Open Access
Add to BibSonomy
Abstract
A micromechanical target tracking system based on polarization grating (PG) is designed to meet the conformal design of laser communication systems and to realize the lightweight and miniaturization of space laser communication networking. The rotating dual PGs are applied to the dynamic tracking of laser targets for the first time, the relationship between the target position and the dual polarization gratings (PGs) angles is defined, and the PG beam deflection multi-coordinate construction and decoupling are carried out. A dual PGs mathematical model was established, and a controller based on the dual PGs system loop was designed. After calibration and dynamic verification of the dual PGs, the unmanned aerial vehicle (UAV) tracking experiment is conducted for the first time, and the dual axis closed-loop tracking error of the dynamic target is within 300µrad (RMSE). The feasibility of dual PGs tracking formula, the feasibility of laser target fixed-point closed-loop control, and the dynamic closed-loop tracking performance are verified. In engineering applications, the dual PGs tracking system has guiding significance for realizing the lightweight and miniaturization of system integration, as well as the possibility to replace the traditional tracking control system.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Space laser communication has been steadily developing from key technology research and demonstration verification to commercialization. With the shift of aircraft and the demand for flexibility, in order to meet the new airborne environment to realize the laser communication system conformal design, a compact, robust and cost-effective beam control device is usually required, so the lightweight and miniaturization of the communication terminal is an inevitable development trend [1–3].
Typical structures of traditional mechanical beam deflection technology include gimbal structure [4,5] and single reflector structure [6]. The gimbal structure is a two-axis two-frame form with azimuth and pitch. The advantage lies in the large-angle servo of the telescopic optical sight axis. The disadvantage is that the payload inside the platform is relatively large, and the stiffness and resonance frequency of the universal joint servo structure are not easy to improve, with relatively large line disturbance torque influence. The single reflector structure is to use the two-degree-of-freedom movement of a mirror to realize the deflection of the optical path. The advantage is that the overall rotational inertia of the system is small. Its disadvantage lies in the limited optical path adjustment range, so that it cannot realize rapid tracking and pointing in a large range.
It is quite difficult to miniaturize the above-mentioned traditional beam deflection structure. Steering units with rotary displacement architectures, typically dual prisms and dual PGs, make it easier to realize the lightweight and miniaturization of system. Dual prisms beam pointing control is an extension of the Risley prism scanning technology. The original Risley prism consists of a pair of optical wedges, which can only realize a small angle of beam deflection [7]. For the control of rotating Risley prisms, a nonparaxial ray tracing method was applied to derive the exact path of the beam scanning, the forward and reverse solutions for the beam pointing of rotating Risley prisms were given, and a two-step optimization algorithm was proposed to find the altitude and azimuth of the beam pointing [8–11]. In [12], a method based on genetic algorithm is proposed to identify the system, which the pointing error is less than 1 arcsec in the range of 3°.
However, the use of Risley prisms is often limited by small steering angles and poor scalability due to the bulk prism structure. In 2009, Kim proposed the beam control concept of the “Risley gratings”, which consists of two independently rotating linearly PGs [13,14]. The concept of the Risley grating is to replace the bulky prism elements with thin plates containing PG and to take advantage of their highly polarization-sensitive diffraction. The PG has many useful advantages as a compact and lightweight micromechanical beam steering device, especially when wide angle and large aperture steering is required [15]. When the dual PGs are rotated, the outgoing beam, which is diffracted by the two PGs, is scanned into a range defined by the periods of the PGs and their relative orientations [16,17]. When circularly polarized (CP) beam is incident, it can diffract the incident beam into a single-stage diffraction direction with approximately 100% efficiency [18,19]. In [20], a polarized laser beam steering system based on multistage rotating PGs was proposed, and the beam steering performance of the two-rotating PGs scheme and the four-rotating PGs scheme was theoretically analyzed. It is derived that the PG can provide faster rotation than the prism. To improve the system stability, in [21], the perturbation of the embedded sensor to the body material is explored based on strain transfer analysis to improve the sensor durability. In [22], the use of fiber optic sensors in monitoring is introduced to compensate the technical difficulties of traditional monitoring methods.
The premise of the above control algorithm is to ensure that the beam enters the PG perpendicularly along the optical axis, but the existence of miss distance in the actual closed-loop control process cannot ensure that the beam enters perpendicularly, so the correlation between the PG beam deflection problem and the target miss distance needs to be determined. Aiming at the discrepancy between the practical application of rotationally PG and the theory, through the multi-coordinate construction and decoupling of PG beam deflection, the PG beam deflection problem with the target miss distance is correlated and the relationship between target position and dual PGs angle is redefined. The closed-loop control idea of rotating PG is verified for the first time, for the discrepancy of two PGs angles and the discontinuity problem in the PG closed-loop control, the PG angle optimized selection control algorithm is applied to the planning of the PG rotation path. For this purpose, a micromechanical target tracking system based on PGs tracking system is designed, and a controller based on the dual PGs system loop is designed. Through the indoor dynamic test and UAV dynamic tracking test, the applicability of dual PGs for the target closed-loop tracking is tested, and the tracking performance of dual PGs for dynamic targets is verified.
2. Grating beam control system
2.1 Grating beam pointing mechanism
PG is a diffractive element composed of periodic optical anisotropy, which enables selective beam splitting according to the polarization state of the incident light. When the incident light is right circularly polarized light (RCP), the outgoing light is +1 level left circularly polarized light. When the incident light is left circularly polarized light (LCP), the outgoing light is −1 right circularly polarized light.
For normal incidence, the diffraction angle Ф can be determined by the Fraunhofer diffraction equation, as shown in Eq. (1).
where λ is the wavelength of incident light, and Λ is the grating period.In order to achieve multi-angle and large-angle beam deflection, multiple subsystems must be combined to construct a cascaded system. Figure 1 shows a schematic diagram of the structure used for the dual PGs. Two circularly PGs with the same grating period are coaxial and independently rotatable. According to the diffraction principle of the PG on the beam, the incident light is incident from the center of the PG. When the beam passes through a rotating PG, the outgoing light is a cone scanned at a certain top angle. When the beam passes through two adjacent freely rotatable PGs, the outgoing light can be diffracted and deflected at different angles in a fixed area. The directions of the outgoing light are described in polar coordinate space as the azimuth angle Θ and the altitude angle Φ.
Usually, the pointing mechanism uses the miss distance to define the position of the target. The azimuth angle Θ and the altitude angle Φ of the light emitted from the dual PGs system are converted into the azimuth and pitch axis components relative to the camera coordinate system. The conversion diagram is shown in the target plane in Fig. 1, and the azimuth and pitch angle conversion relationship are x=Φcos(Θ), y=Φsin(Θ), respectively. The diffraction angle of the outgoing light is constrained by the wavelength of the incident light, the period of grating, and the rotation angle of the two gratings. and the control has diversity and nonlinear properties. Therefore, the direction cosine space is introduced for simplified representation. The control equation of the dual PGs beam pointing is derived as shown in Eq. (2).
Modeling is conducted in Matlab. The rotation angles of dual PGs are set to be combined at any position between 0 and 360°, and the corresponding azimuth and pitch angles of the outgoing light are shown in Fig. 2. It can be found that there are multiple sets of PG angles corresponding to the azimuth and pitch angles pointed by any beam.
The PG target position pointing problem can be given by the inverse solution of Eq. (2). Based on the azimuth and pitch angles of the outgoing beam, the rotation angles of the dual PGs can be inferred as shown in Eq. (3).
Modeling is conducted in Matlab. The azimuth and pitch angle of the outgoing light are set at any combination between −10° and 10°. The corresponding rotation angle information of the dual PGs is shown in Fig. 3.
According to Fig. 3 and Eq. (3), there are two sets of PG angles corresponding to the same target azimuth and pitch angle position. The azimuth angle and pitch angle of the outgoing light and the rotation angle information of the dual PGs have nonlinear properties. In the next modeling step, the rotation of the dual PGs azimuth axis is set to perform a sinusoidal motion with an amplitude of 5° and a frequency of 0.2 Hz, and maintain the pitch axis at 0. In the verification of Eq. (3), the relationship between the rotation angles of PG1 and PG2 is shown in Fig. 4.
Fig. 4. Rotation angle relationship of dual PGs. (a) and (d) are the solutions to condition 1; (b) and (e) are the solutions to condition 2; (c) and (f) are the dual PGs rotation angle processed by path planning algorithm.
As shown in Eq. (3), (a) and (d) in Fig. 4 represent the first set of dual PGs angle values satisfying a sinusoidal motion with an amplitude of 5° and a frequency of 0.2 Hz, and (b) and (e) represent the second set of dual PGs angle values satisfying this condition. The two sets of rotation angle values are different, and each set of angle values undergoes a jump. The discontinuity caused by the jump phenomenon makes the PG control more difficult and requires the grating motor to have extremely high speed acceleration. In practical applications, the performance of peripheral supporting devices is limited. Therefore, it is necessary to reasonably select two sets of PGs angle values to optimize the PG rotation angle. Firstly, the optimization and selection control algorithm for PG rotation angle is used to judge the angle value of the azimuth axis and the pitch axis. Then, the rotation angle circumferential processing of the two sets of PGs, the initial rotation angle rotation judgment processing, the PG path judgment processing, the adjacent angle judgment processing, and the minimum rotation angle optimization algorithms are carried out to provide an optimal set of PG rotation angle solutions. For the position changes of the azimuth axis and the pitch axis mentioned above, the rotation angle optimization selection control algorithm is adopted. The rotation angles of PG1 and PG2 are (c) and (f), respectively. By comparison, it can be found that the optimized PG rotation angle value has the optimal state of small and stable angle changes.
Through the simulation of different motion states of the target and multiple modeling and simulations of the dual PGs closed-loop control, multiple sets of data obtained are used to verify the applicability of the PG rotation angle optimization selection control algorithm and the necessity of adding the algorithm. The addition of the algorithm can not only ensure the stability and continuity of target tracking, but also prevent target loss, which has guiding significance for engineering applications.
2.2 Multi-coordinate construction and decoupling
It should be noted that the formula proposed above requires strict usage conditions. It is necessary to ensure that the target is centered on the optical axis and perpendicular to the PG incidence. However, there is a certain angular difference between the target and the PG optical axis in practical applications, and vertical incidence cannot be guaranteed. Therefore, the intrinsic relationship between the target position and the rotation position of the two PGs should be redefined. At the same time, the cascaded PG also exhibits strong coupling and nonlinearity, which increases the complexity of practical applications.
Figure 5 shows the usage scenario of dual PGs. When the target enters the observation field, the target light forms an image point on the detector after being diffracted by PG1 and PG2. The idea of the closed-loop control of PG is to obtain the compensation rule of the PG through the deviation degree of the image point given by the detector at this time. The motor is controlled to rotate the PG to the corresponding angle position, so that the image point imaged on the detector points towards the center of the detector’s field of view as much as possible. At the same time, the reversible optical path can realize the precise tracking of the target. In the practical application of the closed-loop control of PG, it is necessary to redefine the relationship between the position of the target, the angle of the PG, and the position of the image point in the detector.
The incident vector is introduced into the direction cosine of the outgoing beam of the dual PGs, and the relationship between the direction cosine of the outgoing beam’s miss distance, the position of the target, and the rotation angle of the dual PGs is established as follows:
Therefore, the position of the target azimuth axis and pitch axis can be expressed as follows.
2.3 Target closed-loop control process
In order to achieve fast capture in practical applications, the target position is given by GPS, and then the dual PGs is directed according to the position information to image the laser target on the detector. Then, the target is imaged at the center of the detector’s field of view through the closed-loop control of the following dual PGs.
First, when the laser target forms an image point on the dual PGs detector, the azimuth miss distance information (aD) and pitch miss distance information (pD) of the imaging point calculated by the detector are obtained. Through the PG angle encoder, the current PG1 position information θ1 and PG2 position information θ2 are obtained. By bringing them into Eq. (4) and Eq. (5), the position information of the azimuth axis (aT) and the pitch axis (pT) where the laser target is located can be derived. After obtaining the position information of the target, the problem of solving the rotation angle of the dual PGs can be transformed into the case of the target incident perpendicular to the axis.
The next step is to bring the calculated azimuth and pitch position information of the target into the PG inverse solution Eq. (3) to solve the rotation angle information of PG1 and PG2 required for dual PGs tracking at the target position at this time, which is denoted as θ1’ and θ2’. Moreover, Δθ1=θ1-θ1’ and Δθ2=θ2-θ2’ are the angle values of PG1 and PG2 to be rotated respectively.
Finally, the grating motor is controlled to drive the PG to rotate the corresponding angle, thus achieving stable tracking of the laser target.
3. Dual grating laser target tracking system
Different from the traditional tracking systems, as shown in Fig. 1 above, the laser target position information in the closed-loop process of the dual PGs tracking system is jointly constrained by the angle information of PG1 and PG2. Therefore, practical applications need to take this coupling relationship into consideration. For the design of tracking control system, decoupling design thought should be incorporated. The design of the tracking control system diagram is shown in Fig. 6 . After decoupling the obtained laser target position information through the above proposed Eq. (3), Eq. (4) and Eq. (5), the position compensation information of the two PGs is solved separately and then closed-loop control is performed, and the grating compensation is carried out through the anti-decoupling algorithm in Eq. (2) to complete the closed-loop control of the target.
The executing component of the coarse tracking system is a DC servo torque motor, which adopts the classical three-loop control strategy. With the pitch axis as an example, the speed closed-loop is located at the innermost point. During the adjustment process, the adjustment variable of the speed closed-loop is the rotational speed of the system. Through the speed closed-loop, the system’s ability to suppress external disturbances is improved, which is conducive to the smooth operation of the system. Through testing, the mechanical resonance frequency of the system is 500 Hz. The bandwidth of the speed closed-loop is designed according to 1/5 of the resonance frequency. The speed loop is calibrated to a type-2 system using PID control algorithm, and the open loop transfer function of the calibrated speed loop is:
Since the motor characteristics of each tracking unit are consistent, the closed-loop model of the motor speed loop is:
For the design of circuit compensation devices, the differences between each control circuit need to be taken into account. The bandwidth of the optical closed-loop is limited by several factors, such as camera frame rate, and data processing transmission delay. In order to ensure the stability of the system, the loop bandwidth should not be too high. The position closed-loop is digital tracking. In order to reduce the loop phase loss, measures such as increasing the sampling rate of the controller and reducing the execution cycle can be taken to obtain a higher servo bandwidth. The bandwidth of the position closed-loop is designed according to 1/2 of the bandwidth of the speed closed-loop.
The position loop is calibrated to a type-1 system using PID control algorithm, the corrected open-loop transfer function of the position loop is:
Since the motor characteristics of each tracking unit are consistent, the closed-loop model of the motor position loop is:
The optical closed-loop is not only the outermost part of the control system, but also the loop with the lowest bandwidth. As the main link that affects the servo bandwidth of the system, its bandwidth is limited by the bandwidth of the position loop and smaller than the bandwidth of the position loop. Generally, the bandwidth of the optical closed-loop is less than 1/10 of the sampling frequency. The frame rate of CCD in this system is 100 Hz. The servo bandwidth of the optical closed-loop is designed according to 1/20 of the CCD frame rate. Based on the accuracy requirements and calibration principles of the servo system, the optical closed-loop is calibrated according to a canonical type-1 system using PID control algorithm.
The corrected open-loop transfer function of the optical loop is:
The closed-loop transfer function of the optical loop is:
Perform amplitude frequency characteristic analysis on the designed speed loop, position loop, and optical closed-loop loop models. The closed-loop characteristic of the speed loop is shown in Fig. 7(a), the servo bandwidth of the speed loop is 103.6 Hz, the closed-loop characteristic of the position loop is shown in Fig. 7(b), the servo bandwidth of the position loop is 47.3 Hz, the optical closed-loop characteristic is shown in Fig. 7(c), the optical closed-loop servo bandwidth is 4.6 Hz, and the bandwidth indicators of the three loops are consistent with the design,
Fig. 7. The amplitude-frequency characteristic curve of three-loop. (a) is the curve of speed loop closed-loop, (b) is the curve of position loop closed-loop, (c) is the curve of optical closed-loop.
The speed loop satisfies the fast and accurate tracking control of the target by the dual PGs. The position loop can realize precise position control and ensure the position accuracy of the system. The optical closed-loop is located on the outermost side of the control loop, the adjustment amount of the optical closed-loop is the miss distance signal given by charge coupled device (CCD). Through the dynamic closed-loop control of the laser target, the tracking accuracy of the system can be improved.
4. Dual-grating closed-loop performance verification
4.1 Grating corner continuity test
The physical testing environment is set up as shown in Fig. 8. The light source is a fiber laser. The wavelength of the laser is 1064 nm. After polarization adjustment and parallel light tube, a beam of parallel polarized light is generated and enters the dual PGs, with grating periods of 8.222µm and coaxial. The miss distance information of the laser target is calculated through the CCD, and the image display unit can display the position of the spot in real time. By controlling the continuous deflection of the dual PGs, the deviation degree between the theoretical azimuth and pitch values and the azimuth and pitch values presented by the CCD is measured.
In Experiment 1, the two-dimensional deflection turntable is adjusted the pitch position of the incident light of 7°, and the dual PGs are adjusted, so that the light spot appears in the field of view and placed in the center. This moment is defined for the zero position of the dual PGs. By measurement, the PG1 angle is 294°, and the PG2 angle is 240°. The miss distance information of the detector at this moment is defined as zero position. The azimuth angle is 0.3563°, and the pitch angle is 6.8379°. The theoretical azimuth and pitch angle values at this moment are defined as zero position. The azimuth angle is 0.3585°, and the pitch angle is 6.8402°. The single step size of PG rotation is set to 6°. In the first step of the experiment, the PG1 remains stationary at zero position, and the PG2 rotates clockwise and counterclockwise continuously for one cycle with zero position as the center. In the second step of the experiment, the PG1 rotates clockwise and counterclockwise continuously for one cycle with zero position as the center, while PG2 remains stationary at zero position. Table 1 shows some experimental data of the first step of Experiment 1. Among them, the azimuth angle comparison diagram obtained by the formula and the detector is shown in Fig. 9, the pitch angle comparison is shown in Fig. 10, and the azimuth and pitch angle errors between the formula and the detector are shown in Fig. 11.
Table 1. Difference between the target positions obtained from the formula and detector.
According to the data curve, the azimuth and pitch angle presented by the detection camera are consistent with the theoretical azimuth and pitch angle of the target solved by Eq. (3), Eq. (4) and Eq. (5), with a relatively small deviation. In the actual calibration experiment process, the formula has a singularity. When the rotation angle of the dual PGs reaches the singularity position, the formula has no solution. Therefore, in practical use, optimize it through the algorithm, and the processing does not affect the pointing accuracy. Through this, the coarse tracking accuracy desired leaves a large margin for mechanical errors and other systematic errors, which conforms to engineering requirements.
In Experiment 2, the two-dimensional deflection turntable is adjusted to the azimuth position of the incident light of −6°, and the dual PGs is adjusted, so that the spot appears in the field of view and placed in the center. This moment is defined for the zero position of the dual PGs. By measurement, the PG1 angle is 325°, and the PG2 angle is 24°. The miss distance information of the detector at this moment is defined as zero position. The azimuth angle is 7.3970°, and the pitch angle is −0.7152°. The theoretical azimuth and pitch angle values at this moment are defined as zero position. The azimuth angle is 7.3988°, and the pitch angle is −0.7124°. In the first step of the experiment, the PG1 remains stationary at zero position, while the PG2 rotates clockwise and counterclockwise continuously for one cycle with zero position as the center. In the second step of the experiment, the PG1 rotates clockwise and counterclockwise continuously for one cycle with zero position as the center, while the PG2 remains stationary at zero position. Through data comparison, this is basically the same as Table 1, Fig. 9, Fig. 10, and Fig. 11, which will not be provided here. Through multiple experiments, the feasibility of dual PGs tracking formula and the laser target fixed-point closed-loop control has been verified. The next step is to verify the dynamic closed-loop test of the dual PGs and the optimal path planning of PG rotation theory.
4.2 Closed-loop tracking test of grating moving stage
As an important part of the dual PGs servo control system, the coarse tracking servo unit is responsible for high probability, fast acquisition, high stability, and high precision tracking. Therefore, it is necessary and important to test the coarse tracking accuracy index of the system. In more detail, it is necessary to evaluate whether it can meet the technical specifications of not more than 0.3 mrad (RMSE). In order to simultaneously verify the dynamic closed-loop tracking performance of the dual PGs and the optimal path planning performance of the PG rotation theory, an experimental system was built. The testing of the tracking accuracy of the dual PGs tracking system is carried out in an indoor environment.
The experimental test structure is shown in Fig. 12, and the physical test environment is shown in Fig. 13. The experimental devices used include a laser, a collimator, a six-degree-of-freedom pendulum, an off-axis optical antenna, and a CCD. The frame rate of the detector is 100fps. The focal length is 960 mm. The angular resolution is 15.625µrad. The unit size is 15µm. The number of units is 640 × 512. The laser wavelength is 1064 nm. The grating period is 8.222µm. The 26 bits absolute grating encoder from Renishao Company is selected as the angle detection component. The detection field of view of the CCD is 8 mrad. The STM32 chip is chosen as its core controller. Discretization of the compensation function is simulated by bilinear transformation. Through programming, digital control can be realized. The main control software of the upper computer is written based on the Qt environment. All sub-units are connected to the coarse tracking servo control system and communicate with the upper computer through the RS-422 serial port, which are uniformly controlled by the upper computer.
After the laser beam is polarized, it is shaped by a 200 mm collimator before exiting. The dual PGs system is coaxial with the CCD and placed on a six-degree-of-freedom pendulum. In the laser link, a six-degree-of-freedom turntable is used to add a disturbance to the whole system, thereby simulating the target motion trajectory. Based on the calculation based on the laser wavelength and the period of the grating, the single-side deflection angle of the single grating is about 7.4°, and the deflection range of the dual PGs to the beam is ±14.8°. Through the simulation of the grating formula, it can be found that the PG has nonlinearity when it is close to the maximum deflection angle. Therefore, it is defined that the final deflection range of the dual PGs is ±12°. Firstly, the six-degree-of-freedom pendulum is controlled to keep static after horizontal translational of 6.5°, and the dual PGs are adjusted to make the light spot located in the center of the CCD’s field of view. Then, the six-degree-of-freedom pendulum is set to make a single axis sinusoidal motion with amplitude of ±5° and frequency of 0.2 Hz, which simulates the motion of the target source. The CCD captures the motion state of the target. After image processing, the target miss distance information is transmitted to the dual PGs system. After calculation, the grating motor is controlled to make the PG rotate to the corresponding position, that is, the closed-loop control of the CCD and the dual PGs is formed. During the entire closed-loop control process, the position of the light spot observed by the unit and whether the closed-loop control is effective can be displayed through the image. The 3000 sets of tracking data obtained by recording can draw the following azimuth and pitch miss distance curves, and dual PGs rotation angle curves.
Figure 14 reflects the closed-loop residual of the dual PGs miss distance. By processing the obtained 3000 sets of data, the closed-loop residual error of the dual PGs azimuth axis miss distance is 169.6779µrad (RMSE), and the closed-loop residual of pitch axis miss distance is 135.2973µrad (RMSE). The main indicators of the system are shown in Table 2, where the closed-loop residuals include the detector target detection error, and the pointing error is composed of three parts: the axis system error, the encoder error, and the system dynamic hysteresis error. It can be seen from Fig. 15 that during the whole tracking process, the rotation angle values of the dual PGs change continuously and smoothly without any jump values, which verifies the feasibility of the control algorithm for optimal selection of the rotation angle. Meanwhile, the target is always placed within the CCD’s field of view throughout the tracking process, with the tracking accuracy within 300µrad (RMSE), and the real-time smooth tracking performance of the target can be realized.
Table 2. Main indicators of the system.
4.3 Closed-loop tracking test for grating moving targets
In order to test the applicability of dual PGs dynamic target closed-loop tracking, a dual PGs tracking system is constructed for external tracking experiments. The experimental site is shown in Fig. 16.
Based on the design of this project and the characteristics of the PG, On the basis of the testing structure in section 4.2, the GPS positioning technology can solve the limitation of the small visual range of the dual PGs to the laser target, and the infrared tracking unit realizes the initial pointing of the target. The experimental device is equivalent to two parts: transmitting and receiving. In the transmitting part, the UAV is selected as the simulated target source. The supporting devices include GPS, heat source lamp, and corner cone prisms. The receiving end is a dual PGs tracking system. Only the modules used are introduced here. The system consists of an off-axis antenna, a beam splitting system, an infrared detector, a coarse tracking detector, an infrared tracking unit, and a coarse tracking unit.
In the first step, the test UAV takes off at a straight-line distance of 1.1 km from the dual PGs system, and hovers in the air after reaching a flight altitude of 200 meters. In the second step, the system calculates the position information of the UAV based on the external guidance data provided by GPS, and controls the target area pointed by the system. Infrared detectors then detect heat source lights on the UAV for initial tracking. After the UAV enters the coarse tracking field of view, the system turns on the laser to emit 808 nm light waves to illuminate the target. The laser beam returns to the original path through the corner cube prism of the UAV, and is imaged on the detector. At this time, the system controls the dual PGs to track and control the incident laser, so that the laser spot is located at the center of the field of view. In the third step, the UAV is controlled to perform dynamic cyclic flight, and the system tracks the UAV according to the closed-loop principle given in the second step to achieve closed-loop control of the laser target.
Based on 5000 sets of tracking data in the process of dynamic target closed-loop tracking control, the closed-loop curve of azimuth and pitch miss distance of the dual PGs dynamic target can be plotted, as shown in Fig. 17. In view of the fact that the cyclic flight of the UAV can be equivalent to sinusoidal motion, the miss distance also exhibits a sinusoidal motion trend. Through the processing of the obtained 5000 sets of data, the closed-loop residual of the azimuth axis miss distance of the dynamic target closed-loop is 130.6060µrad (RMSE), the closed-loop residual of the pitch axis miss distance is 212.6517µrad (RMSE), the dynamic target closed-loop control with dual axis residual is 249.5570µrad (RMSE), and the system dynamic target dual axis closed-loop tracking control accuracy is controlled within 300µrad (RMSE). During the whole tracking process, the UAV is always guaranteed to be within the field of view of the detector to achieve dynamic and real-time smooth tracking performance, which has guiding significance for engineering applications.
5. Conclusion
For the traditional theoretical analysis of dual PGs beam pointing and target position pointing, in response to the difference between the practical application and theory of rotating PG, the multi-coordinate construction and decoupling of PG beam deflection is carried out. Through the relationship between the grating beam deflection problem and the target miss distance, the relationship between target position and dual PGs angle is redefined. The relevant analytical formulas are given, modeled and analyzed in the Matlab environment. For the discrepancy of dual PGs rotation angles and the discontinuity problem arising in the PG closed-loop control, the PG rotation path is planned by adding the optimal selection control algorithm of the PG rotation angle. The rotating dual PGs are first applied to the laser target dynamic tracking system to verify the closed-loop control idea of the rotating dual PGs. The mathematical model of the system design and the design idea of each control loop controller are used to describe the dynamic tracking process of laser targets based on dual PGs. Subsequently, the test environment is established. Through the continuous deflection calibration test of the dual PGs, the feasibility of dual PGs tracking formula and the laser target fixed-point closed-loop control is verified. Through indoor dynamic experiment, the optimal path planning performance of PG rotation theory and the dynamic closed-loop tracking performance of dual PGs are verified. The residual error of single axis tracking is within 200µrad (RMSE), and the system bandwidth is 4.6 Hz, achieving a deflection range of 12° on one side of the beam. Compared to the Risley prism less than 1 arcsec in the range of 3° in [12], the beam deflection range based on dual PGs is increased by 4 times, and the accuracy is improved by 27.8%. Through the field UAV dynamic tracking experiment, the applicability of the dual PGs dynamic target closed-loop tracking is tested, and the tracking performance of the dual PGs on dynamic target is verified. During the whole tracking process, the target is always guaranteed to be within the CCD’s field of view, and the system’s dynamic target dual-axis closed-loop tracking control accuracy is controlled within 300µrad (RMSE), which reflects the dynamic and smooth tracking performance. The stable closed-loop tracking control of dual PGs dynamic targets provides technical support for the later dual-axis disturbance. Compared with the gimbal coarse tracking or Risley prisms, the tracking system based on dual PGs can not only realize the miniaturization of the system, but also is more suitable for the airborne environment, which has guiding significance for engineering applications.
With compact system structure and good dynamic performance, dual PGs system can balance large scanning range, high pointing accuracy, and high response frequency, so that it has a strong alternative to the traditional beam pointing system, especially the gimbal structure with large volume and mass. With broad prospects for development, it is considered to be a popular direction in the field of beam control research technology in recent years. Since the rotation axis are on the same straight line, the system does not require torque and slip rings, thus avoiding the problem of wire winding. This has become an important supplement in beam deflection control technology. By improving the dual PGs based on the Risley prism, it replaces the large prism components in the Risley prism and utilizes its highly polarization sensitive diffraction. Able to achieve conformal design of laser communication systems, providing technical support for space laser communication networking.
Funding
Key R&D Plan for Science and Technology Development in Jilin Province, Project Name (20210201022GX).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. A. Carrasco-Casado and R. Mata-Calvo, “Space Optical Links for Communication Networks,” Springer Handbook of Optical Networks (Springer, 2020), pp. 1057–1103.
2. M. Toyoshima, T. Fuse, D. R. Kolev, H. Takenaka, Y. Munemasa, N. Iwakiri, and H. Kunimori, “Current status of research and development on space laser communications technologies and future plans in NICT,” in 2015 IEEE International Conference on Space Optical Systems and Applications (ICSOS), New Orleans, LA, USA, 2015.
3. D. R. Gao, T. L. Li, Y. Sun, W. Wang, H. Hu, J. C. Meng, Y. Q. Zheng, and X. P. Xie, “Latest developments and trends of space laser communication,” Chin. Opt. 11(06), 901–913 (2018). [CrossRef]
4. T. Chi, L. Z. Zhang, and L. X. Meng, “Single Reflect-Mirror Laser Communication Tracking-Pointing System Load Technology for Micronanosatellite,” Advances in Mathematical Physics 2022, 1–11 (2022). [CrossRef]
5. H. Li, K. Han, X. M. Wang, S. He, Q. W. Wu, and Z. B. Xu, “A compact and lightweight two-dimensional gimbal for inter-satellite laser communication applications,” Opt. Express 27(17), 24060–24071 (2019). [CrossRef]
6. H. G. Li, F. L. Peng, X. Jiang, S. W. Chi, and Z. L. Hu, “Stabilization platform of complex axes embedded into optical path for optics-electricity system with upside mirror,” Opt. Precis. Eng. 27(10), 22242232 (2019).
7. D. P. Fan, Y. Zhou, Y. F. Lu, M. Hei, F. R. Xiong, and K. Li, “Overview of beam steering technology based on rotational double prisms,” Chin. Opt. 6(02), 136–150 (2013). [CrossRef]
8. Y. J. Li, “Closed form analytical inverse solutions for Risley-prism-based beam steering systems in different configurations,” Appl. Opt. 50(22), 4302–4309 (2011). [CrossRef]
9. Y. J. Li, “Third-order theory of the Risley-prism-based beam steering system,” Appl. Opt. 50(5), 679–686 (2011). [CrossRef]
10. Y. Zhou, Y. F. Lu, M. Hei, G. C. Liu, and D. P. Fan, “Motion control of the wedge prisms in Risley-prism-based beam steering system for precise target tracking,” Appl. Opt. 52(12), 2849–2857 (2013). [CrossRef]
11. Y. Zhou, Y. F. Lu, M. Hei, F. R. Xiong, K. Li, and D. P. Fan, “Analytic solution of optical beam steering based on rotational double prisms,” Opt. Precis. Eng. 21(6), 1373–1379 (2013). [CrossRef]
12. J. Y. Li, K. Chen, P. Qi, Z.K. Wang, J. Yang, C. G. Fu, and R. Ge, “Improvement of pointing accuracy for Risley prisms by parameter identification,” Appl. Opt. 56(26), 7358–7366 (2017). [CrossRef]
13. C. Oh, J. Kim, J. F. Muth, and M. J. Escuti, “A new beam steering concept: Risley gratings,” in Proceedings of Advanced Wavefront Control: Methods, Devices, and Applications VII (2009), pp. 179–186.
14. C. Oh, J. Kim, J. J. Muth, S. Serati, and M. J. Escuti, “High-throughput continuous beam steering using rotating polarization gratings,” IEEE Photonics Technol. Lett. 22(4), 200–202 (2010). [CrossRef]
15. K. Zou, Y. Shi, and D. Luo, “A Review of Two-Dimensional Liquid Crystal Polarization Gratings,” Crystals 11(9), 1015 (2021). [CrossRef]
16. Y. Zhou, D. P. Fan, S. X. Fan, Y. Chen, and G. C. Liu, “Laser scanning by rotating polarization gratings,” Appl. Opt. 55(19), 5149–5157 (2016). [CrossRef]
17. J. Wang, L. Gao, L. Jiang, Y. Liu, Y. Dong, and Y. S. Song, “Establishment and verification of formulas of target tracking based on dual liquid crystal polarization gratings,” Opt. Express 30(24), 43062–43077 (2022). [CrossRef]
18. J. Tervo and J. Turunen, “Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings,” Opt. Lett. 25(11), 785–786 (2000). [CrossRef]
19. Y. Zhou, Y. F. Lu, M. Hei, F. R. Xiong, K. Li, and D. P. Fan, “Analytical inverse solutions for rotational double prism beam steering,” Opt. Precis. Eng. 21(07), 1693–1700 (2013). [CrossRef]
20. M. Sakamoto, H. T. Nhan, K. Noda, T. Sasaki, T. Kamei, T. Sakai, Y. Hattori, N. Kawatsuki, and H. Ono, “Polarized beam steering using multiply-cascaded rotating polarization gratings,” Appl. Opt. 60(7), 2062–2068 (2021). [CrossRef]
21. H. P. Wang, L. Z. Jiang, and P. Xiang, “Improving the durability of the optical fiber sensor based on strain transfer analysis,” Opt. Fiber Technol. 42, 97–104 (2018). [CrossRef]
22. X. B. Zhang, L. Wang, S. H. Tang, H. T. Cui, X. N. Xie, H. Wu, X. C. Liu, D. L. Yang, H. P. Wang, and P. Xiang, “Investigations on the shearing performance of ballastless CRTS II slab based on quasi-distributed optical fiber sensing,” Opt. Fiber Technol. 75, 103129 (2023). [CrossRef]
