Control singularity elimination method of Risley prism tracking system

Abstract

The invention discloses a control singularity elimination method for a Risley prism tracking system, and the method comprises the steps: collecting a target miss distance by taking a period as a unit, and calculating an emergent beam direction cosine vector of a target beam after the target beam is refracted by a Risley prism; calculating a target orientation; judging whether the target is in the center of the field of view; fitting to obtain a target trajectory function; predicting a target orientation in a future period based on the target trajectory function until the target leaves the center of the field of view; obtaining rotation angles of two prisms in the Risley prism in each future period based on the predicted target orientation of the future period; and switching the rotation angles of the two prisms in the period before the target leaves the center of the field of view to obtain a rotation control strategy, and controlling the two prisms to act according to the rotation control strategy. The method is used for solving the problem that the control singularity of the Risley prism cannot be eliminated when the target trajectory deviates from the optical axis in the prior art, can effectively reduce the control singularity of the Risley prism, is not limited by the deviation of the optical axis, and can realize smooth tracking of the target in a full-view-field area.

Description

Technical Field

[0001] The 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] Risley prism is a kind of rotating biprism, which is a pair of coaxially arranged optical wedges. It uses the principle of refraction to achieve the deflection of the light beam. Through the independent rotation of the two prisms, the light 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, 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 has singularity: when the scanning beam tracks the target close to the center of the field of view, the angular velocity of the prism increases sharply; limited by the motor acceleration performance, it is difficult to achieve smooth tracking in the center of the field of view and its vicinity, resulting in frequent large oscillations of the visual axis and even loss of the target field of view, which poses a huge challenge to the tracking performance in practical applications. At present, there is an existing technology that proposes a method to avoid singularity by switching between two sets of solutions, but this method is only effective under the special condition that the target trajectory strictly passes through the optical axis, and does not consider the situation where the path is slightly offset relative to the optical axis. It has extremely low versatility and cannot smoothly track the entire field of view area. Summary of the invention

[0004] The present invention provides a method for eliminating the control singularity of a Risley prism tracking system, so as to solve the problem in the prior art that the control singularity of a Risley prism cannot be eliminated when a target trajectory deviates from an optical axis. The method can effectively reduce the control singularity of the Risley prism, is not limited by the optical axis deviation, and can realize smooth tracking of a 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 cycle, and calculate the direction cosine vector of the outgoing light beam after the target light 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 the future period 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 of the future period, obtaining 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] In view of the problem that the control singularity of the Risley prism cannot be eliminated by the prior art when the target trajectory deviates from the optical axis, the present invention proposes a control singularity elimination method for a Risley prism tracking system. The method first continuously collects the target miss amount in units of cycles, calculates the cosine vector of the outgoing light beam direction after the target light beam is refracted by the Risley prism, and then calculates the target orientation according to the cosine vector of the outgoing light beam direction. The calculation process of the method up to now can be implemented by the prior art, and it is not difficult for technical personnel in this field to implement. Afterwards, it is determined whether the target is in the center of the field of view: if the target is in the center of the field of view, the target trajectory function is fitted according to the target orientation obtained in the previous cycles; if the target is not in the center of the field of view, there is no need to consider the control singularity temporarily, and return to step S1 to collect the target miss amount of the next cycle and cycle. For the case where the target is in the center of the field of view, the next target orientation is predicted in units of cycles according to the fitted target trajectory function, and the prediction stops until the target leaves the center of the field of view. At this time, the two prisms in the Risley prism can be obtained, and the rotation angles corresponding to each cycle before the target leaves the center of the field of view can be 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, and the movement of the two prisms is controlled by the optimized rotation control strategy.

[0014] The present 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 vicinity; the present application overcomes the defect of the prior art that it can only work when the target trajectory passes through the optical axis, and is no longer limited 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, to obtain the direction cosine vector of the outgoing light beam.

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

[0019] Furthermore, the target orientation includes an azimuth angle and an elevation 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 elevation 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 of the target with the boundary of the restricted area in the center of the field of view; if the azimuth 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 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 by 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 for fitting the target trajectory function includes:

[0033] S301, converting the target orientation in the historical period from the polar coordinate system to the 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 relative to the period;

[0036] S304: Substitute the function of the independent variable relative 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, taking the rotation angle of the current prism one cycle before the target enters the center of the field of view as the starting point and taking the rotation angle of another prism one cycle before the target leaves the center of the field of view as the end point, establish a linear function of the current prism based on the rotation angle and the cycle;

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

[0041] S603: Correct the first straight line function and the second straight line function to obtain a first swing control curve and a second swing control curve, and use the first swing control curve and the second swing control curve as a swing 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 straight line 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, respectively 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, recorded 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 when the target is in the center of the field of view in each period, recorded as Δθ2i ;

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

[0047] In this solution, the first straight line function and / or the second straight line 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. A control singularity elimination method for a Risley prism tracking system of the present invention overcomes the defect of the prior art that the target trajectory can only work when it passes through the optical axis, is no longer limited 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. A control singularity elimination method for a Risley prism tracking system of the present invention 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 schematic diagram of a flow chart of a specific embodiment of the present invention;

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

[0055] Figure 4 This is a comparison diagram of the angular velocities 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 embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0057] Embodiment 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 cycle, and calculate the direction cosine vector of the outgoing light beam after the target light 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 a detector.

[0061] The calculation method of the direction cosine vector of the outgoing beam is:

[0062] First, the direction cosine (k, l, m) of the target beam after refraction into the Risely prism is 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, (k, l, m) is substituted into Snell's law in vector form as the incident beam, and the outgoing beam direction cosine vector (K, L, M) can be calculated after four iterations. 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 is located; is the direction vector of the incident light, i.e., 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 periods 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 with the prior art, this application predicts the target trajectory through curve fitting, and replans the motion profile of the dual prism using the optimized rotation control strategy, which greatly reduces the angular velocity of the prism and improves the dynamic performance and tracking accuracy of the system. This method expands the action area of ​​the traditional method to the center of the entire field of view, thereby achieving smooth tracking of the entire field of view.

[0078] Embodiment 2:

[0079] A method for eliminating control singularity 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 of the target with the boundary R of the restricted area in the center of the field of view; if the azimuth 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 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.

[0081] In step S5, the rotation angles of the two prisms in the Risley prism in each future cycle are calculated by 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 in the historical period from the polar coordinate system to the 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 relative to the period;

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

[0091] Embodiment 3:

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

[0093] S601, for any prism, taking the rotation angle of the current prism one cycle before the target enters the center of the field of view as the starting point and taking the rotation angle of another prism one cycle before the target leaves the center of the field of view as the end point, establish a linear function of the current prism based on the rotation angle and the cycle;

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

[0095] S603: Correct the first straight line function and the second straight line function to obtain a first swing control curve and a second swing control curve, and use the first swing control curve and the second swing control curve as a swing 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, respectively 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, recorded 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 when the target is in the center of the field of view in each period, recorded as Δθ 2i ;

[0099] S6033, maintain Δθ 1i The rotation angle in the first straight line function and / or the second straight line 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 are θ 1o ,θ 2o ) is switched, that is, the rotation angle of the two prisms is switched. 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 straight line equation l1. Do the same for prism 2 to obtain the straight line equation l2. In each cycle predicted in the center of the field of view, keep the predicted angle Δθ between the two prisms unchanged, let θ1 fit to l1, and θ2 fit to l2, and use the inverse solution after fitting as the new rotation angle.

[0101] Embodiment 4:

[0102] A method for eliminating control singularity of Risley prism tracking system, such as Figure 1 As shown, the CCD array is 1280×1024, the pixel size is 4μm, the focal length is f=75mm, and the acquisition frequency is 25Hz; the refractive index of the two prisms is n1=n2=1.515, and the wedge angle is α1=α2=18.15°. The plane where the target is located is L=2000m away from the Risley prism system, the target speed is v=200m / s, and it moves in a straight line in the horizontal direction. The vertical distance from the horizontal line is h=8m, and l is the initial horizontal position of the target. In this embodiment, l=200m. The acquisition number n=20 is defined, and it is updated in real time 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, we can obtain its direction vector (i.e., the direction cosine vector of the outgoing light beam): (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 formula (3), we can get 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 the target enters the center of the field of view. The target orientations collected during this period are shown in Table 1.

[0109] Table 1 The 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] According to the data collected in Table 1, the target trajectory is curve fitted 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, and the formula is as follows:

[0114]

[0115] The transformed 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 trajectory function of the target 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; therefore, it is also necessary 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 position 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 position 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) to (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] Switch the rotation angles of the two prisms at t = 24, and connect the solutions at t = 20 and t = 24 to obtain the expressions of the two straight lines as follows:

[0133]

[0134] For the inverse solution in the three periods of t = 21 to 23, keep the angle Δθ of the two prisms unchanged and fit them to two straight lines respectively to make the motion profile of the prism as smooth as possible. Taking t = 21 as an example, substitute into formula (6) to obtain the rotation angle of the two prisms (y1, y2) = (284.1295°, 102.6615°). At this time, the angle Δθ' = 181.4680°, which is 0.3840° different from the original angle Δθ' = 181.8520°. In order to compensate for the difference in the angle, the angles of the two prisms are moved outward by half of the difference, and (θ1, θ2) = (284.3215°, 102.4695°) is obtained. The fitting principle for the remaining periods is the same as above.

[0135] The effect of eliminating singularity in this embodiment can be achieved by Figure 3-4 reflect. Figure 3 Comparison of tracking error and miss distance before and after eliminating singularity. It can be seen that after eliminating 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 article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

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 cycle, and calculate the direction cosine vector of the outgoing light beam after the target light 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 the future period based on the target trajectory function until the target leaves the center of the field of view; S5, based on the predicted target orientation of the future period, obtaining the rotation angle of the two prisms in the Risley prism in each future period; 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.

2. The method for eliminating control singularity of a Risley prism tracking system according to claim 1, characterized in that: The method for calculating the direction cosine vector of the outgoing light beam after the target light beam is refracted by the Risley prism comprises: 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, to obtain 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, characterized in that: 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, characterized in that: The direction cosine vector of the outgoing light beam is (K, L, M), and the formula for calculating the target orientation 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, characterized in that: The method for determining whether a target is in the center of the field of view comprises: 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.

6. The method for eliminating control singularity of a Risley prism tracking system according to claim 1, characterized in that: The rotation angle of the two prisms in the Risley prism in each future cycle is 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, characterized in that: 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, characterized in that: The method for fitting to obtain the target trajectory function comprises: S301, converting the target orientation in the historical period from the polar coordinate system to the 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 relative to the period; S304: Substitute the function of the independent variable relative to the period into the target trajectory curve expression to obtain a target trajectory function.

9. The method for eliminating control singularity of a Risley prism tracking system according to claim 1, characterized in that: The method for obtaining the slewing control strategy comprises: S601, for any prism, taking the rotation angle of the current prism one cycle before the target enters the center of the field of view as the starting point and taking the rotation angle of another prism one cycle before the target leaves the center of the field of view as the end point, establish a linear function of the current prism based on the rotation angle and the cycle; S602, defining the straight line functions obtained by the two prisms as a first straight line function and a second straight line function respectively; S603: Correct the first straight line function and the second straight line function to obtain a first swing control curve and a second swing control curve, and use the first swing control curve and the second swing control curve as a swing control strategy.

10. The method for eliminating control singularity of a Risley prism tracking system according to claim 9, characterized in that: 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, respectively 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, recorded 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 when the target is in the center of the field of view in each period, recorded as Δθ 2i ; S6033, maintain Δθ 1i The rotation angle in the first straight line function and / or the second straight line function is adjusted so that Δθ 2i =Δθ 1i .

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