Multi-node collaborative navigation method for flexible lander with limited navigation information

Abstract

The present invention discloses a method for multi-node collaborative navigation of a flexible lander under limited navigation information, belonging to the field of deep space exploration technology. The present invention is implemented as follows: based on the current altitude and the associated observation information between nodes, an indirect observation equation for navigation landmarks is constructed based on homography transformation or epipolar geometry to build a transmission path for observation information between nodes; the Fisher information matrix is ​​used to analyze node observability, and multi-node information interaction conditions are established with node observability and the flexible lander altitude as indicators; the information interaction conditions are used to determine the information transmission direction between nodes that makes the positions of all nodes observable and the minimum transmitted observation information in the corresponding information transmission direction; a single node uses the observation information obtained by the node itself and the observation information transmitted by other nodes to estimate the node state through a nonlinear filtering algorithm, and all nodes synchronously perform state estimation according to the single node state estimation method to achieve multi-node collaborative navigation under limited navigation information.

Description

Technical Field

[0001] The present invention relates to a multi-node collaborative navigation method for a flexible lander under limited navigation information, belonging to the technical field of deep space exploration. Background Art

[0002] Small celestial bodies have complex morphologies and weak, irregular gravitational fields, making stable attachment to their surfaces difficult. In recent years, researchers have proposed a new flexible attachment method. Compared to traditional rigid landers, flexible landers increase the contact area with the surface of the small celestial body and utilize internal damping to dissipate residual kinetic energy, thereby improving the robustness of the attachment.

[0003] Existing research has established a simplified model for a flexible lander, using the states of at least three nodes to equivalently represent the position, velocity, and attitude of the flexible lander. This approach, through independent estimation, mutual correction, and synthesis of node states, enables collaborative estimation of the flexible lander's state. In existing methods, independent estimation of node states is a prerequisite for flexible lander state estimation, requiring each node to obtain sufficient navigation information to estimate its own state. However, the surface topography of small celestial bodies is complex and rugged, and prior information is scarce, resulting in a limited number of navigation landmarks that can be used for absolute positioning. Furthermore, as the altitude of the flexible lander decreases, the field of view of the node camera decreases, and the number of observable navigation landmarks also decreases accordingly. When there are insufficient navigation landmarks within the node's field of view, the lack of observation information will result in incomplete or even unobservable node states, thereby reducing the navigation performance of the flexible attachment process. Summary of the Invention

[0004] The main purpose of the present invention is to provide a multi-node collaborative navigation method for a flexible lander under limited navigation information. In response to the state estimation requirements of multiple nodes of a flexible lander under limited navigation information, according to the current altitude of the flexible lander and the associated observation information between nodes, an indirect observation equation of a navigation landmark is constructed based on homography transformation or epipolar geometry to construct a transmission path of observation information between nodes; based on the transmission path, the Fisher information matrix is ​​used to analyze the observability of node positions, and the multi-node information interaction conditions are established with the node position observability and the flexible lander altitude as indicators; the multi-node information interaction conditions are used to determine the information transmission direction between nodes that makes the positions of all nodes observable and the minimum transmitted observation information in the corresponding information transmission direction; a single node uses the observation information obtained by the node itself and the observation information transmitted by other nodes to estimate the node state through a nonlinear filtering algorithm, and all nodes synchronously perform state estimation according to the single node state estimation method, thereby realizing multi-node collaborative navigation of a flexible lander under limited navigation information.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] The flexible lander multi-node collaborative navigation method under limited navigation information disclosed in the present invention includes the following steps:

[0007] Step 1: To meet the need for multi-node state estimation of the flexible lander under limited navigation information, according to the current altitude of the flexible lander and the associated observation information between nodes, the indirect observation equations of the navigation landmarks are constructed based on homography transformation or epipolar geometry, and the transmission path of observation information between nodes is established.

[0008] In order to meet the state estimation requirements of multiple nodes of the flexible lander under limited navigation information, an optical camera is installed on each node of the flexible lander, and a laser rangefinder is installed on some nodes. For node i (i = 1, ..., M), let the set of nodes with overlapping observation areas with the field of view of the optical camera of node i be For nodes Let the observation value of any navigation landmark observed within its field of view be z j By matching the associated observation information in the overlapping observation area of ​​node i and node j, the navigation landmark observation quantity z can be achieved. j The transmission from node j to node i, let the observation quantity transmitted from node j to node i be z j→i , hereinafter referred to as the indirect observation.

[0009] The associated observation information includes characteristic points, characteristic lines, and characteristic curves.

[0010] The following is the specific implementation method of transmitting observation information between nodes:

[0011] Define the height H of the flexible lander as the average height of all nodes

[0012]

[0013] Among them H i is the height of node i. Given a height threshold When the flexible lander height H satisfies When the target surface is equivalent to an approximate plane, the homography transformation is used to establish the node j navigation landmark observation z j and the indirect observation z j→i Constraints between

[0014]

[0015] Where f is the focal length of the optical camera; H ij is the homography matrix from node j to node i, which is determined by matching the associated observation information in the observation area where nodes i and j overlap. j→i , establish the indirect observation equation of node i

[0016]

[0017] where h j→i (·) represents the indirect observation equation under homography transformation, x i is the state of node i under the fixed connection of the attachment point, is the position vector of the navigation landmark in the node camera system, satisfying

[0018]

[0019] where r L is the position of the navigation landmark when it is fixed to the attachment point, r i is the position of node i under the fixed connection of the attachment point, is the rotation matrix of the system that is fixed to node i at the attachment point.

[0020] As the height of the flexible lander decreases, the target surface can no longer be equivalent to an approximate plane. When the epipolar geometry is used to establish the node j navigation landmark observation z j and the indirect observation z j→i Constraints between

[0021]

[0022] Among them E ij is the essential matrix from node j to node i, which is determined by matching the associated observation information in the overlapping observation area of ​​node i and node j.

[0023]

[0024] and e ij =[e ij,1 ,e ij,2 ,e ij,3 ], substitute formula (3) and formula (6) into formula (5) to obtain the indirect observation equation of node i

[0025] [e ij,1 ,e ij,2 ]h j→i (x i )+e ij,3 f0 (7)

[0026] Let the indirect observation equation h′ under epipolar geometry be j→i (x i )=[e ij,1 ,e ij,2 ]h j→i (x i )+e ij,3 f.

[0027] Formula (3) and formula (7) respectively use homography transformation and epipolar geometry to construct indirect observation equations of navigation landmarks between nodes. The indirect observation equations of navigation landmarks are the transmission paths of the constructed observation information between nodes.

[0028] Step 2: Based on the indirect observation equation of the navigation landmark constructed in Step 1, the Fisher information matrix is ​​used to analyze the observability of the node position. The multi-node information interaction condition is established with the node position observability and the flexible lander height as indicators. The multi-node information interaction condition is used to determine the information transmission direction between nodes that makes all node positions observable and the minimum transmitted observation information in the corresponding information transmission direction.

[0029] The Fisher information matrix is ​​used to analyze the observability of node positions. Based on the indirect observation equation of navigation landmarks established in step 1, the observation information that a single node can obtain includes the observation information obtained by the node itself and the observation information transmitted by other nodes.

[0030] First, we analyze the observability of node positions when the node itself obtains observation information. When the navigation landmark with a known absolute position is observed within the field of view of the optical camera of node i, the observation equation is established:

[0031]

[0032] where [u L ,v L ] T is the coordinate of the navigation landmark in the pixel system. The corresponding Fisher information matrix is

[0033]

[0034] where σ i,C is the standard deviation of the optical camera measurement error. When a navigation landmark is observed, the matrix F i,C The rank is 2. When N L When the navigation landmark is For each navigation landmark τ L , corresponding to the Fisher information matrix According to formula (9), the matrix F i,C The rank of the matrix is ​​calculated by The rank is determined.

[0035] When a laser rangefinder is installed on node i, it can measure the distance from the node to the specified point on the target surface (x P ,y P ,z P ) The observation equation is

[0036]

[0037] where x i ,y i ,z i is the position vector r of node i i The corresponding Fisher information matrix is

[0038]

[0039] where σ i,LRF is the standard deviation of the laser rangefinder measurement error, n iP For point (x P ,y P ,z P ) points to the unit vector of node i, matrix F i,LRF The rank of is 1.

[0040] After analyzing the observability of node positions when the node itself obtains observation information, we analyze the observability of node positions when other nodes transmit observation information. For the indirect observation equation (3) of the navigation landmark, the Fisher information matrix is

[0041]

[0042] where σ j→i is the standard deviation of the indirect observation error under homography transformation, is the indirect observation equation h under homography transformation j→i The two components of the matrix F j→i The rank of is 2. For the indirect observation equation (7), the Fisher information matrix is

[0043]

[0044] where σ′ j→i is the standard deviation of the indirect observation error under epipolar geometry, and the matrix F′ j→i The rank of is 1.

[0045] Taking the observability of node positions and the height of the flexible lander as indicators, the multi-node information interaction conditions are established; using the multi-node information interaction conditions, the information transmission direction between nodes that makes the positions of all nodes observable and the minimum transmitted observation information in the corresponding information transmission direction are determined.

[0046] According to formula (9) to formula (13), the indicator function is constructed using the observability of node positions

[0047] I i =N i -rank(F i ) (14)

[0048] where N irepresents the dimension of the node i position vector, rank(F i ) represents the rank of the Fisher information matrix of node i under direct observation information. When node i is only equipped with an optical camera, F i =F i,C ; When node i is equipped with both an optical camera and a laser rangefinder, F i =F i,C F i,LRF .

[0049] Taking the observability of node positions represented by the indicator function and the height of the flexible lander as indicators, the multi-node information interaction conditions are established as shown in conditions ①②③④:

[0050] ①When I i When ≤0, other nodes do not transmit indirect observation information to node i;

[0051] ②When I i =1 or I i =2 and When , other nodes transmit indirect observation information of one navigation landmark to node i;

[0052] ③When I i =2 and or I i =3 and When , other nodes transmit indirect observation information of two navigation landmarks to node i;

[0053] ④When I i =3 and When , other nodes transmit indirect observation information of three non-collinear navigation landmarks to node i.

[0054] Since the navigation landmark that maximizes the trace of the Fisher information matrix can obtain the minimum navigation error lower bound, according to formula (12) and formula (13), the navigation landmark observation quantity transmitted in the multi-node information interaction condition ② is Need to meet

[0055]

[0056] Where tr represents the trace of the matrix. The navigation landmark observations transmitted in the multi-node information interaction conditions ③④ Need to meet

[0057]

[0058] Among them, n=2 in multi-node information interaction condition ③, n=3 in multi-node information interaction condition ④, and Represents node j under homography transformation and epipolar geometry respectively kFisher information matrix corresponding to the k-th navigation landmark.

[0059] By using the multi-node information interaction conditions ①②③④, the information transmission direction between nodes that makes the positions of all nodes observable and the minimum transmitted observation information in the corresponding information transmission direction are determined.

[0060] Step 3. Based on the multi-node information interaction conditions established in step 2, a single node uses the observation information obtained by itself and the observation information transmitted by other nodes to estimate the node state through a nonlinear filtering algorithm. All nodes perform state estimation synchronously according to the single node state estimation method, thereby realizing multi-node collaborative navigation of the flexible lander under limited navigation information.

[0061] The state equation of node i is

[0062] x i,t =f i (x i,t1 ,u i,t )+q i,t (17)

[0063] where x i,t is the state of node i at time t, x i,t-1 is the state of node i at time t-1, u i,t is the control quantity of node i at time t, f i (·) is the state transfer equation, q i,t is the system noise.

[0064] According to the multi-node information interaction conditions ①②③④, the observation equation of node i is established. Under the multi-node information interaction condition ①, the observation equation constructed based on the observation information obtained by the node itself is

[0065] z i,t =h i (x i,t )+w i,t (18)

[0066] where z i,t is the observation quantity of node i at time t, h i (·) is the observation equation, w i,t is the observation noise. Under the multi-node information interaction condition ②, the observation equation constructed by combining the observation information obtained by the node itself and the observation information transmitted by other nodes is:

[0067]

[0068] in is the navigation landmark observation quantity obtained at time t according to formula (15), is the corresponding observation equation, is the observation noise. Under the multi-node information interaction conditions ③④, the observation equation constructed by combining the observation information obtained by the node itself and the observation information transmitted by other nodes is:

[0069]

[0070] in is the navigation landmark observation quantity obtained at time t according to formula (16), is the corresponding observation equation, is the observation noise.

[0071] Combining formulas (17) to (20), a nonlinear filtering algorithm is used to obtain the state estimate of node i at time t: and the estimated error covariance P i,t , achieving single node state estimation under limited navigation information.

[0072] All nodes synchronously perform state estimation of node 1 to node M according to the single node state estimation method, thereby realizing multi-node collaborative navigation of the flexible lander under limited navigation information.

[0073] Preferably, the nonlinear filtering algorithm includes extended Kalman filtering, unscented Kalman filtering, and particle filtering.

[0074] It also includes step four: under limited navigation information, the multi-node state of the flexible lander estimated in step three is transmitted through observation information between nodes to avoid unobservable node states due to insufficient navigation information, thereby improving the navigation accuracy of the flexible lander, and using the state estimation results to realize real-time trajectory planning and guidance control of the flexible lander.

[0075] Beneficial effects:

[0076] 1. The present invention discloses a method for collaborative navigation of multiple nodes of a flexible lander under limited navigation information. Aiming at the state estimation requirements of multiple nodes of a flexible lander under limited navigation information, the present invention constructs indirect observation equations of navigation landmarks based on homography transformation or epipolar geometry according to the current altitude of the flexible lander and the associated observation information between nodes, and builds a transmission path for observation information between nodes. By transmitting observation information between nodes, the method avoids unobservable node states due to insufficient navigation information, thereby improving the navigation accuracy of the flexible lander.

[0077] 2. The present invention discloses a method for multi-node collaborative navigation of a flexible lander under limited navigation information. By constructing a transmission path for observation information between nodes and analyzing the observability of node positions using the Fisher information matrix, the multi-node information interaction condition is established with the observability of node positions and the height of the flexible lander as indicators. The multi-node information interaction condition is used to determine the information transmission direction between nodes that makes the positions of all nodes observable and the minimum transmitted observation information in the corresponding information transmission direction. While ensuring the observability of node positions, the amount of information transmission and the amount of node state estimation calculation are reduced, thereby improving the real-time performance of the multi-node collaborative navigation of the flexible lander under the condition of limited onboard computing resources of the flexible lander.

[0078] 3. The present invention discloses a method for collaborative navigation of multiple nodes of a flexible lander under limited navigation information. A single node uses the observation information obtained by itself and the observation information transmitted by other nodes to estimate the state of the node through a nonlinear filtering algorithm. All nodes perform state estimation synchronously according to the single node state estimation method, thereby realizing collaborative navigation of multiple nodes of a flexible lander under limited navigation information, and using the state estimation results to realize real-time trajectory planning and guidance control of the flexible lander. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 This is a flow chart of the flexible lander multi-node collaborative navigation method under limited navigation information disclosed in the present invention;

[0080] Figure 2 is the three-node nominal attachment trajectory of the flexible lander;

[0081] Figure 3 is the state estimation error curve of flexible lander node 1;

[0082] Figure 4 is the state estimation error curve of flexible lander node 2 based on direct observation information;

[0083] Figure 5 is the state estimation error curve of flexible lander node 3 based on direct observation information;

[0084] Figure 6 is the state estimation error curve of flexible lander node 2 under multi-node information interaction;

[0085] Figure 7 This is the state estimation error curve of flexible lander node 3 under multi-node information interaction. DETAILED DESCRIPTION

[0086] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0087] Example 1:

[0088] In order to verify the feasibility of the method, the flexible attachment scenario of the small celestial body is simulated based on the gravitational field of the small celestial body 433Eros. The node dynamic equation is established under the fixed connection system of the landing point of the small celestial body.

[0089]

[0090] where r i ,v i are the position and velocity of node i, u i is the control quantity of node i, u i,F is the flexible connection acceleration, g(r i ) is the gravitational acceleration, q i is the system noise, satisfying q i ~N(0,1e -4 ).

[0091] The flexible lander uses a simplified three-node model, with an optical camera installed at each node, and a laser rangefinder at node 3. The optical camera has a focal length of f = 0.02m and a field of view of 40°. The observation noise satisfies a zero-mean Gaussian distribution, with a standard deviation of 2 pixels for camera observation noise and 0.1m for laser rangefinder measurement noise.

[0092] Node 1 initial position r 10 =[-9,25,10,300] T m, target landing point position r 1f =[0.75,0,10] T m, initial position of node 2 r 20 =[-10.38,10.65,300] T m, target landing point position r 2f =[-0.38,0.65,10] T m, initial position of node 3 r 30 =[-10.38,9.35,300] T m, target landing point position r 3f =[-0.38,-0.65,10] T m. The initial and terminal velocities of all nodes are the same, v 10 =v 20 =v 30 =[0,0,-0.2] T m / s,v 1f =v 2f =v 3f =[0,0,0] T m / s.

[0093] The nominal attachment trajectory of the three-node flexible lander is as follows: Figure 2 shown.

[0094] like Figure 1 As shown, the flexible lander multi-node collaborative navigation method under limited navigation information disclosed in this embodiment is specifically implemented in the following steps:

[0095] Step 1: To meet the need for multi-node state estimation of the flexible lander under limited navigation information, according to the current altitude of the flexible lander and the associated observation information between nodes, the indirect observation equations of the navigation landmarks are constructed based on homography transformation or epipolar geometry, and the transmission path of observation information between nodes is established.

[0096] During the attachment process, node 1 can always observe two navigation landmarks, node 2 can always observe one navigation landmark, and node 3 cannot observe the navigation landmark but can always obtain the measurement information of the laser rangefinder. Using the observation information obtained by each node, the observation equation is established

[0097] z i,t =h i (x i,t )+w i,t (twenty two)

[0098] The three-node state is estimated by extended Kalman filtering, and the state estimation error curve is as follows: Figures 3 to 5 shown. Figure 3 In the example, due to sufficient observation information, the three-axis position estimation errors of node 1 converge to near 0 quickly; Figure 4 In the figure, due to insufficient observation information, the three-axis position estimation error of node 2 diverges to varying degrees; Figure 5 In the example, since node 3 can only obtain the ranging information in the height direction, the Z-axis position estimation error quickly converges to near 0, while the position estimation errors of the other two axes diverge.

[0099] Considering that the height fluctuation of the surface of small celestial bodies reaches the order of 10m, the height threshold Selected That is, during the entire flexible attachment process According to formula (5), the epipolar geometry is used to establish the navigation landmark observation z of node j j and the indirect observation z j→i Based on formula (7), the indirect observation equation h′ under epipolar geometry is obtained j→i (x i )=[e ij,1 ,e ij,2 ]h j→i (x i )+e ij,3 f.

[0100] Step 2: Based on the indirect observation equation of the navigation landmark constructed in Step 1, the Fisher information matrix is ​​used to analyze the observability of the node position. The multi-node information interaction condition is established with the node position observability and the flexible lander height as indicators. The multi-node information interaction condition is used to determine the information transmission direction between nodes that makes all node positions observable and the minimum transmitted observation information in the corresponding information transmission direction.

[0101] Establish the multi-node information interaction conditions. Since N1=N2=N3=3, rank(F1)=4, rank(F2)=2, rank(F3)=1 in the indicator function of formula (14), the indicator functions of the three nodes are I1=-1, I2=1, and I3=2 respectively.

[0102] because According to the indicator function and the height of the flexible lander, node 1 meets the multi-node information interaction condition ①, that is, other nodes do not transmit indirect observation information to node 1; node 2 meets the multi-node information interaction condition ②, that is, other nodes transmit indirect observation information of a navigation landmark to node 2, and the transmitted navigation landmark observation quantity satisfy

[0103]

[0104] Node 3 meets the multi-node information interaction condition ③, that is, other nodes transmit indirect observation information of two navigation landmarks to node 3, and the transmitted navigation landmark observation quantity satisfy

[0105]

[0106] Thus, the information transmission direction between nodes that makes the positions of node 2 and node 3 observable and the minimum transmitted observation information in the corresponding information transmission direction are determined.

[0107] Step 3. Based on the multi-node information interaction conditions established in step 2, a single node uses the observation information obtained by itself and the observation information transmitted by other nodes to estimate the node state through a nonlinear filtering algorithm. All nodes perform state estimation synchronously according to the single node state estimation method, thereby realizing multi-node collaborative navigation of the flexible lander under limited navigation information.

[0108] According to the multi-node information interaction conditions established in step 2, the observation information obtained by the node itself and the observation information transmitted by other nodes are used to form the observation equations of node 2 and node 3. The observation equation of node 2 is

[0109]

[0110] The observation equation of node 3 is

[0111]

[0112] The indirect observation noise satisfies the zero-mean Gaussian distribution, and the standard deviation of the indirect observation noise used is three times the standard deviation of the camera observation noise.

[0113] Combining formula (21), formula (25), and formula (26), the extended Kalman filter is used to estimate the states of node 2 and node 3 under multi-node information interaction. The state estimation error curve is as follows: Figure 6 and Figure 7 As shown. Figure 4 and Figure 5 By comparison, it is found that after the introduction of multi-node information interaction, nodes 2 and 3 obtain the observation information transmitted by other nodes, and the observability of node status is improved. Figure 4 and Figure 5 The originally divergent state estimation error is effectively suppressed and can converge to near 0 quickly, thereby realizing the collaborative navigation of flexible lander multi-nodes under limited navigation information through the collaborative estimation of the flexible lander multi-node states.

[0114] Step 4: Based on the multi-node states of the flexible lander estimated in step 3 under limited navigation information, observation information is transmitted between nodes to avoid unobservable node states caused by insufficient navigation information, improve the navigation accuracy of the flexible lander, and use the state estimation results to realize real-time trajectory planning and guidance control of the flexible lander.

[0115] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description 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 multi-node collaborative navigation method for a flexible lander with limited navigation information, characterized by: The following steps are included: Step 1: To meet the need for multi-node state estimation of the flexible lander under limited navigation information, based on the current altitude of the flexible lander and the associated observation information between nodes, the indirect observation equations of the navigation landmarks are constructed based on homography transformation or epipolar geometry, and the transmission path of observation information between nodes is established; Step 2: Based on the indirect observation equations for navigation landmarks constructed in Step 1, the Fisher information matrix is ​​used to analyze the observability of node positions. Using the node position observability and the flexible lander's altitude as indicators, a multi-node information interaction condition is established. Using this multi-node information interaction condition, the information transmission direction between nodes that makes all node positions observable and the minimum transmitted observation information in the corresponding information transmission direction are determined. Step 3. Based on the multi-node information interaction conditions established in step 2, a single node uses the observation information obtained by itself and the observation information transmitted by other nodes to estimate the node state through a nonlinear filtering algorithm. All nodes perform state estimation synchronously according to the single node state estimation method, thereby realizing multi-node collaborative navigation of the flexible lander under limited navigation information.

2. The method for multi-node collaborative navigation of a flexible lander under limited navigation information as claimed in claim 1, characterized in that: It also includes step 4, which is to estimate the multi-node status of the flexible lander according to step 3 under limited navigation information, and transmit observation information between nodes to avoid unobservable node status due to insufficient navigation information, thereby improving the navigation accuracy of the flexible lander, and using the state estimation results to realize real-time trajectory planning and guidance control of the flexible lander.

3. The method for multi-node collaborative navigation of a flexible lander under limited navigation information according to claim 1 or 2, characterized in that: The implementation method of step one is: Aiming at the state estimation requirements of multiple nodes of flexible lander under limited navigation information, an optical camera is installed on each node of the flexible lander, and a laser rangefinder is installed on some nodes. For node i (i=1,...,M), let the set of nodes with overlapping observation areas with the field of view of the optical camera of node i be For nodes Let the observation value of any navigation landmark observed within its field of view be z j By matching the associated observation information in the observation area where nodes i and j overlap, the navigation landmark observation quantity z can be achieved. j The transmission from node j to node i, let the observation quantity transmitted from node j to node i be z j→i , hereinafter referred to as the indirect observation; The associated observation information includes characteristic points, characteristic lines, and characteristic curves; The following is the specific implementation method of transmitting observation information between nodes: Define the height H of the flexible lander as the average height of all nodes Among them H i is the height of node i; given height threshold When the flexible lander height H satisfies When the target surface is equivalent to an approximate plane, the homography transformation is used to establish the node j navigation landmark observation z j and the indirect observation z j→i Constraints between Where f is the focal length of the optical camera; H ij is the homography matrix from node j to node i, which is determined by matching the associated observation information in the observation area where nodes i and j overlap; using the indirect observation quantity z j→i , establish the indirect observation equation of node i where h j→i (·) represents the indirect observation equation under homography transformation, x i is the state of node i under the fixed connection of the attachment point, is the position vector of the navigation landmark in the node camera system, satisfying where r L is the position of the navigation landmark when it is fixed to the attachment point, r i is the position of node i under the fixed connection of the attachment point, is the rotation matrix of the system that is fixedly connected to node i at the attachment point; As the height of the flexible lander decreases, the target surface can no longer be equivalent to an approximate plane; when the height H of the flexible lander satisfies When the epipolar geometry is used to establish the node j navigation landmark observation z j and the indirect observation z j→i Constraints between Among them E ij is the essential matrix from node j to node i, which is determined by matching the associated observation information in the overlapping observation area of ​​node i and node j; let and e ij =[e ij,1 ,e ij,2 ,e ij,3 ], substitute formula (3) and formula (6) into formula (5) to obtain the indirect observation equation of node i [e ij,1 ,e ij,2 ]h j→i (x i )+e ij,3 f=0 (7) Let the indirect observation equation h′ under epipolar geometry be j→i (x i )=[e ij,1 ,e ij,2 ]h j→i (x i )+e ij,3 f; Formula (3) and formula (7) respectively use homography transformation and epipolar geometry to construct indirect observation equations of navigation landmarks between nodes. The indirect observation equations of navigation landmarks are the transmission paths of the constructed observation information between nodes.

4. The method for multi-node collaborative navigation of a flexible lander under limited navigation information as claimed in claim 3, characterized in that: The implementation method of step 2 is: The Fisher information matrix is ​​used to analyze the observability of node positions. Based on the indirect observation equation of navigation landmarks established in step 1, the observation information that a single node can obtain includes the observation information obtained by the node itself and the observation information transmitted by other nodes. First, the observability of node position under the observation information obtained by the node itself is analyzed; when the navigation landmark with known absolute position is observed within the field of view of the optical camera of node i, the observation equation is established where [u L ,v L ] T is the coordinate of the navigation landmark in the pixel system; the corresponding Fisher information matrix is where σ i,C is the standard deviation of the optical camera measurement error; When a navigation landmark is observed, the matrix F i,C The rank is 2; when N is observed L When there are navigation landmarks, the matrix For each navigation landmark τ L , corresponding to the Fisher information matrix According to formula (9), the matrix F i,C The rank of the matrix is ​​calculated by The rank of is determined; When a laser rangefinder is installed on node i, it can measure the distance from the node to the specified point on the target surface (x P ,y P ,z P ) The observation equation is where x i ,y i ,z i is the position vector r of node i i The three-axis components of ; the corresponding Fisher information matrix is where σ i,LRF is the standard deviation of the laser rangefinder measurement error, n iP For point (x P ,y P ,z P ) points to the unit vector of node i, matrix F i,LRF The rank of is 1; After analyzing the observability of node positions when the node itself obtains observation information, we analyze the observability of node positions when other nodes transmit observation information. For the indirect observation equation (3) of navigation landmarks, the Fisher information matrix is: where σ j→i is the standard deviation of the indirect observation error under homography transformation, is the indirect observation equation h under homography transformation j→i The two components of the matrix F j→i The rank of is 2; for the indirect observation equation (7), the Fisher information matrix is where σ′ j→i is the standard deviation of the indirect observation error under epipolar geometry, and the matrix F′ j→i The rank of is 1; Using node position observability and flexible lander height as indicators, a multi-node information interaction condition is established. Using the multi-node information interaction condition, the information transmission direction between nodes that makes all node positions observable and the minimum transmitted observation information in the corresponding information transmission direction are determined. According to formula (9) to formula (13), the indicator function is constructed using the observability of node positions I i =N i -rank(F i ) (14) where N i represents the dimension of the node i position vector, rank(F i ) represents the rank of the Fisher information matrix of node i under direct observation information; When node i is only equipped with an optical camera, F i =F i,C ; When node i is equipped with both an optical camera and a laser rangefinder, F i =F i,C +F i,LRF ; Taking the observability of node positions represented by the indicator function and the height of the flexible lander as indicators, the multi-node information interaction conditions are established as shown in conditions ①②③④: ①When I i When ≤0, other nodes do not transmit indirect observation information to node i; ②When I i =1 or I i =2 and When , other nodes transmit indirect observation information of one navigation landmark to node i; ③When I i =2 and or I i =3 and When , other nodes transmit indirect observation information of two navigation landmarks to node i; ④When I i =3 and When , other nodes transmit indirect observation information of three non-collinear navigation landmarks to node i; Since the navigation landmark that maximizes the trace of the Fisher information matrix can obtain the minimum navigation error lower bound, according to formula (12) and formula (13), the navigation landmark observation quantity transmitted in the multi-node information interaction condition ② is Need to meet Where tr represents the trace of the matrix; the navigation landmark observations transmitted in the multi-node information interaction conditions ③④ are Need to meet Among them, n=2 in multi-node information interaction condition ③, n=3 in multi-node information interaction condition ④, and Represents node j under homography transformation and epipolar geometry respectively k Fisher information matrix corresponding to the k-th navigation landmark; By using the multi-node information interaction conditions ①②③④, the information transmission direction between nodes that makes the positions of all nodes observable and the minimum transmitted observation information in the corresponding information transmission direction are determined.

5. The method for multi-node collaborative navigation of a flexible lander under limited navigation information as claimed in claim 4, characterized in that: The implementation method of step three is: The state equation of node i is x i,t =f i (x i,t-1 ,u i,t )+q i,t (17) where x i,t is the state of node i at time t, x i,t-1 is the state of node i at time t-1, u i,t is the control quantity of node i at time t, f i () is the state transfer equation, q i,t is the system noise; According to the multi-node information interaction conditions ①②③④, the observation equation of node i is established; under the multi-node information interaction condition ①, the observation equation constructed based on the observation information obtained by the node itself is z i,t =h i (x i,t )+w i,t (18) where z i,t is the observation quantity of node i at time t, h i (·) is the observation equation, w i,t is the observation noise; under the multi-node information interaction condition ②, the observation equation constructed by combining the observation information obtained by the node itself and the observation information transmitted by other nodes is: in is the navigation landmark observation quantity obtained at time t according to formula (15), is the corresponding observation equation, is the observation noise; under the multi-node information interaction conditions ③④, the observation equation constructed by combining the observation information obtained by the node itself and the observation information transmitted by other nodes is in is the navigation landmark observation quantity obtained at time t according to formula (16), is the corresponding observation equation, is the observation noise; Combining formulas (17) to (20), a nonlinear filtering algorithm is used to obtain the state estimate of node i at time t: and the estimated error covariance P i,t , to achieve single node state estimation under limited navigation information; All nodes synchronously perform state estimation of node 1 to node M according to the single node state estimation method, thereby realizing multi-node collaborative navigation of the flexible lander under limited navigation information.

6. The method for multi-node collaborative navigation of a flexible lander under limited navigation information as claimed in claim 5, characterized in that: The nonlinear filtering algorithms include extended Kalman filtering, unscented Kalman filtering, and particle filtering.

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