin θa cos θa 0 ⎟ ⎜ ωeY ⎟ + ⎜ 0 ⎟ ⎜ ⎟ ⎟ ⎜ ⎝ ωaZ ⎠ ⎝ 0 0 1 ⎠ ⎝ ωeZ ⎠ ⎝ θ˙aZ ⎠
(4)
Where ωeX , ωeY , ωeZ denote the disturbance of the interior pitch frame (e), θ˙aZ denotes the angular velocity of the interior azimuth frame driven by its motor. Because of the lack of freedom in X-axis (i.e. the roll motion of the carrier), when the azimuth of the interior azimuth frame (a) is zero, the angular motion of the axis rotates around the optical axis of the instrument, so only the angular motion of azimuth and pitch axis needs to be considered. All of the above, the angular motion of the platform can be simplified as follows:
ω ω ω ω ⎡ aY ⎤ = ⎡ cos θa 0 ⎤ ⎡ eY ⎤ − sin θa⋅⎡ eX ⎤ = ⎡ cos θa 0 ⎤ ⎡ eY ⎤ − sin θa⋅ 1 ⎦ ⎣ ωaZ ⎦ 1 ⎦ ⎣ ωaZ ⎦ ⎣ 0 ⎦ ⎣ 0 ⎣ ωaZ ⎦ ⎣ 0 T
0 ⎤ ωbX ⎧ ⎡ cos θe cos θE cos θA ⎫ ⎪ ⎤ ⎡ sin θe (sin θE + cos θE ) ⎤ ⎪ ⎢ cos θe cos θE sin θA 0 ⎥ ⎢ ωbY ⎥ − θ˙AZ ⋅⎡ ⎨⎢ 0 ⎣ ⎦⎬ ωbZ ⎦ ⎪ ⎣−sin θe (sin θE + cos θE ) 0 ⎥ ⎪ ⎦ ⎣ ⎩ ⎭ 777
(5)
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
M. Xie, et al.
According to the upper formula, the motion of the platform can be divided into two parts: one part is transmitted to the platform along the axis of the inner frames, such as servo control angle motion transfer, friction constraint coupling and etc.; the other one is transmitted to the platform through the rigid geometric constraint of the supporting shaft by the angular velocity of the exterior frame (A) and the exterior pitch frame (E). The prominent feature of the A-E-e-a structure is to ensure that the interior pitch frame (e) and the interior azimuth frame (a) are perpendicular to each other (θa = 0 ), thus eliminating the block. Therefore the upper formula can be further simplified as:
ω ω ω + θ˙eY ⎤ ⎡ ωAY + θ˙ EY + θ˙eY ⎤ ⎡ θ˙ EY + θ˙eY ⎤ ω ⎡ aY ⎤ = ⎡ eY ⎤ = ⎡ EY ⎡ AY ⎤ =⎢ ⎢ ⎥ = ⎢ θ˙ ⎥ + ⎣ ωeZ ⎦ ω ω aZ aZ ˙aZ ⎣ ⎦ ⎣ ⎦ ⎣ ωeZ + θ˙aZ ⎥ ω + θ eZ aZ ⎦ ⎣ ⎦ ⎣ ⎦ ωAY θ˙ EY + θ˙eY 0 ⎡ ⎤ ⎤ ⎡ ⎤ ⎡ =⎢ ⎥ + ωAX ⋅sin(θe + θE ) ⎦ + ωbz ⋅cos(θe + θE ) ˙ ˙ ⎣ ⎦ ⎣ θaZ + θAZ ⋅cos(θe + θE ) ⎦ ⎣
(6)
Then we can know that the first part is the active control angular motion of the motor, the second part is the friction coupling angular motion, and the third part is the disturbance of the aircraft azimuth axis. 3. High-precision beam pointing algorithms in external guidance The airborne aiming pod achieves high precision pointing to the target through the external guidance. We suppose that the space coordinate position of the aircraft is (xp, yp, zp) and the target space coordinate position is (xT , yT , zT ) in the WGS84 coordinate system. So the unit pointing vector of the optic axis of an airborne pod can be expressed as:
D=⎛ ⎝
xT − xP yT − yP zT − zP ⎞ , , L L L ⎠
where L = (xT − xT )2 + (yT − yP )2 + (zT − zP )2 denotes the absolute distance between the target and the airborne aiming pod [9,10]. According to the current aircraft position information, the unit pointing vector D can be converted to the navigation coordinate system as DN : Then, the DN can be converted to the body coordinate system as DP :
0 0 ⎞ ⎛ cos P 0 − sin P ⎞ ⎛ cos A′ sin A′ 0 ⎞ ⎛1 DP = 0 cos R sin R ⋅ 0 1 0 ⎟⋅⎜− sin A′ cos A′ 0 ⎟⋅DN ⎟⎜ ⎜ 0 1⎠ ⎝ 0 − sin R cos R ⎠ ⎝ sin P 0 cos P ⎠ ⎝ 0
(7)
Where A′ denotes the direction angle of aircraft; P denotes the pitch angle of aircraft; R denotes the rolling angle of aircraft. The LOS (line-of-sight) vectors N in the body coordinate system can be expressed by the following formula:
0 0 ⎞ ⎛ cos E − sin E 0 ⎞ ⎛1 N = 0 cos A sin A ⋅ sin E cos E 0 ⋅N0 ⎟ ⎟⎜ ⎜ 0 1⎠ ⎝ 0 − sin A cos A ⎠ ⎝ 0
(8)
Where A denotes the azimuth angle of the airborne aiming pod; E denotes the pitch angle of the airborne aiming pod; N0 denotes the LOS Initial Vector when the A and E are 0. According to the upper formula, the A and E can be obtained if DP = N . But the angle calculated is not accurate in practical situations as the factors such as flight speed of aircraft, data update rate of inertial navigation system, delay of other systems and so on. Therefore, it is necessary to design a delay compensation algorithm to ensure the real-time performance of the system as far as possible, that is to say, the target is in the center of the field of view. Generally, Kalman filter or other filtering algorithms are used to predict the current direction of the turntable in combination with the current motion state. 4. Study on optical axis drift and beam spread in atmospheric turbulence 4.1. Optical axis drift in atmospheric turbulence Turbulence intensity is affected by many factors. The state of atmospheric turbulence near the surface is easily affected by topography and landform, which is called boundary layer. The upper atmosphere turbulence is little affected by the ground condition, which is called free atmosphere. The intensity of atmospheric turbulence near the ground has obvious diurnal variation and geographic variation. Cn2 denotes the refractive index structure constant, which is a key parameter for evaluating atmospheric turbulence intensity. It can be calculated by the Hufnagel-valley(HV) model as follows:
Cn2 (h) = 5.94 × 10−53 (w /27)2h10 exp( −h/1000) + 2.7 × 10−16 exp( −h/1500) + A exp( −h/100)
Cn2
10−14m−2 3
(9)
Where A denotes the typical number of the as 1.7 × . Optical axis drift and beam spread in atmospheric turbulence are shown as Fig. 3: Where RLT denotes the equivalent spot size; rc denotes the spot drift size; RST denotes the spot size after beam expansion. And the three 778
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
M. Xie, et al.
Fig. 3. Diagram of beam drift and spread caused by turbulence. 2 2 = rc2 + RST factors satisfy the formula: RLT The variance of spot centroid drift in turbulence can be obtained by the Kolmogrov Formula: 1
σρ2 = 2.03Cn2 L3 (D)− 3
(10)
Where D denotes the beam emission diameter; L denotes the distance of the beam. Then we get the relationship between spot position drift and propagation distance under different turbulence intensity shown as Fig. 4: 4.2. Extended dimensions in atmospheric turbulence The RMS (root mean square) width of a beam in turbulent environment can be expressed as follows:
W (L) =
ω02 2L2 ⎛ 1 1⎞ + 2 ⎜ 2 + 2 ⎟ + 4(0.545Cn2 )6 5k 2 5L16 k ⎝ ω0 2 σg ⎠
5
(11)
Where the first two are the expansion of light in free space, and the third is the expansion of light beam caused by turbulence, σg2 = 0.005 m. Then we get the extended dimensions due to turbulence shown as Fig. 5: 5. Effects of atmospheric attenuation and atmospheric turbulence on light intensity distribution The attenuation effect of laser in the atmosphere can be expressed by the beer’s law as follows:
Pλ (L) = Pλ0 exp[−σ (λ ) L] σ (λ ) =
3.912 ⎛ λ ⎞−q V ⎝ 0.55 ⎠
(12)
Where V denotes the visibility, q takes values as follows:
Fig. 4. Spot position drift and propagation distance under different turbulence intensity. 779
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
M. Xie, et al.
Fig. 5. Extended dimensions due to turbulence.
Fig. 6. Laser energy attenuation ratio under different turbulence intensity.
Fig. 7. Aircraft flight trajectory.
780
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
M. Xie, et al.
Fig. 8. The simulation system of the airborne aiming pod control system. Table 1 Initial Parameter Settings. Parameters
values
Measurement errors of POS
Pitch error Roll error Direction error BeiDou II differential positioning error 5m Azimuth axis Pitch axis
Flight target trajectory error Pod shafting errors Spatial directional instability of beams
10″(3δ ) 10″(3δ ) 25″(3δ ) 0.1 m (on 20 km baseline condition) 5″(3δ ) 8″(3δ ) 0.03mrad(1σ)
Fig. 9. The beam pointing error of the whole system.
⎧1.6, (Highvisibility) q = 1.3, (Moderatevisibility) ⎨ 1 3 ⎩ 0.585V , (V ≤ 6km)
(13)
Then the intensity distribution of Gauss beams propagating through atmospheric turbulence can be deduced, according to the generalized Huygens-Fresnel principle. 2
P (r , z ) = Where B =
k , 2z
2B2P0 B2 r exp[−σ (λ ) z /1000] × exp[−2 2 ⎛ ⎞ ] 2 2 G ⎝ ω0 ⎠ πG ω0
G=
⎜
1 ω04
+
2 ρ02 ω02
+
k2 4z 2
⎟
(14)
, ρ0 = (0.545Cn2 k 2z )−3/5, k = 2π / λ
Then we get the laser energy attenuation ratio under different turbulence intensity shown as Fig. 6: 6. Simulation and analysis of servo pointing accuracy As shown in Fig. 7, the flight trajectory of the aircraft is simulated in Simulink. Suppose there is a target to be hit at a certain position on the ground. The point at which the ground is pointed is located at (108.975 °E, 34.6 °N, Height: 1000 m). As shown in Fig. 8, the simulation system of the airborne aiming pod control system is built which the disturbance torques such as Coulomb friction and viscous friction, the data delay of POS and angular sensor and many factors shown in Table 1 are taken into account by calculating the pointing angles according to the directional algorithm deduced in this paper. 781
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
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Comparing the calculated beam pointing angles with the actual angles, the beam pointing error of the whole system can be obtained, as shown in Fig. 9. The maximum pointing error is 0.015 ° and the RMS(root mean square) value is 0.0075 °, which meets the pointing requirement. 7. Conclusion A new generation of photoelectric reconnaissance laser indicator system with the ability of searching, tracking, ranging and locating targets day and night is mainly used for target reconnaissance and attack. It provides data support for the whole system and irradiation guidance for semi-active laser guidance equipment. In this paper, the directional accuracy of laser beams is systematically analyzed from three aspects: one is that a high-precision laser pointing algorithm which takes both real-time and accuracy into account on moving base is derived; the second one is that the optical axis drift, beam spread and intensity distribution caused by atmospheric turbulence are quantitatively analyzed based on the theory; the third one is that the simulation results of the pointing accuracy of the servo control system show the effectiveness of the control strategy by considering the shafting sloshing, disturbance moment and sensor delay of the pod. The research on laser beam pointing of airborne aiming pod can be widely used in anti-terrorism stabilization, maritime law enforcement, forest fire prevention and other fields, which provides reliable data reference for the calculation and analysis of laser transmission in the atmosphere. References [1] Junlan Yang, Dan Schonfeld, Magdi Mohamed, Robust video stabilization based on particle filter tracking of projected camera motion, IEEE Trans. Circuits Syst. 19 (7) (2009) 945–954. [2] Xie Meilin, Liu Peng, Caiwen Ma, Research on key technologies of active polarization imaging system, Optik 157 (2018) 556–564. [3] Xie Meilin, Caiwen Ma, Liu Kai, The application of active polarization imaging technology of the vehicle theodolite, Opt. Commun. 433 (2019) (2019) 74–80. [4] Joon Lyou, Min Sig Kang, Hwy Kuen Kwak, Dual stage and digital image basedmethod for sight stabilization, J. Mech. Sci. Technol. 5 (2008) 1114–1119. [5] S. Zhao, K.K. Tan, Adaptive feedforward compensation of force ripples in linear motors, Control Eng. Pract. 13 (9) (2005) 1081–1092. [6] George W. Younkin, Compensating structural dynamics for servo driven industrial machines with acceleration feedback, Industry Applications Conference, 2004, 39th IAS Annual Meeting. Conference Record of the 2004 IEEE vol.3, (2004) 1881–l890. [7] Hucheng He, Yiqun Ji, Jiankang Zhou, Weimin Shen. Imaging quality analysis and evaluation of optical polarization imaging system with optical transfer matrix, Optik 124 (24) (2013) 6557–6560. [8] Tyo J. Scott, L. Goldstein Dennis, B. Chenault David, et al., Review of passive imaging polarimetry for remote sensing applications, Appl. Opt. 45 (22) (2006) 5453–5469. [9] Li Yanan, Sun Xiaobing, Mao Yongna, et al., Spectral polarization characteristic of space target, Infrared Laser Eng. 41 (1) (2012) 205–210 (in Chinese). [10] J.M. Bueno, P. Artal, Double -pass imaging polarimetry in the human eye, Opt. Lett. 24 (1) (1999) 64–66.
782
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Application research of high-precision laser beam pointing technology in airborne aiming pod
T
⁎
Meilin Xiea,b, , Peng Liua,b, Caiwen Maa, Wei Haoa, Furui Zhanga,b, Wei Huanga, Xuezheng Liana a b
Xi’an Institute of Optics and Precision Mechanics of CAS, Xi’an, 710119, China University of Chinese Academy of Sciences, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Airborne aiming pod Composite axis Laser beam pointing technology Atmospheric turbulence
Airborne aiming pod is mainly used for searching, capturing and tracking the target indicated by the laser, and then dropping the laser-guided weapons precisely to complete the close-range support attack or dual-aircraft cooperative instruction/attack. High-precision laser beam pointing technology is the core of the airborne aiming pod, and the accuracy of it is fatal for the realization of the final tactical index. In this paper, the factors affecting the beam pointing accuracy based on the research of airborne aiming pod platform are analyzed. At first, the composition of the pod system and the motion coupling of the composite axis pod are introduced; and then the beam pointing algorithm under the external guidance combined with aircraft disturbance and the effects of atmospheric turbulence and atmospheric attenuation on beam quality, including optical axis drift, beam spread and intensity distribution variation are discussed. Finally, the performance of the pod servo system is simulated and verified in Simulink. The simulation result of the real flight situation with disturbance moment shows that the pointing accuracy of the airborne aiming pod can reach 0.0075 degrees. The data analyzed in this paper can provide technical reference for other aiming photoelectric platforms.
1. Introduction Airborne aiming pod is mainly used to provide target indication function for various laser guided weapons. The basic principle of the airborne aiming pod is that the laser indicator emits a beam to illuminate the target, and the laser receiving device mounted on the missile body receives the irradiated signal or the reflected signal of the target, and then calculates the degree of the missile body deviating from the irradiated or reflected laser beam, and continuously adjusts the flight trajectory so that the missile body moves along the irradiated laser until it hits the target. Airborne targeting pod will play a greater role in the future wars. According to the characteristics of modern warfare, the ways to improve the photoelectric targeting pod are as follows: firstly, the resolution of day and night forward-looking infrared sensors, television cameras and the effective detection distance under various adverse weather conditions should be continuously improved; secondly, the maximum action distance of laser indicators should be increased to enable aircraft to launch attacks from high altitude or outside enemy defense areas; thirdly, the pod should be equipped with more advanced target recognition. The system and data link should be separated to enhance the cooperative combat capability and improve the combat response speed [1]. It can be seen from the above that the operating distance and pointing accuracy of laser indication is one of the key technical ⁎
Corresponding author at: Xi’an Institute of Optics and Precision Mechanics of CAS, Xi’an, 710119, China. E-mail address: [email protected] (M. Xie).
https://doi.org/10.1016/j.ijleo.2019.02.152 Received 23 January 2019; Accepted 26 February 2019 0030-4026/ © 2019 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
M. Xie, et al.
Fig. 1. Composition of Airborne Aiming Pod.
indexes of aiming pod. The main factors affecting the high accuracy of beam pointing include the real-time and accuracy of the pointing algorithm, the optical axis drift caused by atmospheric turbulence and beam expansion, the change of light intensity distribution caused by atmospheric turbulence and atmospheric attenuation, and the performance of pod servo system [2,3]. In view of the above problems, this paper makes a comprehensive and quantitative analysis of many factors affecting the beam pointing accuracy. The method proposed in this paper can be quickly transplanted to other photoelectric platforms on moving bases, and the analysis data are instructive to other laser indication systems. 2. Composition and motion coupling of the airborne aiming pod system 2.1. Composition of the airborne aiming pod system As shown in Fig. 1, the airborne aiming pod is designed in the form of two axes and four frames. The load of it is mainly a three axes fiber optic gyroscope, a laser illumination and indication system, a visible zoom TV and an infrared TV. The airborne aiming pod realizes high precision stabilization and pointing through two-stage shafting. The platform has two degrees of freedom, namely, azimuth and pitch. There are two frames for each degree of freedom, and their names are the exterior frame (A), the exterior pitch frame (E), the interior pitch frame (e) and the interior azimuth frame (a). Consequently, the structure of this platform is also called the A-E-e-a structure. The outer frames are driven by DC motor through reducer, and the inner frames are driven by DC torque motor directly. In order to overcome the problem that the accuracy of the airborne aiming pod decreases when it operates in a wide range, this paper adopts the design of the inner frames which are always stable while the outer frames follow the inner frames. The details are as follows. When the carrier of the airborne aiming pod moves, the interference angle motion generated by the carrier is coupled to the load axis step by step, which affects the stability of the load axis. The gyroscopes installed on the inner frames send the measured coupling interference rates in azimuth and pitch axes to the interior pitch frame (e) and the interior azimuth frame (a) motors respectively. Then the two motors generate angular motion with equal disturbance speed in the opposite direction to counteract disturbance speed and ensure stable direction of load sight axis [4,5]. While the angle sensors installed on the axes of the interior pitch frame (e) and the interior azimuth frame (a) send the angle deviation signals of the two inner frames relative to the outer frames to the servo motors on the two outer frames respectively through the control loop to control the outer frames and the outer pitch frame to follow the inner frames. Then, the airborne aiming pod can track the target directly below and near the carrier. 2.2. Solution of motion coupling relation Multiple aiming pods isolate the interference motion by four pods. As shown in Fig. 2, the isolation principle of multiple systems to carrier interference motion is simply analyzed. Where the OXb Yb Zb denotes the carrier coordinate system; the OXA YA ZA denotes the outer azimuth coordinate system which rotates θA around the outer azimuth axis ZA , relative to the carrier coordinate system; the OXE YE ZE denotes the outer pitch coordinate system which rotates θE around the outer pitch axis YE , relative to the outer azimuth coordinate system; the OXe Ye Ze denotes the inner pitch coordinate system which rotates θe around the outer pitch axis Ye , relative to the outer pitch coordinate system; the OXa Ya Za denotes the inner azimuth 776
Optik - International Journal for Light and Electron Optics 183 (2019) 775–782
M. Xie, et al.
Fig. 2. A-E-e-a coordinate rotation.
coordinate system which rotates θa around the inner azimuth axis Za , relative to the inner pitch coordinate system [6–8]. According to the Fig.2, the angular velocity expressions of the motion of each frame are calculated as follows.
• the exterior frame (A): 0 cos θA sin θA 0 ⎞ ωbx ω ⎛ ⎞ ⎛ ⎞ ⎛ AX ⎞ ⎛ ωA = ⎜ ωAY ⎟ = ⎜− sin θA cos θA 0 ⎟ ⎜ ωby ⎟ + ⎜ 0 ⎟ ⎜ ⎟ ⎝ ωAZ ⎠ ⎝ 0 0 1 ⎠ ⎝ ωbz ⎠ ⎝ θ˙AZ ⎠
(1)
Where ωbx , ωby , ωbz denote the disturbance of the carrier, θ˙AZ denotes the angular velocity of the exterior frame driven by its motor
• the exterior pitch frame (E): 0 ⎞ cos θE 0 − sin θE ⎞ ωAX ω ⎛ EX ⎞ ⎛ ⎛ ⎞ ⎛ ωE = ⎜ ωEY ⎟ = ⎜ 0 1 0 ⎟ ⎜ ωAY ⎟ + ⎜ θ˙ EY ⎟ ⎜ ⎟ ⎝ ωEZ ⎠ ⎝ sin θE 0 cos θE ⎠ ⎝ ωAZ ⎠ ⎝ 0 ⎠
(2)
Where ωAX , ωAY , ωAZ denote the disturbance of the exterior frame (A), θ˙ EY denotes the angular velocity of the exterior pitch frame driven by its motor
• the interior pitch frame (e): 0 ω cos θe 0 − sin θe ⎞ ωEX ⎛ eX ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ωe = ⎜ ωeY ⎟ = ⎜ 0 1 0 ⎟ ⎜ ωEY ⎟ + ⎜ θ˙eY ⎟ ⎜ ⎟ ⎟ ⎜ ⎝ ωeZ ⎠ ⎝ sin θe 0 cos θe ⎠ ⎝ ωEZ ⎠ ⎝ 0 ⎠
(3)
Where ωEX , ωEY , ωEZ denote the disturbance of the exterior pitch frame (E), θ˙eY denotes the angular velocity of the interior pitch frame driven by its motor.
• the interior azimuth frame (a): 0 ω cos θa sin θa 0 ⎞ ωeX ⎞ ⎛ ⎞ ⎛ ⎛ aX ⎞ ⎛ ωa = ⎜ ωaY ⎟ = ⎜− sin θa cos θa 0 ⎟ ⎜ ωeY ⎟ + ⎜ 0 ⎟ ⎜ ⎟ ⎟ ⎜ ⎝ ωaZ ⎠ ⎝ 0 0 1 ⎠ ⎝ ωeZ ⎠ ⎝ θ˙aZ ⎠
(4)
Where ωeX , ωeY , ωeZ denote the disturbance of the interior pitch frame (e), θ˙aZ denotes the angular velocity of the interior azimuth frame driven by its motor. Because of the lack of freedom in X-axis (i.e. the roll motion of the carrier), when the azimuth of the interior azimuth frame (a) is zero, the angular motion of the axis rotates around the optical axis of the instrument, so only the angular motion of azimuth and pitch axis needs to be considered. All of the above, the angular motion of the platform can be simplified as follows:
ω ω ω ω ⎡ aY ⎤ = ⎡ cos θa 0 ⎤ ⎡ eY ⎤ − sin θa⋅⎡ eX ⎤ = ⎡ cos θa 0 ⎤ ⎡ eY ⎤ − sin θa⋅ 1 ⎦ ⎣ ωaZ ⎦ 1 ⎦ ⎣ ωaZ ⎦ ⎣ 0 ⎦ ⎣ 0 ⎣ ωaZ ⎦ ⎣ 0 T
0 ⎤ ωbX ⎧ ⎡ cos θe cos θE cos θA ⎫ ⎪ ⎤ ⎡ sin θe (sin θE + cos θE ) ⎤ ⎪ ⎢ cos θe cos θE sin θA 0 ⎥ ⎢ ωbY ⎥ − θ˙AZ ⋅⎡ ⎨⎢ 0 ⎣ ⎦⎬ ωbZ ⎦ ⎪ ⎣−sin θe (sin θE + cos θE ) 0 ⎥ ⎪ ⎦ ⎣ ⎩ ⎭ 777
(5)
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According to the upper formula, the motion of the platform can be divided into two parts: one part is transmitted to the platform along the axis of the inner frames, such as servo control angle motion transfer, friction constraint coupling and etc.; the other one is transmitted to the platform through the rigid geometric constraint of the supporting shaft by the angular velocity of the exterior frame (A) and the exterior pitch frame (E). The prominent feature of the A-E-e-a structure is to ensure that the interior pitch frame (e) and the interior azimuth frame (a) are perpendicular to each other (θa = 0 ), thus eliminating the block. Therefore the upper formula can be further simplified as:
ω ω ω + θ˙eY ⎤ ⎡ ωAY + θ˙ EY + θ˙eY ⎤ ⎡ θ˙ EY + θ˙eY ⎤ ω ⎡ aY ⎤ = ⎡ eY ⎤ = ⎡ EY ⎡ AY ⎤ =⎢ ⎢ ⎥ = ⎢ θ˙ ⎥ + ⎣ ωeZ ⎦ ω ω aZ aZ ˙aZ ⎣ ⎦ ⎣ ⎦ ⎣ ωeZ + θ˙aZ ⎥ ω + θ eZ aZ ⎦ ⎣ ⎦ ⎣ ⎦ ωAY θ˙ EY + θ˙eY 0 ⎡ ⎤ ⎤ ⎡ ⎤ ⎡ =⎢ ⎥ + ωAX ⋅sin(θe + θE ) ⎦ + ωbz ⋅cos(θe + θE ) ˙ ˙ ⎣ ⎦ ⎣ θaZ + θAZ ⋅cos(θe + θE ) ⎦ ⎣
(6)
Then we can know that the first part is the active control angular motion of the motor, the second part is the friction coupling angular motion, and the third part is the disturbance of the aircraft azimuth axis. 3. High-precision beam pointing algorithms in external guidance The airborne aiming pod achieves high precision pointing to the target through the external guidance. We suppose that the space coordinate position of the aircraft is (xp, yp, zp) and the target space coordinate position is (xT , yT , zT ) in the WGS84 coordinate system. So the unit pointing vector of the optic axis of an airborne pod can be expressed as:
D=⎛ ⎝
xT − xP yT − yP zT − zP ⎞ , , L L L ⎠
where L = (xT − xT )2 + (yT − yP )2 + (zT − zP )2 denotes the absolute distance between the target and the airborne aiming pod [9,10]. According to the current aircraft position information, the unit pointing vector D can be converted to the navigation coordinate system as DN : Then, the DN can be converted to the body coordinate system as DP :
0 0 ⎞ ⎛ cos P 0 − sin P ⎞ ⎛ cos A′ sin A′ 0 ⎞ ⎛1 DP = 0 cos R sin R ⋅ 0 1 0 ⎟⋅⎜− sin A′ cos A′ 0 ⎟⋅DN ⎟⎜ ⎜ 0 1⎠ ⎝ 0 − sin R cos R ⎠ ⎝ sin P 0 cos P ⎠ ⎝ 0
(7)
Where A′ denotes the direction angle of aircraft; P denotes the pitch angle of aircraft; R denotes the rolling angle of aircraft. The LOS (line-of-sight) vectors N in the body coordinate system can be expressed by the following formula:
0 0 ⎞ ⎛ cos E − sin E 0 ⎞ ⎛1 N = 0 cos A sin A ⋅ sin E cos E 0 ⋅N0 ⎟ ⎟⎜ ⎜ 0 1⎠ ⎝ 0 − sin A cos A ⎠ ⎝ 0
(8)
Where A denotes the azimuth angle of the airborne aiming pod; E denotes the pitch angle of the airborne aiming pod; N0 denotes the LOS Initial Vector when the A and E are 0. According to the upper formula, the A and E can be obtained if DP = N . But the angle calculated is not accurate in practical situations as the factors such as flight speed of aircraft, data update rate of inertial navigation system, delay of other systems and so on. Therefore, it is necessary to design a delay compensation algorithm to ensure the real-time performance of the system as far as possible, that is to say, the target is in the center of the field of view. Generally, Kalman filter or other filtering algorithms are used to predict the current direction of the turntable in combination with the current motion state. 4. Study on optical axis drift and beam spread in atmospheric turbulence 4.1. Optical axis drift in atmospheric turbulence Turbulence intensity is affected by many factors. The state of atmospheric turbulence near the surface is easily affected by topography and landform, which is called boundary layer. The upper atmosphere turbulence is little affected by the ground condition, which is called free atmosphere. The intensity of atmospheric turbulence near the ground has obvious diurnal variation and geographic variation. Cn2 denotes the refractive index structure constant, which is a key parameter for evaluating atmospheric turbulence intensity. It can be calculated by the Hufnagel-valley(HV) model as follows:
Cn2 (h) = 5.94 × 10−53 (w /27)2h10 exp( −h/1000) + 2.7 × 10−16 exp( −h/1500) + A exp( −h/100)
Cn2
10−14m−2 3
(9)
Where A denotes the typical number of the as 1.7 × . Optical axis drift and beam spread in atmospheric turbulence are shown as Fig. 3: Where RLT denotes the equivalent spot size; rc denotes the spot drift size; RST denotes the spot size after beam expansion. And the three 778
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Fig. 3. Diagram of beam drift and spread caused by turbulence. 2 2 = rc2 + RST factors satisfy the formula: RLT The variance of spot centroid drift in turbulence can be obtained by the Kolmogrov Formula: 1
σρ2 = 2.03Cn2 L3 (D)− 3
(10)
Where D denotes the beam emission diameter; L denotes the distance of the beam. Then we get the relationship between spot position drift and propagation distance under different turbulence intensity shown as Fig. 4: 4.2. Extended dimensions in atmospheric turbulence The RMS (root mean square) width of a beam in turbulent environment can be expressed as follows:
W (L) =
ω02 2L2 ⎛ 1 1⎞ + 2 ⎜ 2 + 2 ⎟ + 4(0.545Cn2 )6 5k 2 5L16 k ⎝ ω0 2 σg ⎠
5
(11)
Where the first two are the expansion of light in free space, and the third is the expansion of light beam caused by turbulence, σg2 = 0.005 m. Then we get the extended dimensions due to turbulence shown as Fig. 5: 5. Effects of atmospheric attenuation and atmospheric turbulence on light intensity distribution The attenuation effect of laser in the atmosphere can be expressed by the beer’s law as follows:
Pλ (L) = Pλ0 exp[−σ (λ ) L] σ (λ ) =
3.912 ⎛ λ ⎞−q V ⎝ 0.55 ⎠
(12)
Where V denotes the visibility, q takes values as follows:
Fig. 4. Spot position drift and propagation distance under different turbulence intensity. 779
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Fig. 5. Extended dimensions due to turbulence.
Fig. 6. Laser energy attenuation ratio under different turbulence intensity.
Fig. 7. Aircraft flight trajectory.
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Fig. 8. The simulation system of the airborne aiming pod control system. Table 1 Initial Parameter Settings. Parameters
values
Measurement errors of POS
Pitch error Roll error Direction error BeiDou II differential positioning error 5m Azimuth axis Pitch axis
Flight target trajectory error Pod shafting errors Spatial directional instability of beams
10″(3δ ) 10″(3δ ) 25″(3δ ) 0.1 m (on 20 km baseline condition) 5″(3δ ) 8″(3δ ) 0.03mrad(1σ)
Fig. 9. The beam pointing error of the whole system.
⎧1.6, (Highvisibility) q = 1.3, (Moderatevisibility) ⎨ 1 3 ⎩ 0.585V , (V ≤ 6km)
(13)
Then the intensity distribution of Gauss beams propagating through atmospheric turbulence can be deduced, according to the generalized Huygens-Fresnel principle. 2
P (r , z ) = Where B =
k , 2z
2B2P0 B2 r exp[−σ (λ ) z /1000] × exp[−2 2 ⎛ ⎞ ] 2 2 G ⎝ ω0 ⎠ πG ω0
G=
⎜
1 ω04
+
2 ρ02 ω02
+
k2 4z 2
⎟
(14)
, ρ0 = (0.545Cn2 k 2z )−3/5, k = 2π / λ
Then we get the laser energy attenuation ratio under different turbulence intensity shown as Fig. 6: 6. Simulation and analysis of servo pointing accuracy As shown in Fig. 7, the flight trajectory of the aircraft is simulated in Simulink. Suppose there is a target to be hit at a certain position on the ground. The point at which the ground is pointed is located at (108.975 °E, 34.6 °N, Height: 1000 m). As shown in Fig. 8, the simulation system of the airborne aiming pod control system is built which the disturbance torques such as Coulomb friction and viscous friction, the data delay of POS and angular sensor and many factors shown in Table 1 are taken into account by calculating the pointing angles according to the directional algorithm deduced in this paper. 781
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Comparing the calculated beam pointing angles with the actual angles, the beam pointing error of the whole system can be obtained, as shown in Fig. 9. The maximum pointing error is 0.015 ° and the RMS(root mean square) value is 0.0075 °, which meets the pointing requirement. 7. Conclusion A new generation of photoelectric reconnaissance laser indicator system with the ability of searching, tracking, ranging and locating targets day and night is mainly used for target reconnaissance and attack. It provides data support for the whole system and irradiation guidance for semi-active laser guidance equipment. In this paper, the directional accuracy of laser beams is systematically analyzed from three aspects: one is that a high-precision laser pointing algorithm which takes both real-time and accuracy into account on moving base is derived; the second one is that the optical axis drift, beam spread and intensity distribution caused by atmospheric turbulence are quantitatively analyzed based on the theory; the third one is that the simulation results of the pointing accuracy of the servo control system show the effectiveness of the control strategy by considering the shafting sloshing, disturbance moment and sensor delay of the pod. The research on laser beam pointing of airborne aiming pod can be widely used in anti-terrorism stabilization, maritime law enforcement, forest fire prevention and other fields, which provides reliable data reference for the calculation and analysis of laser transmission in the atmosphere. References [1] Junlan Yang, Dan Schonfeld, Magdi Mohamed, Robust video stabilization based on particle filter tracking of projected camera motion, IEEE Trans. Circuits Syst. 19 (7) (2009) 945–954. [2] Xie Meilin, Liu Peng, Caiwen Ma, Research on key technologies of active polarization imaging system, Optik 157 (2018) 556–564. [3] Xie Meilin, Caiwen Ma, Liu Kai, The application of active polarization imaging technology of the vehicle theodolite, Opt. Commun. 433 (2019) (2019) 74–80. [4] Joon Lyou, Min Sig Kang, Hwy Kuen Kwak, Dual stage and digital image basedmethod for sight stabilization, J. Mech. Sci. Technol. 5 (2008) 1114–1119. [5] S. Zhao, K.K. Tan, Adaptive feedforward compensation of force ripples in linear motors, Control Eng. Pract. 13 (9) (2005) 1081–1092. [6] George W. Younkin, Compensating structural dynamics for servo driven industrial machines with acceleration feedback, Industry Applications Conference, 2004, 39th IAS Annual Meeting. Conference Record of the 2004 IEEE vol.3, (2004) 1881–l890. [7] Hucheng He, Yiqun Ji, Jiankang Zhou, Weimin Shen. Imaging quality analysis and evaluation of optical polarization imaging system with optical transfer matrix, Optik 124 (24) (2013) 6557–6560. [8] Tyo J. Scott, L. Goldstein Dennis, B. Chenault David, et al., Review of passive imaging polarimetry for remote sensing applications, Appl. Opt. 45 (22) (2006) 5453–5469. [9] Li Yanan, Sun Xiaobing, Mao Yongna, et al., Spectral polarization characteristic of space target, Infrared Laser Eng. 41 (1) (2012) 205–210 (in Chinese). [10] J.M. Bueno, P. Artal, Double -pass imaging polarimetry in the human eye, Opt. Lett. 24 (1) (1999) 64–66.
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