Robust selection method for autonomous optical navigation landmarks for planetary landing

Abstract

The present invention discloses a robust optimization method for autonomous optical navigation landmarks for planetary landing, which belongs to the field of deep space exploration technology. The implementation method of the present invention is as follows: using the height information of the lander to determine the scale of the image plane projected onto the planetary surface, and deriving the quadrilateral vertex expression of the field of view based on the geometric relationship; using the relationship between the field of view vertex deviation and the lander posture error, converting the posture uncertainty to the field of view vertex uncertainty, and using the error ellipse to describe the field of view vertex uncertainty distribution; screening the quadrilateral area formed by the intersection of common tangents, which is the field of view intersection under the lander posture uncertainty; using the nominal trajectory and camera parameters to estimate the field of view sequence, combining the field of view intersection acquisition method to obtain the field of view intersection sequence, the field of view intersection sequence is obtained by offline estimation, and the amount of onboard calculation of the lander is reduced; using the observability of the navigation system to establish the landmark optimization index, optimize the selection of the landmarks in the field of view intersection sequence, and reduce the influence of posture uncertainty on the selected landmarks.

Description

Technical Field

[0001] The invention relates to a robust optimization method for autonomous optical navigation landmarks for planetary landing, and belongs to the technical field of deep space exploration. Background Art

[0002] Planetary exploration missions, such as Mars exploration missions and small celestial body exploration missions, require landing and conducting exploration activities in areas of high scientific value. Since the target planet is far away from the Earth, the communication method based on the ground tracking and control station has a large delay. In order to meet the needs of obstacle avoidance and precise landing, the lander has autonomous navigation capabilities. At the same time, the uncertainty factors such as environmental disturbances in the target celestial body put forward higher requirements for the autonomous navigation system.

[0003] Autonomous optical navigation is an important autonomous navigation method for planetary landing exploration at this stage. Since there are observation landmarks such as craters and rocks on the surface of the planet, the landmarks can be obtained by using optical cameras, and the lander state can be directly solved according to the geometric relationship, so that the lander posture estimation can be realized. The navigation camera can observe a large number of landmarks. Due to the limited online computing power and storage space of the onboard computer at this stage, it is difficult to process a large number of landmarks online at the same time. Therefore, it is necessary to optimize the selection of observation landmarks to improve the accuracy of autonomous navigation and onboard computing efficiency of planetary landing.

[0004] During the planetary landing process, as the altitude of the lander gradually decreases, the navigation landmarks used at the previous moment gradually move out of the camera's field of view. Continuously re-extracting and matching new landmarks can achieve high-precision navigation, but the limited onboard computing power cannot meet the real-time extraction and matching requirements of observed landmarks. To this end, an offline method is used to pre-select navigation landmarks to obtain the optimal landmark sequence and store the required landmark data. During the actual landing process, as the altitude of the lander decreases, the observed landmarks are switched according to the optimal landmark sequence to avoid processing a large number of landmarks, thereby reducing the amount of onboard computing and storage and improving navigation accuracy.

[0005] Due to factors such as environmental disturbances, the position uncertainty of the lander causes a certain deviation between the actual field of view and the estimated field of view. The offline planned navigation landmarks may not be in the actual field of view, resulting in the failure of landmark planning and seriously affecting the navigation accuracy. Therefore, it is necessary to consider the uncertainty of the lander's position in the off-line landmark selection to improve the effectiveness of off-line landmark selection. Summary of the invention

[0006] The main purpose of the present invention is to provide a method for robust optimization of autonomous optical navigation landmarks for planetary landing. The method uses the height information of the lander to determine the scale of the image plane projected onto the planetary surface, derives the quadrilateral vertex expression of the field of view based on the geometric relationship, and realizes the field of view representation under arbitrary posture of the lander; uses the relationship between the field of view vertex deviation and the lander posture error to convert the lander posture uncertainty into the field of view vertex uncertainty, and uses the error ellipse to describe the field of view vertex uncertainty distribution; uses the quadrilateral area formed by the intersection of the selected common tangent lines to be the lander posture uncertainty under the uncertainty of the lander posture. The field of view intersection is obtained by using the nominal trajectory and camera parameters to estimate the field of view sequence, and the field of view intersection sequence is obtained by combining the given field of view intersection acquisition method. Since the field of view intersection sequence is obtained through offline estimation, it does not need to be calculated on the onboard computer, thus avoiding real-time image processing during the landing process and reducing the onboard calculation amount of the lander. The observability of the navigation system is used to establish the landmark selection index, optimize the selection of the landmarks in the field of view intersection sequence, reduce the influence of the uncertainty of the lander's posture on the selected landmarks, improve the robustness of the planetary landing autonomous optical navigation landmark selection, and obtain a highly robust optimal landmark sequence.

[0007] The purpose of the present invention is achieved through the following technical solutions.

[0008] The present invention discloses a robust optimization method for autonomous optical navigation landmarks for planetary landing. The method uses the height information of the lander to determine the scale of the image plane projected onto the planetary surface, and derives the quadrilateral vertex expression of the field of view based on geometric relationships to achieve the field of view characterization under arbitrary postures of the lander. The relationship between the field of view vertex deviation and the lander posture error is used to convert the lander posture uncertainty into the field of view vertex uncertainty, and the error ellipse is used to describe the field of view vertex uncertainty distribution, thereby obtaining four error ellipses describing the four field of view vertex uncertainty distributions. Sixteen common tangents are obtained through adjacent error ellipses. The required solutions are screened by judging whether the field of view vertex is on the same side of the common tangent, and the field of view vertex and the camera optical center are projected at both ends of the common tangent to obtain four required common tangents. The quadrilateral area formed by the intersection of the screened common tangents is the field of view intersection under the uncertainty of the lander posture. The field of view sequence is estimated using the nominal trajectory and camera parameters, and the field of view intersection sequence is obtained by combining the given field of view intersection acquisition method. Since the field of view intersection sequence is obtained through offline estimation, it does not need to be calculated on the onboard computer, avoiding real-time image processing during the landing process and reducing the amount of onboard calculation of the lander. The landmark selection index is established using the observability of the navigation system, and the landmarks in the field of view intersection sequence are optimized to reduce the impact of the uncertainty of the lander's posture on the selected landmarks, improve the robustness of the planetary landing autonomous optical navigation landmark selection, and obtain a highly robust optimal landmark sequence.

[0009] The present invention discloses a robust optimization method for planetary landing autonomous optical navigation landmarks, comprising the following steps:

[0010] Step 1: Establish a planetary landing dynamics model and an optical navigation observation model, and optimize the lander state by considering multiple constraints and requirements of the mission to obtain the lander trajectory as the nominal landing trajectory. The multiple constraints include the planetary landing dynamics model and the optical navigation observation model. The nominal landing trajectory includes the nominal position and nominal attitude.

[0011] In the landing point coordinate system, the six-degree-of-freedom dynamic model of planetary landing is:

[0012]

[0013] in, L r and L v represents the position and velocity vector of the lander, respectively; T represents the thrust vector of the thruster; is the planetary gravitational acceleration vector; Describes the rotation vector from the landing point coordinate system to the camera coordinate system; is the planet's rotational angular velocity; J is the lander's moment of inertia; B ω represents the lander angular velocity vector; B M is the torque applied to the lander; The representation is as follows.

[0014]

[0015] Considering the multiple constraints and requirements of the mission, the optimization algorithm is combined to optimize the lander state, and the optimized trajectory is obtained as the nominal trajectory, including the nominal position and nominal attitude

[0016] In order to simplify the notation, the camera coordinate system is defined to coincide with the lander coordinate system. The navigation camera model uses the pinhole projection model. L p i (i=1,…,n) is projected on the camera image plane as

[0017]

[0018] Among them, u i for L p j 2D projection on the image plane; p i ,l i for u i The two-axis components of; f represents the focal length of the camera; C x i , C y i , C z i for L p jThe three-axis components in the camera system are expressed as follows

[0019]

[0020] Among them, R CL The rotation matrix from the landing point coordinate system to the camera coordinate system.

[0021] Step 2: Use the lander height information to determine the scale of the image plane projection onto the planetary surface, and derive the field of view vertex expression based on the geometric relationship. Use the relationship between the field of view vertex deviation and the lander posture error to convert the lander posture uncertainty into the field of view vertex uncertainty, use the error ellipse to describe the field of view vertex uncertainty distribution, and then obtain four error ellipses describing the uncertainty distribution of the four field of view vertices.

[0022] The camera field of view is the area observable by the navigation camera, which is the projection of the image plane onto the planet surface. The image plane is a square, and the side length of the image plane is expressed as Combined with equation (4), the relationship between the image plane vertex position and the field of view vertex under the camera system is expressed as

[0023]

[0024] in, for u j The homogeneous coordinate form of represents the vertex position of the image plane; C p j is the vertex position of the camera field of view in the camera system; K = diag[f,f,1] represents the camera parameters. Combining equation (3) with equation (5), the vertex of the camera field of view in the landing point system is expressed as

[0025]

[0026] The direction vector of the optical axis in the camera's viewing cone is expressed as in, C e o is the camera optical axis direction vector under the camera system; is the normal vector perpendicular to the landing plane. The camera cone edge length direction is expressed as in, is the direction vector of the viewing cone length under the camera system; Represents the rotation matrix that transforms the camera optical axis direction to the edge length direction. According to the geometric relationship,

[0027]

[0028] Among them, α j is the angle between the camera optical axis and the edge length direction vector; β j for C e j and The angle α j ,β j Respectively expressed as

[0029]

[0030]

[0031] Combining equations (6) and (7), the vertex of the field of view in the landing point coordinate system is expressed as

[0032]

[0033] The uncertainty of the lander’s position is expressed as Among them, δρ represents the small perturbation of the lander position, and δφ represents the small perturbation of the lander attitude. The relationship between the field of view vertex in the lander point coordinate system and the camera coordinate system is expressed as

[0034]

[0035] in, and is the homogeneous coordinate form, T v is the transformation matrix, expressed as

[0036]

[0037] in, is the rotation matrix from the camera system to the landing point system, φ v represents the rotation from the camera system to the landing point system; t v , t are translation vectors, and T is the transformation matrix. Considering the posture disturbance in, Considering the uncertainty of the lander's posture, the vertex position of the field of view is expressed in the landing point coordinate system as

[0038]

[0039] Through formula (13), we can get From formula (12), we can get exp(ξ v )=exp(ξ) -1 =exp(-ξ), and then we get ξ v = -ξ. The relationship between the field of view vertex deviation and the lander posture error is derived as shown in formula (14).

[0040]

[0041] Formula (14) is simplified to

[0042] Δ L p j =-(δφ^L p+δρ)= L p^δφ-δρ=Zδξ (15)

[0043] Where Z = [-I 3 L p^].

[0044] δρ and δφ are Gaussian white noises that do not affect each other and satisfy and The variance of δξ is expressed as

[0045]

[0046] Using the large Δ in formula (16) L p j The variance of is shown in formula (17).

[0047]

[0048] consider L x- L The two-axis components on the y plane make H represents the following

[0049]

[0050] According to formula (17), The variance is expressed as

[0051]

[0052] According to formula (19), Δ L p jx and Δ L p jy The variance is expressed as

[0053]

[0054] definition The above formula is rewritten as shown in formula (21).

[0055]

[0056] The error ellipse is described by the major and minor semi-axes E j ,F j The ellipse is expressed in the error ellipse coordinate system as

[0057]

[0058] in,

[0059]

[0060] in,

[0061]

[0062] Q is The covariance matrix of the error ellipse; the angle between the major axis of the error ellipse and the landing point coordinate system Expressed as

[0063]

[0064] According to equations (22) to (25), the error ellipse is used to describe the uncertainty distribution of the field of view vertex.

[0065] Step 3: Based on the four error ellipses describing the uncertainty distribution of the field of view vertices obtained in step 2, 16 common tangents are obtained through adjacent error ellipses. The required solution is screened by judging whether the field of view vertex is on the same side of the common tangent, and the field of view vertex and the camera optical center are projected at both ends of the common tangent to obtain the four required common tangents. The quadrilateral area formed by the intersection of the screened common tangents is the field of view intersection under the uncertainty of the lander's posture.

[0066] According to equations (22) to (25), the four error ellipses describing the uncertainty distribution of the field of view vertices are used to obtain 16 common tangents through adjacent error ellipses, and the four required common tangents are screened to obtain the field of view intersection using the intersection of the screened common tangents.

[0067] By combining adjacent tangent equations, we can get the coordinates k of the four tangent points. 1 ,k 2 ,k 3 ,k 4 , which is expressed as follows

[0068] Any point on the error ellipse E q i exist L x- L The y coordinate system is expressed as

[0069] E q i =R EL ( L q i -t j ) (26)

[0070] in, E q i =[ E x i , E y i ] T is the position of any point on the error ellipse; L q i =[L x i , L y i ] T express E q i exist L x- L Position in the y coordinate system; t j =[ L p jx , L p jy ] T represents the translation vector; R EL Indicates from L x- L The rotation matrix from the y plane coordinate system to the error ellipse coordinate system is expressed as follows

[0071]

[0072] Combining equations (22), (26) and (27), the error ellipse is L x- L The y-plane coordinate system is expressed as

[0073] A j L x 2 +B j L x L y+D j L y 2 +O j L x+P j L y+1=0 (28)

[0074] in,

[0075]

[0076] Formula (28) is converted into a quadratic form, as shown below

[0077]

[0078] in, for L x=[ L x, L y] T The homogeneous coordinate form of M j Expressed as

[0079]

[0080] The tangent line equation is defined as follows

[0081]

[0082] Among them, L m =[a m ,b m ,1] T represents the tangent coefficient. Combining equation (30) and equation (32), we get the following formula.

[0083]

[0084] Where ε is the proportional factor. Combining equations (30) and (33), we get the relationship between the error ellipse and the tangent line of the error ellipse as shown in equation (34).

[0085]

[0086] Through equation (34), the common tangent of two adjacent error ellipses is the solution of equation group (35).

[0087]

[0088] Since equation (35) has four solutions, the required solution is screened by judging whether the field of view vertex is on the same side of the common tangent line, and whether the field of view vertex and the camera optical center projection are at both ends of the common tangent line. The camera optical center projection is expressed as

[0089]

[0090] Use the above screening method to screen the required solution and obtain 4 common tangent coefficients L 1 ,L 2 ,L 3 ,L 4 , expressed as

[0091]

[0092] By combining adjacent tangent equations, we can get the coordinates k of the four tangent points. 1 ,k 2 ,k 3 ,k 4 , which is expressed as follows

[0093]

[0094] By k 1 ,k 2 ,k 3 ,k 4 The quadrilateral area formed is the intersection of the field of view under the uncertainty of the lander's posture.

[0095] Step 4: Use the nominal trajectory and camera parameters obtained in step 1 to estimate the field of view sequence, and combine it with the field of view intersection acquisition method given in step 3 to obtain the field of view intersection sequence. Since the field of view intersection sequence is obtained through offline estimation, it does not need to be calculated on the onboard computer, avoiding real-time image processing during the landing process and reducing the amount of onboard calculations of the lander. Use the observability of the navigation system to establish landmark selection indicators, optimize the selection of landmarks in the field of view intersection sequence, reduce the impact of the uncertainty of the lander's posture on the selected landmarks, improve the robustness of the planetary landing autonomous optical navigation landmark selection, and obtain a highly robust optimal landmark sequence.

[0096] Consider the camera sampling period is Δt, satisfying t k+1 -t k =Δt, where k = 0, 1, ..., n-1. The nominal trajectory obtained in step 1 is combined with the camera parameter estimation to obtain a set of field of view sequences. The field of view intersection calculation method given in step 3 is used to obtain the field of view intersection sequence. The landmark optimization index is established using the observability of the navigation system. The Fisher information matrix is ​​expressed as follows:

[0097]

[0098] Among them, σ i represents the standard deviation of the observation noise, w is the number of observed landmarks, and h i (r) represents the observed quantity, and x is the lander state. Combined with the Cramér-Rao lower bound, the trace of the estimated error variance matrix is ​​expressed as

[0099] tr(P)≥tr(FIM -1 ) (40)

[0100] Using tr(FIM -1 ) is used as the performance index to optimize the selection of landmarks in the field of view intersection sequence and obtain the optimal landmark sequence.

[0101] The method also includes step five: during the landing process, the optimal landmark sequence obtained in step four is used for navigation, and the lander continuously switches the observed landmarks according to the optimal landmark sequence to improve the overall navigation accuracy and robustness during the landing phase.

[0102] Beneficial effects:

[0103] 1. The present invention discloses a robust optimization method for autonomous optical navigation landmarks for planetary landing, which uses the height information of the lander to determine the scale of the image plane projected onto the planetary surface, derives the quadrilateral vertex expression of the field of view based on geometric relationships, and realizes the field of view representation under any posture of the lander.

[0104] 2. The present invention discloses a robust optimization method for autonomous optical navigation landmarks for planetary landing. The relationship between the field of view vertex deviation and the lander posture error is used to convert the lander posture uncertainty into the field of view vertex uncertainty. The error ellipse is used to describe the field of view vertex uncertainty distribution, and then four error ellipses describing the four field of view vertex uncertainty distributions are obtained. 16 common tangents are obtained through adjacent error ellipses. The required solutions are screened by judging whether the field of view vertex is on the same side of the common tangent, and the field of view vertex and the camera optical center are projected at both ends of the common tangent to obtain the four required common tangents. The quadrilateral area formed by the intersection of the screened common tangents is the field of view intersection under the uncertainty of the lander posture, which greatly improves the effectiveness of offline landmark planning.

[0105] 3. The present invention discloses a robust optimization method for autonomous optical navigation landmarks for planetary landing, which plans landmarks offline, uses nominal trajectories and camera parameters to estimate the field of view sequence, and optimizes the selection of observed landmarks within the estimated field of view sequence, avoiding real-time image processing during the landing process and reducing the amount of onboard computing for the lander.

[0106] 4. The method for robust selection of autonomous optical navigation landmarks for planetary landing disclosed in the present invention utilizes the observability of the navigation system to establish landmark selection indicators, optimizes the selection of landmarks within the field of view intersection sequence, reduces the impact of the uncertainty of the lander's posture on the selected landmarks, and improves the robustness of the selection of autonomous optical navigation landmarks for planetary landing.

[0107] 5. The present invention discloses a robust optimization method for autonomous optical navigation landmarks for planetary landing. During the landing process, the lander continuously switches the observed landmarks according to the optimal landmark sequence, and uses the obtained optimal landmark sequence for navigation, thereby improving the overall navigation accuracy and robustness during the landing phase. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 It is a flow chart of the robust optimization method for autonomous optical navigation landmarks for planetary landing disclosed in the present invention;

[0109] Figure 2 It is a sequence diagram of the nominal trajectory and nominal field of view obtained in step 1 of the specific implementation case;

[0110] Figure 3 A diagram showing a method for calculating the intersection of fields of view obtained in steps 2 and 3 of a specific implementation case;

[0111] Figure 4 It is a comparison diagram of the optimal landmark sequence under the nominal field of view and the field of view intersection obtained in step 4 of the specific implementation case;

[0112] Figure 5 This is a comparison diagram of the effectiveness of landmark optimization under the nominal field of view and the field of view intersection obtained in step 4 of the specific implementation case. DETAILED DESCRIPTION

[0113] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below in conjunction with an embodiment and corresponding drawings.

[0114] Embodiment 1:

[0115] In order to verify the feasibility and beneficial effects of the method of the present invention, this embodiment takes landing on the asteroid Castalia 4769 as an example.

[0116] like Figure 1 As shown, the present invention discloses a robust optimization method for autonomous optical navigation landmarks for planetary landing, comprising the following steps:

[0117] Step 1: Establish a planetary landing dynamics model and an optical navigation observation model, and optimize the lander state by considering multiple constraints and requirements of the mission to obtain the lander trajectory as the nominal landing trajectory. The multiple constraints include the planetary landing dynamics model and the optical navigation observation model. The nominal landing trajectory includes the nominal position and nominal attitude.

[0118] In the landing point coordinate system, the six-degree-of-freedom dynamic model of planetary landing is:

[0119]

[0120] in, L r and L v represents the position and velocity vector of the lander, respectively; T represents the thrust vector of the thruster; is the planetary gravitational acceleration vector; Describes the rotation vector from the landing point coordinate system to the camera coordinate system; is the planet's rotational angular velocity; J is the lander's moment of inertia; B ω represents the lander angular velocity vector; B M is the torque applied to the lander; The representation is as follows.

[0121]

[0122] Considering the multiple constraints and requirements of the task, combined with the optimization algorithm, the optimized trajectory is obtained as the nominal trajectory, including the nominal position and nominal attitude

[0123] Using the convex optimization algorithm, the nominal trajectory is optimized with fuel consumption as the performance indicator. Figure 2 The simulation parameters under the planetary fixed connection system are shown in Table 1.

[0124] Table 1 Nominal trajectory simulation parameters

[0125]

[0126] To simplify notation, it is assumed that the camera coordinate system coincides with the lander coordinate system. The navigation camera model uses a pinhole projection model. L p i (i=1,…,n) is projected on the camera image plane as

[0127]

[0128] Among them, u i for L p j 2D projection on the image plane; p i ,l i for u i The two-axis components of; f represents the focal length of the camera; C x i , C y i , C z i for L p j The three-axis components in the camera system are expressed as follows

[0129]

[0130] Among them, R CL The rotation matrix from the landing point coordinate system to the camera coordinate system.

[0131] Step 2: Use the lander height information to determine the scale of the image plane projection onto the planetary surface, and derive the field of view vertex expression based on the geometric relationship. Use the relationship between the field of view vertex deviation and the lander posture error to convert the lander posture uncertainty into the field of view vertex uncertainty, use the error ellipse to describe the field of view vertex uncertainty distribution, and then obtain four error ellipses describing the uncertainty distribution of the four field of view vertices.

[0132] The camera field of view is the area observable by the navigation camera, which is the projection of the image plane onto the planet surface. Assuming the image plane is a square, the side length of the image plane can be expressed as Combined with equation (4), the relationship between the image plane vertex position and the field of view vertex under the camera system can be expressed as

[0133]

[0134] in, for u j The homogeneous coordinate form of represents the vertex position of the image plane; C p jis the vertex position of the camera field of view in the camera system; K = diag[f,f,1] represents the camera parameters. Combining equation (3) with equation (5), the vertex of the camera field of view in the landing point system is expressed as

[0135]

[0136] The direction vector of the optical axis in the camera's viewing cone is expressed as in, C e o is the camera optical axis direction vector under the camera system; is the normal vector perpendicular to the landing plane. The camera cone length direction can be expressed as in, is the direction vector of the viewing cone length under the camera system; Represents the rotation matrix that transforms the camera optical axis direction to the edge length direction. According to the geometric relationship, we can get

[0137]

[0138] Among them, α j is the angle between the camera optical axis and the edge length direction vector; β j for C e j and The angle α j ,β j Respectively expressed as

[0139]

[0140]

[0141] Combining equations (6) and (7), the vertex of the field of view in the landing point coordinate system can be expressed as

[0142]

[0143] Convert the nominal trajectory in the planet-fixed system to the landing point system, combine the camera parameters as shown in Table 2, set t = 60s to t = 300s as the navigation camera working time, and you can get a set of field of view sequences as follows: Figure 2 shown.

[0144] Table 2 Navigation camera parameters

[0145]

[0146] The uncertainty of the lander’s posture can be expressed as Among them, δρ represents the small perturbation of the lander position, and δφ represents the small perturbation of the lander attitude. The relationship between the field of view vertex in the lander point coordinate system and the camera coordinate system can be expressed as

[0147]

[0148] in, and is the homogeneous coordinate form, T v is the transformation matrix, which can be expressed as

[0149]

[0150] in, is the rotation matrix from the camera system to the landing point system, φ v represents the rotation from the camera system to the landing point system; t v , t are translation vectors, and T is the transformation matrix. Considering the posture disturbance in, Considering the uncertainty of the lander's posture, the vertex position of the field of view can be expressed in the landing point coordinate system as

[0151]

[0152] Through formula (13), we can get From formula (12), we can see that exp(ξ v )=exp(ξ) -1 =exp(-ξ), and then we get ξ v =-ξ. The formula can be derived as shown below.

[0153]

[0154] Formula (14) can be simplified as

[0155] Δ L p j =-(δφ ^L p+δρ)= L p^δφ-δρ=Zδξ (55)

[0156] Where Z = [-I 3 L p^].

[0157] Assume that δρ and δφ are Gaussian white noises that do not affect each other and satisfy and The variance of δξ can be expressed as

[0158]

[0159] Table 3 System and measurement errors

[0160]

[0161] The system and measurement errors are shown in Table 3. Using formula (16), ΔL p j The variance of can be calculated as follows.

[0162]

[0163] consider L x- L The two-axis components on the y plane make H represents the following

[0164]

[0165] According to formula (17), The variance of can be expressed as

[0166]

[0167] According to formula (19), Δ L p jx and Δ L p jy The variance of can be expressed as

[0168]

[0169] definition The above formula can be rewritten as shown below.

[0170]

[0171] The error ellipse is described by the major and minor semi-axes E j ,F j The ellipse can be expressed in the error ellipse coordinate system as

[0172]

[0173] in,

[0174]

[0175] in,

[0176]

[0177] Q is The covariance matrix of the error ellipse; the angle between the major axis of the error ellipse and the landing point coordinate system It can be expressed as

[0178]

[0179] Step 3: Based on the four error ellipses describing the uncertainty distribution of the field of view vertices obtained in step 2, 16 common tangents are obtained through adjacent error ellipses. The required solution is screened by judging whether the field of view vertex is on the same side of the common tangent, and the field of view vertex and the camera optical center are projected at both ends of the common tangent to obtain the four required common tangents. The quadrilateral area formed by the intersection of the screened common tangents is the field of view intersection under the uncertainty of the lander's posture.

[0180] Any point on the error ellipse E q i exist L x- L In the y coordinate system, it can be expressed as

[0181] E q i =R EL ( L q i -t j ) (66)

[0182] in, E q i =[ E x i , E y i ] T is the position of any point on the error ellipse; L q i =[ L x i , L y i ] T express E q i exist L x- L Position in the y coordinate system; t j =[ L p jx , L p jy ] T represents the translation vector; R EL Indicates from L x- L The rotation matrix from the y plane coordinate system to the error ellipse coordinate system is expressed as follows

[0183]

[0184] Combining equations (22), (26) and (27), the error ellipse is L x- L In the y-plane coordinate system, it can be expressed as

[0185] A jL x 2 +B j L x L y+D j L y 2 +O j L x+P j L y+1=0 (68)

[0186] in,

[0187]

[0188] Formula (28) can be converted into a quadratic form as shown below:

[0189]

[0190] in, for L x=[ L x, L y] T The homogeneous coordinate form of M j It can be expressed as

[0191]

[0192] The tangent line equation is defined as follows

[0193]

[0194] Among them, L m =[a m ,b m ,1] T represents the tangent coefficient. Combining equation (30) and equation (32), we can get the following formula.

[0195]

[0196] Where ε is the proportional factor. Combining equation (30) and equation (33), we can get the following formula.

[0197]

[0198] Through equation (34), the common tangent of two adjacent error ellipses is the solution of the following system of equations.

[0199]

[0200] Since equation (35) has four solutions, the required solution is screened by judging whether the field of view vertex is on the same side of the common tangent line, and whether the field of view vertex and the camera optical center projection are at both ends of the common tangent line. The camera optical center projection can be expressed as

[0201]

[0202] Using the above screening method, we can get 4 common tangent coefficients L 1 ,L 2 ,L 3 ,L 4 , expressed as

[0203]

[0204] By combining adjacent tangent equations, we can get the coordinates of the four tangent points k 1 ,k 2 ,k 3 ,k 4 , which is expressed as follows

[0205]

[0206] By k 1 ,k 2 ,k 3 ,k 4 The quadrilateral area formed is the intersection of the field of view under the uncertainty of the lander's posture. Figure 3 This is a diagram of the field of view intersection calculation method (t=300s).

[0207] Step 4: Use the nominal trajectory and camera parameters obtained in step 1 to estimate the field of view sequence, and combine it with the field of view intersection acquisition method given in step 3 to obtain the field of view intersection sequence. Since the field of view intersection sequence is obtained through offline estimation, it does not need to be calculated on the onboard computer, avoiding real-time image processing during the landing process and reducing the amount of onboard calculations of the lander. Use the observability of the navigation system to establish landmark selection indicators, optimize the selection of landmarks in the field of view intersection sequence, reduce the impact of the uncertainty of the lander's posture on the selected landmarks, improve the robustness of the planetary landing autonomous optical navigation landmark selection, and obtain a highly robust optimal landmark sequence.

[0208] Consider the camera sampling period is Δt, satisfying t k+1 -t k =Δt, where k = 0, 1, ..., n-1. The nominal trajectory obtained in step 1 is combined with the camera parameter estimation to obtain a set of field of view sequences. The field of view intersection calculation method given in step 3 is used to obtain the field of view intersection sequence. The landmark optimization index is established using the observability of the navigation system. The Fisher information matrix is ​​expressed as follows:

[0209]

[0210] Among them, σ i represents the standard deviation of the observation noise, w is the number of observed landmarks, and h i (r) represents the observed quantity, and x is the lander state. Combined with the Cramér-Rao lower bound, the trace of the estimated error variance matrix can be expressed as

[0211] tr(P)≥tr(FIM -1 ) (80)

[0212] Using tr(FIM -1 ) is used as the performance index to optimize the selection of landmarks in the field of view sequence and obtain the optimal landmark sequence. Four landmarks are selected as navigation landmarks for simulation. Figure 4 The results of landmark selection under nominal field of view and field of view intersection are shown. To analyze the effectiveness of landmark planning, the Monte Carlo method is used to perform 1000 random field of view simulations, and the effectiveness of landmark selection under nominal field of view and field of view intersection is statistically analyzed. Figure 5 As shown, it can be seen that the effectiveness of landmark planning has increased from 35.9% to 91.6%.

[0213] The method also includes step five: during the landing process, the optimal landmark sequence obtained in step four is used for navigation, and the lander continuously switches the observed landmarks according to the optimal landmark sequence to improve the overall navigation accuracy and robustness during the landing phase.

[0214] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment 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.

Claims

1. A robust optimization method for autonomous optical navigation landmarks for planetary landing. Features: The following steps are included: Step 1: Establish a planetary landing dynamics model and an optical navigation observation model, and optimize the lander state by considering multiple constraints and requirements of the mission to obtain the lander trajectory as the nominal landing trajectory; the multiple constraints include the planetary landing dynamics model and the optical navigation observation model; the nominal landing trajectory includes the nominal position and the nominal attitude; Step 2: Use the lander height information to determine the scale of the image plane projected onto the planetary surface, and derive the vertex expression of the field of view based on the geometric relationship; By using the relationship between the field of view vertex deviation and the lander posture error, the uncertainty of the lander posture is converted into the field of view vertex uncertainty, and the error ellipse is used to describe the field of view vertex uncertainty distribution, and then four error ellipses describing the uncertainty distribution of the four field of view vertices are obtained respectively; Step 3: Based on the four error ellipses describing the uncertainty distribution of the field of view vertices obtained in step 2, 16 common tangents are obtained through adjacent error ellipses; the required solution is screened by judging whether the field of view vertex is on the same side of the common tangent, and the field of view vertex and the camera optical center are projected at both ends of the common tangent to obtain the four required common tangents. The quadrilateral area formed by the intersection of the screened common tangents is the field of view intersection under the uncertainty of the lander's posture; Step 4: Use the nominal trajectory and camera parameters obtained in step 1 to estimate the field of view sequence, and combine it with the field of view intersection acquisition method given in step 3 to obtain the field of view intersection sequence. Since the field of view intersection sequence is obtained through offline estimation, it does not need to be calculated on the onboard computer, avoiding real-time image processing during the landing process and reducing the amount of onboard calculations of the lander. Use the observability of the navigation system to establish landmark selection indicators, optimize the selection of landmarks in the field of view intersection sequence, reduce the impact of the uncertainty of the lander's posture on the selected landmarks, improve the robustness of the planetary landing autonomous optical navigation landmark selection, and obtain a highly robust optimal landmark sequence.

2. A robust optimization method for autonomous optical navigation landmarks for planetary landing as claimed in claim 1, Features: The method also includes step five, in which the optimal landmark sequence obtained in step four is used for navigation during the landing process. The lander continuously switches the observed landmarks according to the optimal landmark sequence to improve the overall navigation accuracy and robustness during the landing phase.

3. A robust optimization method for autonomous optical navigation landmarks for planetary landing as claimed in claim 1 or 2, Features: The implementation method of step one is: In the landing point coordinate system, the six-degree-of-freedom dynamic model of planetary landing is: in, L r and L v represents the position and velocity vector of the lander, respectively; T represents the thrust vector of the thruster; is the planetary gravitational acceleration vector; Describes the rotation vector from the landing point coordinate system to the camera coordinate system; is the planet's rotational angular velocity; J is the lander's moment of inertia; B ω represents the lander angular velocity vector; B M is the torque applied to the lander; The representation is as follows; Considering the multiple constraints and requirements of the mission, the optimization algorithm is combined to optimize the lander state, and the optimized trajectory is obtained as the nominal trajectory, including the nominal position and nominal attitude In order to simplify the notation, the camera coordinate system is defined to coincide with the lander coordinate system; the navigation camera model adopts the pinhole projection model, and the i-th landmark L p i (i=1,…,n) is projected on the camera image plane as Among them, u i for L p j 2D projection on the image plane; p i ,l i for u i The two-axis components of; f represents the focal length of the camera; C x i , C y i , C z i for L p j The three-axis components in the camera system are expressed as follows Among them, R CL The rotation matrix from the landing point coordinate system to the camera coordinate system.

4. A robust optimization method for autonomous optical navigation landmarks for planetary landing as claimed in claim 3, Features: The implementation method of step 2 is: The camera field of view is expressed as the area observable by the navigation camera, which is the projection of the image plane onto the planetary surface. The image plane is a square, and the side length of the image plane is expressed as Combined with equation (4), the relationship between the image plane vertex position and the field of view vertex under the camera system is expressed as in, for u j The homogeneous coordinate form of represents the vertex position of the image plane; C p j is the vertex position of the camera field of view; K = diag[f,f,1] represents the camera parameters; Combining equation (3) and equation (5), the vertex of the camera field of view in the landing point system is expressed as The direction vector of the optical axis in the camera's viewing cone is expressed as in, C e o is the camera optical axis direction vector under the camera system; is the normal vector perpendicular to the landing plane; the camera cone edge length direction is expressed as in, is the direction vector of the viewing cone length under the camera system; Represents the rotation matrix that transforms the camera optical axis direction to the edge length direction. According to the geometric relationship, Among them, α j is the angle between the camera optical axis and the edge length direction vector; β j for C e j and The angle between j ,β j Respectively expressed as Combining equations (6) and (7), the vertex of the field of view in the landing point coordinate system is expressed as The uncertainty of the lander’s position is expressed as Among them, δρ represents the small perturbation of the lander position, δφ represents the small perturbation of the lander attitude; the relationship between the field of view vertex in the lander point coordinate system and the camera coordinate system is expressed as in, and is the homogeneous coordinate form, T v is the transformation matrix, expressed as in, is the rotation matrix from the camera system to the landing point system, φ v represents the rotation from the camera system to the landing point system; t v , t represent the translation vector, T is the transformation matrix; considering the posture disturbance in, Considering the uncertainty of the lander's posture, the vertex position of the field of view is expressed in the landing point coordinate system as Through formula (13), we can get From formula (12), we can get exp(ξ v )=exp(ξ) -1 =exp(-ξ), and then we get ξ v = -ξ; The relationship between the field of view vertex deviation and the lander posture error is derived as shown in formula (14); Formula (14) is simplified to D L p j =-(δφ^ L p+dr)= L p^δφ-δρ=Zδξ (15) Where Z = [-I 3 L p^]; δρ and δφ are Gaussian white noises that do not affect each other and satisfy and The variance of δξ is expressed as Using the large Δ in formula (16) L p j The variance of is shown in formula (17); consider L x- L The two-axis components on the y plane make H represents the following According to formula (17), The variance of According to formula (19), Δ L p jx and Δ L p jy The variance of definition The above formula is rewritten as shown in formula (21); The error ellipse is described by the major and minor semi-axes E j ,F j The ellipse is expressed in the error ellipse coordinate system as in, in, Q is The covariance matrix of the error ellipse; the angle between the major axis of the error ellipse and the landing point coordinate system Expressed as According to equations (22) to (25), the error ellipse is used to describe the uncertainty distribution of the field of view vertex.

5. A method for robust selection of autonomous optical navigation landmarks for planetary landing as claimed in claim 4, Features: The implementation method of step three is: According to the four error ellipses describing the uncertainty distribution of the field of view vertex according to equations (22) to (25), 16 common tangents are obtained through adjacent error ellipses, and the four required common tangents are screened. The intersection of the screened common tangents is used to obtain the field of view intersection. By combining adjacent tangent equations, we can get the coordinates k of the four tangent points. 1 ,k 2 ,k 3 ,k 4 , represents any point on the following error ellipse E q i exist L x- L The y coordinate system is expressed as E q i =R EL ( L q i -t j ) (26) in, E q i =[ E x i , E y i ] T is the position of any point on the error ellipse; L q i =[ L x i , L y i ] T express E q i exist L x- L Position in the y coordinate system; t j =[ L p jx , L p jy ] T represents the translation vector; R EL Indicates from L x- L The rotation matrix from the y plane coordinate system to the error ellipse coordinate system is expressed as follows Combining equations (22), (26) and (27), the error ellipse is L x- L The y-plane coordinate system is expressed as A j L x 2 +B j L x L y+D j L y 2 +O j L x+P j L y+1=0 (28) in, Formula (28) is converted into a quadratic form, as shown below in, for L x=[ L x, L y] T The homogeneous coordinate form of M j Expressed as The tangent line equation is defined as follows Among them, L m =[a m ,b m ,1] T represents the tangent coefficient; combining equation (30) and equation (32), we get the following formula: Where ε is the proportional factor. By combining equations (30) and (33), the relationship between the error ellipse and the tangent line of the error ellipse is shown in equation (34). Through equation (34), the common tangent of two adjacent error ellipses is the solution of equation group (35); Since equation (35) has four solutions, the required solution is screened by judging whether the field of view vertex is on the same side of the common tangent line, and whether the field of view vertex and the camera optical center projection are at both ends of the common tangent line; the camera optical center projection is expressed as Use the above screening method to screen the required solution and obtain 4 common tangent coefficients L 1 ,L 2 ,L 3 ,L 4 , expressed as By combining adjacent tangent equations, we can get the coordinates k of the four tangent points. 1 ,k 2 ,k 3 ,k 4 , which is expressed as follows By k 1 ,k 2 ,k 3 ,k 4 The quadrilateral area formed is the intersection of the field of view under the uncertainty of the lander's posture.

6. A method for robust selection of autonomous optical navigation landmarks for planetary landing as claimed in claim 5, Features: The implementation method of step 4 is: Consider the camera sampling period is Δt, satisfying t k+1 -t k =Δt, where k = 0, 1, ..., n-1. The nominal trajectory obtained in step 1 is combined with the camera parameter estimation to obtain a set of field of view sequences. The field of view intersection calculation method given in step 3 is used to obtain the field of view intersection sequence. The observability of the navigation system is used to establish the landmark optimization index. The Fisher information matrix is ​​expressed as follows: Among them, σ i represents the standard deviation of the observation noise, w is the number of observed landmarks, and h i (r) represents the observed quantity, x is the lander state; combined with the Cramér-Rao lower bound, the trace of the estimated error variance matrix is ​​expressed as tr(P)≥tr(END -1 ) (40) Using tr(FIM -1 ) is used as the performance index to optimize the selection of landmarks in the field of view intersection sequence and obtain the optimal landmark sequence.

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