A control singularity elimination method for a Risley prism tracking system

Abstract

The application discloses a control singularity elimination method of a Risley prism tracking system, acquires a target off-target amount in a period, calculates a direction cosine vector of an emergent light beam after a target light beam is refracted by Risley prisms, calculates a target azimuth, judges whether the target is at a field center or not, obtains a target trajectory function through fitting, predicts the target azimuth of a future period based on the target trajectory function until the target leaves the field center, obtains rotation angles of two prisms in the Risley prisms in each future period based on the predicted target azimuth of the future period, switches the rotation angles of the two prisms in a period before the target leaves the field center, obtains a rotation control strategy, and controls the two prisms to move according to the rotation control strategy. The application is used to solve the problem that the prior art cannot eliminate the control singularity of the Risley prisms when the target trajectory deviates from an optical axis, can effectively reduce the control singularity of the Risley prisms, is not limited by the deviation of the optical axis, and can realize smooth tracking of the target in a full field area.

Description

Technical Field

[0001] The present invention relates to the technical field of photoelectric tracking, and in particular to a method for eliminating control singularity of a Risley prism tracking system. Background Art

[0002] The Risley prism, a type of rotating biprism, is a pair of coaxially arranged optical wedges that utilize the principle of refraction to deflect a light beam. By independently rotating the two prisms, the beam can be directed to any position within the full field of view. Due to its compact structure, low moment of inertia, fast response speed, and large scanning range, the Risley prism is widely used in infrared countermeasures, aerospace, laser communications, search and rescue, and other fields.

[0003] However, as a beam-pointing device, the control of the Risley prism exhibits singularities: when the scanning beam tracks a target close to the center of the field of view, the prism's angular velocity increases dramatically. Limited by the motor's acceleration performance, smooth tracking in and around the center of the field of view is difficult, resulting in frequent large oscillations in the visual axis and even loss of the target's field of view. This poses a significant challenge to tracking performance in practical applications. Currently, existing technologies have proposed methods to avoid singularities by switching between two sets of solutions. However, this method is only effective under the special condition that the target trajectory strictly passes through the optical axis. It does not account for situations where the path is slightly offset from the optical axis. Consequently, its versatility is extremely low, and it is unable to smoothly track the entire field of view. Summary of the Invention

[0004] The present invention provides a method for eliminating control singularity of a Risley prism tracking system, so as to solve the problem in the prior art that the control singularity of the Risley prism cannot be eliminated when the target trajectory deviates from the optical axis. The method can effectively reduce the control singularity of the Risley prism, is not restricted by the optical axis deviation, and can achieve smooth tracking of the target in the full field of view.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for eliminating control singularity of a Risley prism tracking system comprises the following steps:

[0007] S1. Collect the target miss distance in units of cycles and calculate the direction cosine vector of the outgoing beam after the target beam is refracted by the Risley prism;

[0008] S2. Calculating the target orientation based on the direction cosine vector of the outgoing light beam;

[0009] S3, determine whether the target is in the center of the field of view: if so, fit the target trajectory function; if not, return to step S1;

[0010] S4. predicting the target position in future cycles based on the target trajectory function until the target leaves the center of the field of view;

[0011] S5. Based on the predicted target orientation in the future period, obtain the rotation angle of the two prisms in the Risley prism in each future period;

[0012] S6. Switch the rotation angle of the two prisms in one cycle before the target leaves the center of the field of view, obtain a rotation control strategy, and control the movement of the two prisms with the rotation control strategy.

[0013] To address the problem of the inability to eliminate the control singularity of the Risley prism using existing techniques when the target trajectory deviates from the optical axis, the present invention proposes a method for eliminating the control singularity of a Risley prism tracking system. The method first continuously collects target miss distances in cycles, calculates the direction cosine vector of the target beam after refraction through the Risley prism, and then calculates the target orientation based on the direction cosine vector of the target beam. The calculation process of the method, as of now, can be implemented using existing techniques and is not difficult for those skilled in the art to implement. Next, a determination is made as to whether the target is in the center of the field of view. If the target is in the center of the field of view, a target trajectory function is fitted based on the target orientations obtained in previous cycles. If the target is not in the center of the field of view, the control singularity is temporarily disregarded, and the method returns to step S1 to collect the target miss distance for the next cycle and repeats the process. If the target is in the center of the field of view, the next target orientation is predicted in cycles based on the fitted target trajectory function. This prediction continues until the target leaves the center of the field of view. At this point, the rotation angles of the two prisms in the Risley prism corresponding to each cycle before the target leaves the center of the field of view are obtained. Finally, the rotation angles of the two prisms are swapped in one cycle before the target leaves the center of the field of view, and the optimized rotation control strategy is obtained based on the swapped rotation angles. The optimized rotation control strategy is used to control the movement of the two prisms.

[0014] This application plans a continuous and smooth motion profile for the Risley prism based on the optimized rotation strategy, thereby effectively reducing the angular velocity of the prism in the center of the field of view and its surrounding area; this application overcomes the defect of the existing technology that it can only work when the target trajectory passes through the optical axis, and is no longer restricted by the optical axis offset. It significantly improves the tracking accuracy and dynamic performance of the Risley prism system, is conducive to stabilizing the visual axis, and realizes smooth tracking in the entire field of view area.

[0015] Furthermore, the method for calculating the direction cosine vector of the outgoing light beam after the target light beam is refracted by the Risley prism includes:

[0016] S101, calculating direction cosines based on target miss distance;

[0017] S102 , substituting the direction cosines into Snell's law in vector form, iterating at least four times, and obtaining the direction cosine vector of the outgoing light beam.

[0018] This solution calculates the target's position using Snell's law in vector form, and after at least four iterations, the direction cosine vector of the refracted beam can be calculated.

[0019] Furthermore, the target orientation includes an azimuth angle and a pitch angle.

[0020] Furthermore, the direction cosine vector of the outgoing light beam is (K, L, M), and the formula for calculating the target orientation is:

[0021]

[0022] Φ=arccos(-M)

[0023] Where: Θ is the azimuth angle; Φ is the elevation angle.

[0024] In this scheme, based on the outgoing light beam direction cosine vector (K, L, M), substituting it into the above formula, the azimuth and pitch angles of the target in the field of view can be obtained.

[0025] Furthermore, the method for determining whether the target is in the center of the field of view includes: comparing the azimuth angle of the target with the boundary of the restricted area in the center of the field of view; if the azimuth angle of the target is less than or equal to the boundary of the restricted area in the center of the field of view, the target is in the center of the field of view; if the azimuth angle of the target is greater than the boundary of the restricted area in the center of the field of view, the target is not in the center of the field of view.

[0026] Furthermore, the rotation angles of the two prisms in the Risley prism in each future cycle are calculated using the following formula:

[0027]

[0028] Where: θ1 and θ2 represent the rotation angles of the two prisms respectively; Θ is the azimuth angle; Φ is the pitch angle; δ1 and δ2 are the equivalent beam deflection angles of the two prisms respectively.

[0029] Furthermore, the equivalent beam deflection angle of the two prisms is calculated by the following formula:

[0030]

[0031] Where: n1 and n2 are the refractive indices of the two prisms, and α1 and α2 are the wedge angles of the two prisms.

[0032] Furthermore, the method of fitting the target trajectory function includes:

[0033] S301, converting the target orientation within the historical period from a polar coordinate system to a Cartesian coordinate system;

[0034] S302, performing polynomial fitting on the target orientation in the Cartesian coordinate system to obtain a target trajectory curve expression;

[0035] S303, fitting the independent variables in the target trajectory curve expression to obtain a function of the independent variables with respect to the period;

[0036] S304: Substitute the function of the independent variable with respect to the period into the target trajectory curve expression to obtain a target trajectory function.

[0037] In the process of polynomial fitting and fitting of independent variables, the power of the fitting formula can be selected according to the computing power.

[0038] Furthermore, the method for obtaining the slewing control strategy includes:

[0039] S601: For any prism, establish a linear function based on the rotation angle and period of the current prism, starting from the rotation angle of the current prism one cycle before the target enters the center of the field of view and ending at the rotation angle of the other prism one cycle before the target leaves the center of the field of view;

[0040] S602, defining the linear functions obtained by the two prisms as a first linear function and a second linear function respectively;

[0041] S603: Modify the first linear function and the second linear function to obtain a first rotation control curve and a second rotation control curve, and use the first rotation control curve and the second rotation control curve as a rotation control strategy.

[0042] In this scheme, after switching the rotation angle of the two prisms in one cycle before the target leaves the center of the field of view, two linear functions are obtained respectively, and then corresponding corrections are made. The corrected curves are used as the first rotation control curve and the second rotation control curve to control the movements of the two prisms respectively.

[0043] Furthermore, the method of correcting the first straight line function and the second straight line function includes:

[0044] S6031. Based on the rotation angles of the two prisms in the Risley prism in each future cycle, calculate the rotation angle difference of the two prisms corresponding to each cycle when the target is in the center of the field of view, and record it as Δθ 1i ; i represents the i-th cycle;

[0045] S6032. Calculate the rotation angle difference between the first straight line function and the second straight line function for each period when the target is in the center of the field of view, and record it as Δθ2i ;

[0046] S6033, maintain Δθ 1i The rotation angle in the first linear function and / or the second linear function is adjusted so that Δθ 2i =Δθ 1i .

[0047] In this solution, the first linear function and / or the second linear function are adjusted to obtain the first rotation control curve and the second rotation control curve, under the condition that the standard deviation of the rotation angles of the two prisms before and after correction remains unchanged.

[0048] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0049] 1. The present invention provides a method for eliminating control singularities in a Risley prism tracking system, which overcomes the defect of the prior art that the target trajectory can only be effective when it passes through the optical axis. It is no longer restricted by the optical axis offset, significantly improves the tracking accuracy and dynamic performance of the Risley prism system, is conducive to stabilizing the visual axis, and realizes smooth tracking in the entire field of view.

[0050] 2. The present invention provides a method for eliminating control singularities of a Risley prism tracking system, which plans a continuous and smooth motion profile for the Risley prism, thereby effectively reducing the angular velocity of the prism in the center of the field of view and its vicinity. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0052] Figure 1 Schematic diagram of the Risley prism tracking system;

[0053] Figure 2 It is a flowchart of a specific embodiment of the present invention;

[0054] Figure 3 A comparison diagram of tracking error and miss distance before and after singularity elimination in a specific embodiment of the present invention;

[0055] Figure 4 2 is a comparison diagram of the angular velocity of the prism before and after the singularity is eliminated in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0056] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with examples and drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0057] Example 1:

[0058] A control singularity elimination method for a Risley prism tracking system is used to control Figure 1 The Risley prism tracking system shown in FIG. Figure 2 As shown, the following steps are included:

[0059] S1. Collect the target miss distance in units of cycles and calculate the direction cosine vector of the outgoing beam after the target beam is refracted by the Risley prism;

[0060] In this embodiment, the target miss distance is (Δx, Δy), which is collected by a CCD camera or detector.

[0061] The direction cosine vector of the outgoing beam is calculated as:

[0062] First, the direction cosines (k, l, m) of the target beam after it enters the Risely prism are calculated based on the target miss distance. The calculation formula is as follows:

[0063]

[0064] Where: u is the pixel size, f is the imaging focal length; k, l, and m represent the three direction cosines respectively.

[0065] Then, substitute (k, l, m) as the incident beam into Snell's law in vector form, and after four iterations, the direction cosine vector (K, L, M) of the outgoing beam can be calculated. Among them, Snell's law in vector form is:

[0066]

[0067] Where: n i is the refractive index of the medium where the incident light is located; n r is the refractive index of the medium in which the refracted light occurs; is the direction vector of the incident light, which is the vector (k, l, m) in this embodiment; is the direction vector of the refracted light, is the normal vector of the incident surface.

[0068] S2. Calculate the target orientation based on the direction cosine vector of the outgoing light beam. The specific formula is:

[0069]

[0070] Where: Θ is the azimuth angle; Φ is the elevation angle.

[0071] S3. Determine whether the target is in the center of the field of view: If so, fit the target trajectory function; if not, return to step S1. The target trajectory function f(t) is expressed as follows:

[0072] f(t)=β0+β1t+β2t 2 +…+β n t k ;

[0073] Where: k is the highest power of the polynomial; n is the historical target position that can be used for fitting; t represents the number of cycles; k and n are determined by the trade-off between fitting accuracy and real-time performance.

[0074] S4. Predicting the target position in future cycles based on the target trajectory function until the target leaves the center of the field of view.

[0075] S5. Based on the predicted target orientation in the future period, the rotation angles of the two prisms in the Risley prism in each future period are obtained.

[0076] S6. Switch the rotation angle of the two prisms in one cycle before the target leaves the center of the field of view, obtain a rotation control strategy, and control the movement of the two prisms with the rotation control strategy.

[0077] Compared to existing technologies, this application predicts the target trajectory through curve fitting and uses an optimized rotation control strategy to replan the motion profile of the dual prisms, significantly reducing the prism's angular velocity and improving the system's dynamic performance and tracking accuracy. This method extends the area of ​​action of traditional methods to the center of the entire field of view, thereby achieving smooth tracking across the entire field of view.

[0078] Example 2:

[0079] A method for eliminating control singularities of a Risley prism tracking system, based on Example 1:

[0080] In step S3, the method for determining whether the target is in the center of the field of view is: comparing the azimuth angle of the target with the boundary R of the restricted area at the center of the field of view; if the azimuth angle of the target is less than or equal to the boundary R of the restricted area at the center of the field of view, the target is in the center of the field of view; if the azimuth angle of the target is greater than the boundary R of the restricted area at the center of the field of view, the target is not in the center of the field of view.

[0081] In step S5, the rotation angles of the two prisms in the Risley prism in each future cycle are calculated using the following formula:

[0082]

[0083] Where: θ1 and θ2 represent the rotation angles of the two prisms respectively; Θ is the azimuth angle; Φ is the pitch angle; δ1 and δ2 are the equivalent beam deflection angles of the two prisms respectively, which are calculated by the following formula:

[0084]

[0085] Where: n1 and n2 are the refractive indices of the two prisms, and α1 and α2 are the wedge angles of the two prisms.

[0086] In a more preferred embodiment, the method for fitting the target trajectory function in step S3 includes:

[0087] S301, converting the target orientation within the historical period from a polar coordinate system to a Cartesian coordinate system;

[0088] S302, performing polynomial fitting on the target orientation in the Cartesian coordinate system to obtain a target trajectory curve expression;

[0089] S303, fitting the independent variables in the target trajectory curve expression to obtain a function of the independent variables with respect to the period;

[0090] S304: Substitute the function of the independent variable with respect to the period into the target trajectory curve expression to obtain a target trajectory function.

[0091] Example 3:

[0092] A method for eliminating control singularities of a Risley prism tracking system, based on embodiment 1 or 2, wherein the method for obtaining a slewing control strategy in step S6 includes:

[0093] S601: For any prism, establish a linear function based on the rotation angle and period of the current prism, starting from the rotation angle of the current prism one cycle before the target enters the center of the field of view and ending at the rotation angle of the other prism one cycle before the target leaves the center of the field of view;

[0094] S602, defining the linear functions obtained by the two prisms as a first linear function and a second linear function respectively;

[0095] S603: Modify the first linear function and the second linear function to obtain a first rotation control curve and a second rotation control curve, and use the first rotation control curve and the second rotation control curve as a rotation control strategy.

[0096] The method of correcting the first straight line function and the second straight line function includes:

[0097] S6031. Based on the rotation angles of the two prisms in the Risley prism in each future cycle, calculate the rotation angle difference of the two prisms corresponding to each cycle when the target is in the center of the field of view, and record it as Δθ 1i ; i represents the i-th cycle;

[0098] S6032. Calculate the rotation angle difference between the first straight line function and the second straight line function for each period when the target is in the center of the field of view, and record it as Δθ 2i ;

[0099] S6033, maintain Δθ 1i The rotation angle in the first linear function and / or the second linear function is adjusted so that Δθ 2i =Δθ 1i .

[0100] In summary, this embodiment is based on the predicted target orientation in the future cycle, and the inverse solution of the rotation angle of the target before leaving the center of the field of view (corresponding to the two prisms being θ 1o ,θ 2o ) to switch the rotation angles of the two prisms. Taking prism 1 as an example, connect the rotation angles of the target entering and leaving the center of the field of view to solve the equation of the line l1. Repeat the same process for prism 2 to obtain the equation of the line l2. In each cycle predicted within the center of the field of view, keep the predicted angle Δθ between the two prisms constant, fit θ1 to l1, and θ2 to l2, and use the inverse solution of the fit as the new rotation angle.

[0101] Example 4:

[0102] A method for eliminating control singularities of a Risley prism tracking system, such as Figure 1 As shown, the CCD array is 1280 × 1024, with a pixel size of 4 μm, a focal length of f = 75 mm, and an acquisition frequency of 25 Hz. The refractive indices of the two prisms are n1 = n2 = 1.515, and the wedge angles α1 = α2 = 18.15°. The target plane is located at a distance of L = 2000 m from the Risley prism system, and the target velocity is v = 200 m / s. It moves in a straight horizontal direction, with a vertical distance h = 8 m from the horizontal. l is the target's initial horizontal position, which in this embodiment is 200 m. The number of acquisitions, n = 20, is defined, with real-time updates every cycle.

[0103] This embodiment is based on the method in any of the above embodiments, and the specific steps are as follows:

[0104] Step 1:

[0105] The miss distance collected by CCD in a certain period is (79,143). According to formula (1), the direction cosine of the target beam after refraction is calculated as (k, l, m) = (4.21×10 -3 ,5.33×10 -5 ,-1.00).

[0106] Substituting (k, l, m) into formula (2), after four iterations, the direction vector (i.e., the direction cosine vector of the outgoing light beam) can be obtained as: (K, L, M) = (-0.0040, 0.0035, -1.0000).

[0107] Step 2:

[0108] Substituting the direction cosine vector (K, L, M) of the target beam into Equation (3) yields the target orientation (Φ, Θ) = (0.3051°, 138.6391°). Compare the current target orientation with the boundary R (Θ ≤ 0.6°) of the restricted area at the center of the field of view. If the target does not enter the center of the field of view, repeat steps 1 and 2 until it does. The target orientations collected during this period are shown in Table 1.

[0109] Table 1. Collected target positions

[0110]

[0111] It can be seen from Table 1 that the target enters the center of the field of view at t=20 cycles.

[0112] Step 3:

[0113] Based on the data collected in Table 1, a curve fitting is performed on the target trajectory to obtain the target trajectory function f. Since the target trajectory in this embodiment is a uniform linear motion, a quadratic polynomial function is selected. In order to facilitate fitting, the target orientation needs to be converted from the polar coordinate system to the Cartesian coordinate system. The formula is as follows:

[0114]

[0115] The converted coordinates are shown in Table 2.

[0116] Table 2. Collected target positions (Cartesian coordinate system)

[0117] t / n <![CDATA[Φ x / °]]> <![CDATA[Φ y / °]]> t / n <![CDATA[Φ x / °]]> <![CDATA[Φ y / °]]> 1 4.7984 0.2348 11 2.5196 0.2330 2 4.5714 0.2345 12 2.2890 0.2331 3 4.3447 0.2340 13 2.0618 0.2329 4 4.1152 0.2333 14 1.8315 0.2325 5 3.8892 0.2354 15 1.6045 0.2318 6 3.6603 0.2340 16 1.3744 0.2308 7 3.4317 0.2326 17 1.1446 0.2295 8 3.2034 0.2339 18 0.9149 0.2309 9 2.9753 0.2318 19 0.6883 0.2289 10 2.7473 0.2326 20 0.4585 0.2297

[0118] Step 4:

[0119] The least squares method is used to perform polynomial fitting on the 20 target positions in Table 2, and the target trajectory function is obtained as follows:

[0120] Φ y =-2.0430×10-4 Φ x 2 +0.0023Φ x +0.2283.

[0121] In order to make predictions, we also need to know the independent variable Φ x The value at the next moment; so we also need to fit the independent variable Φ x As a function of period t, the fitting results are as follows:

[0122] Φ x =-4.7939×10 -5 t 2 -0.2275t+5.0267.

[0123] The target orientation at the future moment is predicted until the target leaves the center of the field of view; the prediction results are shown in Table 3.

[0124] Table 3 Target direction at future time

[0125]

[0126] According to the prediction results, it can be seen that the target leaves the center of the field of view at t = 25, and the direction is (Φ, Θ) = (0.7267°, 161.8280°).

[0127] Step 5:

[0128] According to equations (4) and (5), the predicted target orientation is inversely solved to obtain the rotation angle of the prism as shown in Table 4.

[0129] Table 4 Prism rotation angle

[0130]

[0131] Step 6:

[0132] Switching the rotation angles of the two prisms at t = 24 and connecting the solutions at t = 20 and t = 24, we obtain the expressions of the two straight lines as follows:

[0133]

[0134] For the inverse solution within the three periods t = 21 to 23, the angle Δθ between the two prisms is kept constant and fitted to two straight lines to make the prism motion profile as smooth as possible. Taking t = 21 as an example, substituting into equation (6) yields the rotation angles of the two prisms (y1, y2) = (284.1295°, 102.6615°). At this point, the angle Δθ' = 181.4680°, which differs by 0.3840° from the original angle Δθ' = 181.8520°. To compensate for the difference in angles, the angles of the two prisms are each shifted outward by half the difference, yielding (θ1, θ2) = (284.3215°, 102.4695°). The fitting principle for the remaining periods is the same as above.

[0135] The effect of eliminating the singularity in this embodiment can be achieved by Figures 3 and 4 reflect. Figure 3 Comparison of tracking error and miss distance before and after singularity elimination. It can be seen that after eliminating the singularity, the maximum miss distance is reduced from (-540, -443) to (307, -24), and the maximum tracking error is also reduced from 37.2mrad to 16.5mrad, a reduction of 55.6%. Figure 4 To eliminate the angular velocity contrast between the front and rear prisms due to the singularity, the maximum angular velocity was reduced from 15.9 rad / s to 3.8 rad / s, a decrease of 75.9%.

[0136] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

[0137] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

Claims

1. A method for eliminating control singularity of a Risley prism tracking system, characterized in that: The following steps are involved: S1. Collect the target miss distance in units of cycles and calculate the direction cosine vector of the outgoing beam after the target beam is refracted by the Risley prism; S2. Calculating the target orientation based on the direction cosine vector of the outgoing light beam; S3, determine whether the target is in the center of the field of view: if so, fit the target trajectory function; if not, return to step S1; S4. predicting the target position in future cycles based on the target trajectory function until the target leaves the center of the field of view; S5. Based on the predicted target orientation in the future period, obtain the rotation angle of the two prisms in the Risley prism in each future period; S6, switching the rotation angles of the two prisms in one cycle before the target leaves the center of the field of view, obtaining a rotation control strategy, and controlling the movement of the two prisms with the rotation control strategy; The method for obtaining the rotation control strategy includes: S601: For any prism, establish a linear function based on the rotation angle and period of the current prism, starting from the rotation angle of the current prism one cycle before the target enters the center of the field of view and ending at the rotation angle of the other prism one cycle before the target leaves the center of the field of view; S602, defining the linear functions obtained by the two prisms as a first linear function and a second linear function respectively; S603: Modify the first linear function and the second linear function to obtain a first rotation control curve and a second rotation control curve, and use the first rotation control curve and the second rotation control curve as a rotation control strategy; The method for correcting the first straight line function and the second straight line function includes: S6031. Based on the rotation angles of the two prisms in the Risley prism in each future cycle, calculate the rotation angle difference of the two prisms corresponding to each cycle when the target is in the center of the field of view, and record it as Δθ 1i ; i represents the i-th cycle; S6032. Calculate the rotation angle difference between the first straight line function and the second straight line function for each period when the target is in the center of the field of view, and record it as Δθ 2i ; S6033, maintain Δθ 1i The rotation angle in the first linear function and / or the second linear function is adjusted so that Δθ 2i =Δθ 1i .

2. The method for eliminating control singularity of a Risley prism tracking system according to claim 1, wherein: The method for calculating the direction cosine vector of the outgoing light beam after the target light beam is refracted by the Risley prism includes: S101, calculating direction cosines based on target miss distance; S102 , substituting the direction cosines into Snell's law in vector form, iterating at least four times, and obtaining the direction cosine vector of the outgoing light beam.

3. The method for eliminating control singularity of a Risley prism tracking system according to claim 1, wherein: The target orientation includes an azimuth angle and an elevation angle.

4. The method for eliminating control singularity of a Risley prism tracking system according to claim 3, wherein: The direction cosine vector of the outgoing light beam is (K, L, M), and the formula for calculating the target direction is: Φ=arccos(-M) Where: Θ is the azimuth angle; Φ is the elevation angle.

5. The method for eliminating control singularity of a Risley prism tracking system according to claim 3, wherein: The method for determining whether a target is located at the center of the field of view includes: comparing the azimuth angle of the target with the boundary of a restricted area at the center of the field of view; if the azimuth angle of the target is less than or equal to the boundary of the restricted area at the center of the field of view, the target is located at the center of the field of view; if the azimuth angle of the target is greater than the boundary of the restricted area at the center of the field of view, the target is not located at the center of the field of view.

6. The method for eliminating control singularity of a Risley prism tracking system according to claim 1, wherein: The rotation angles of the two prisms in the Risley prism in each future cycle are calculated by the following formula: Where: θ1 and θ2 represent the rotation angles of the two prisms respectively; Θ is the azimuth angle; Φ is the pitch angle; δ1 and δ2 are the equivalent beam deflection angles of the two prisms respectively.

7. The method for eliminating control singularity of a Risley prism tracking system according to claim 6, wherein: The equivalent beam deflection angle of the two prisms is calculated by the following formula: Where: n1 and n2 are the refractive indices of the two prisms, and α1 and α2 are the wedge angles of the two prisms.

8. The method for eliminating control singularity of a Risley prism tracking system according to claim 1, wherein: The method for fitting the target trajectory function includes: S301, converting the target orientation within the historical period from a polar coordinate system to a Cartesian coordinate system; S302, performing polynomial fitting on the target orientation in the Cartesian coordinate system to obtain a target trajectory curve expression; S303, fitting the independent variables in the target trajectory curve expression to obtain a function of the independent variables with respect to the period; S304: Substitute the function of the independent variable with respect to the period into the target trajectory curve expression to obtain a target trajectory function.

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