Failed spacecraft relative pose estimation method based on dual algebra

Abstract

The invention provides a failure spacecraft relative pose estimation method based on dual algebra, and belongs to the field of spacecraft navigation, and the method comprises the following steps: building a failure spacecraft six-degree-of-freedom relative motion and dynamics model under dual algebra description; then, through a matrix vectorization operator, determining analysis forms of a state equation and an observation equation, and establishing a multiplicative extended Kalman filter; finally, unscented transformation is introduced, a process noise covariance and measurement noise covariance adaptive law is designed, the problems that parameter adjustment of a complex system is tedious and convergence is slow are solved, and accurate estimation of the near-operation real-time pose of the failed spacecraft is achieved. According to the invention, successful execution of the capture maintenance task can be ensured.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft navigation, and specifically relates to a method for estimating the relative pose of a failed spacecraft based on dual algebra. The method is mainly used for estimating the relative pose of a failed spacecraft during adjacent operations such as capturing, repairing, cleaning or destroying a failed spacecraft by a space service spacecraft. Background Art

[0002] In-orbit servicing of failed spacecraft mainly refers to using service spacecraft to approach and capture failed space targets, and then perform repair, maintenance, and clean up damage. Since failed spacecraft do not communicate at the information level, do not cooperate in maneuvering, and their parameters such as mass, inertia, and center of mass are unknown, the primary prerequisite for approaching them is accurate estimation of relative pose and precise identification of inertial parameters. This requires the service spacecraft to actively fly around in advance to observe significant visual features on the surface of the failed spacecraft (such as thruster nozzles and solar panels), which brings about the problem of non-inertial observation and attitude-orbit nonlinear coupling. Existing pose estimation methods cannot handle the above difficult problems at the same time. Therefore, in the framework of integrated pose description, it is of great theoretical and engineering significance to design a relative pose estimation method for failed spacecraft during approach operations.

[0003] In response to the current methods for considering the state estimation problem of non-cooperative spacecraft, Chinese patent ZL201910707219.8 uses the attitude kinematics and dynamics of rigid spacecraft to establish a multiplicative extended Kalman filter, and improves the design of a five-step prediction method to achieve rapid estimation of attitude and moment of inertia. However, this method only considers the three-degree-of-freedom attitude estimation problem and cannot handle the problem of determining the motion state of six-degree-of-freedom posture coupling. Chinese patent ZL202110341892.1 uses dual quaternions to describe the six-degree-of-freedom attitude kinematics and dynamics model of rigid spacecraft, establishes a multiplicative extended Kalman filter, and designs a state correction method for error dual quaternions to achieve real-time online estimation of posture and inertial parameters. However, this method relies on the inertial observation system assumption and cannot handle the non-inertial observation problem caused by the active flyby of the service spacecraft body. In addition, this method only models the three-degree-of-freedom dynamics and cannot accurately characterize the six-degree-of-freedom posture coupling relationship.

[0004] Most of the current research results on the integrated spacecraft posture estimation problem are based on the inertial observation system assumption, and are unable to simultaneously and satisfactorily handle the relative posture estimation and inertial parameter identification problems in the non-inertial observation system, which greatly limits actual on-orbit applications and the successful execution of nearby missions. Summary of the invention

[0005] To overcome the deficiencies of the prior art and solve the non-inertial observation problem caused by the active fly-around of the service spacecraft and the pose coupling problem caused by the non-point mass hypothesis of the visual features of the failed spacecraft, the present invention proposes a relative pose estimation method for the failed spacecraft based on dual algebra, solves the problems of cumbersome parameter adjustment and slow convergence in complex systems, realizes the accurate real-time pose estimation of the failed spacecraft during proximity operations, and ensures the successful execution of the capture and repair mission.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] The relative pose estimation method for the failed spacecraft based on dual algebra includes the following steps:

[0008] S1: Establish a six-degree-of-freedom relative motion and dynamics model of the failed spacecraft under dual algebra description;

[0009] S2: Utilize the six-degree-of-freedom relative motion and dynamics model of the failed spacecraft, through the matrix vectorization operator, deduce the analytical forms of the state equation and the observation equation, build a multiplicative extended Kalman filter, and establish a non-linear analytical formula between the system state and the measurement;

[0010] S3: According to the non-linear analytical formula between the system state and the measurement, introduce the unscented transform, design the adaptive laws of the process noise covariance and the measurement noise covariance, and realize the accurate real-time pose estimation of the failed spacecraft during proximity operations.

[0011] Through the above steps, the six-degree-of-freedom relative pose estimation of the failed spacecraft can be completed under the influence of non-inertial observation and severe pose coupling.

[0012] The beneficial effects of the present invention compared with the prior art are as follows:

[0013] (1) Compared with the existing six-degree-of-freedom pose modeling methods of spacecraft, the present invention explores the characteristics of the dual cosine matrix, obtains the expression of the relative dual angular velocity through the error form, and avoids the Coriolis term deviation caused by directly transforming the coordinate system of the three-dimensional dual vector.

[0014] (2) Compared with the existing six-degree-of-freedom pose estimation methods of spacecraft, the present invention gives the analytical form of the filter in the non-inertial observation system, solves the problem that it is difficult to accurately estimate the relative pose and inertial parameters due to the serious coupling of observation information caused by the active fly-around of the service spacecraft.

[0015] (3) Compared with the existing filtering estimation methods, the present invention establishes an adaptive estimation scheme for the observation noise covariance and the process noise covariance, solves the problems of cumbersome parameter adjustment and slow convergence in complex systems, and realizes the accurate real-time pose estimation of the failed spacecraft during proximity operations. Description of the Drawings

[0016] Figure 1 Flow chart of the relative pose estimation method for a failed spacecraft based on dual algebra according to an embodiment of the present invention;

[0017] Figure 2 Graph of attitude Euler angle estimation error;

[0018] Figure 3 Graph of relative angular velocity estimation error;

[0019] Figure 4 Graph of relative position estimation error;

[0020] Figure 5 Graph of relative linear velocity estimation error. Detailed implementation manners

[0021] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0022] As Figure 1 shown, the relative pose estimation method for a failed spacecraft based on dual algebra of the present invention includes the following steps:

[0023] First step, establish a six-degree-of-freedom relative motion and dynamics model of the failed spacecraft under dual algebra description:

[0024] (1)

[0025] (2)

[0026] Wherein, is the pose dual quaternion of the service spacecraft's body frame relative to the failed spacecraft's body frame, is its derivative with respect to time; the coordinate system represents the service spacecraft's body frame, and the coordinate system represents the failed spacecraft's body frame; is the dual angular velocity of the service spacecraft's body frame relative to the failed spacecraft's body frame and is represented in the service spacecraft's body frame; represents the angular velocity, represents the linear velocity; is the dual unit; is the dual angular velocity of the service spacecraft's body frame relative to the inertial frame and is represented in the service spacecraft's body frame; is the dual angular velocity of the failed spacecraft's body system relative to the inertial system, and is expressed in the failed spacecraft's body system; is the derivative with respect to time; is the dual torque and is Gaussian noise; is the dual inertia of the failed spacecraft, defined as , is the 3×3 identity matrix, is the mass of the failed spacecraft, is the moment of inertia of the failed spacecraft, defined as follows:

[0027] (3)

[0028] where, is the principal moment of inertia, is the product of inertia.

[0029] Considering the unobservability of the actual moment of inertia of the failed spacecraft in the visual navigation mission, the moment of inertia ratio is also estimated as a state variable. is the dual cosine matrix. For any unit dual quaternion , is a dual number, is a three-dimensional dual vector, represents the real number field. Its corresponding dual cosine matrix is defined as , represents the cross product matrix. And for the three-dimensional dual vectors in different coordinate systems in space, it has the following coordinate transformation properties:

[0030] (4)

[0031] where, is 's conjugate dual quaternion, and the superscript represents the conjugate of this quaternion.

[0032] Second step, derive the state equation and the observation equation as:

[0033] (5)

[0034] (6)

[0035] where, represents the time , is the measurement noise at time ; is the measurement vector at time . Denote the state transition matrix as a block matrix of Denote as a block matrix of Denote as a block matrix of Denote the zero matrix of dimension The state quantity is , are the process noises of the state quantity respectively, where denotes taking the vector part of this physical quantity, is the vector part of is the vector part of Denote the measurement value at time The error dual quaternion, error dual angular velocity and error moment of inertia ratio are defined as follows:

[0036] (7)

[0037] (8)

[0038] (9)

[0039] In the present invention denotes that this physical quantity is an estimated value.

[0040] The Jacobian matrices in the state equation are as follows:

[0041] (10)

[0042] (11)

[0043] (12)

[0044] (13)

[0045] Among them, denotes the real part of the dual angular velocity , denotes the dual number part of the dual angular velocity . is the Kronecker product, and the matrix vectorization operator is defined as , is an arbitrary matrix, and its dimension is . is an arbitrary matrix, and the matrix truncation function is defined as:

[0046] (14)

[0047] Left multiplication matrix of dual quaternion is defined as:

[0048] (15)

[0049] where the quaternion is defined as , represents the scalar part, represents the vector part

[0050] In addition , , is an arbitrary three-dimensional vector; and are respectively the real part and the dual part of.

[0051] In the present invention, the pose measurement quantity of the failed spacecraft is obtained by taking pictures with a camera installed on the service spacecraft and performing calculation. The pseudo-measurement quantity is the pose dual quaternion of the failed spacecraft. Therefore, we get:

[0052] (16)

[0053] where, represents the time ; is the measurement matrix at time .

[0054] Step 3: Introduce the unscented transform to obtain the measurement noise covariance adaptation law:

[0055] (17)

[0056] where, represents the time, represents the size of the moving window, is the loop variable, is the estimated value of the measurement noise covariance. The measurement innovation sequence is , represents the measurement quantity, represents the prediction of the measurement quantity. The innovation matrix is estimated by the moving window method:

[0057] (18)

[0058] Define the measurement residual as , represents the observation function of the sampling point. The measurement residual covariance Given by unscented transform:

[0059] (19)

[0060] where represents the system dimension, is the loop variable, is the corresponding weight, is the sampling point, and the total number is points, obtained by the Sigma sampling function through the state estimation at the current time and the error covariance calculated as:

[0061] (20)

[0062] (21)

[0063] (22)

[0064] Usually, the sampling point distribution adjustment parameter is taken as .

[0065] The adaptive law design of the process noise covariance is:

[0066] (23)

[0067] (24)

[0068] where is the estimated value of the process noise covariance, is the prior process noise covariance, is the adaptive adjustment coefficient, is the numerator of the adjustment coefficient, is the denominator of the adjustment coefficient, represents taking the trace of the matrix, is the prediction residual , represents the measurement at time . And the state error covariance adjustment factor , the process noise covariance adjustment factor are obtained by real-time iteration of unscented transform and filter update

[0069] where: (25)

[0070] (26)

[0071] (27)

[0072] (28)

[0073] Then, numerical simulation is carried out to verify the estimation performance of the proposed method. The initial values of the relative state of the target spacecraft are set as follows: relative attitude , relative angular velocity , moment of inertia , relative position , relative linear velocity . Gaussian white noise with an amplitude of 2 degrees is added to the attitude measurement, and Gaussian white noise with a variance of is added to the position measurement. The measurement frequency is 2 Hz. The filter parameters are set as follows:

[0074] (29)

[0075] (30)

[0076] Since the proposed adaptive filtering method can estimate the measurement noise and process noise covariance, there is no need to perform cumbersome and complex parameter tuning for these two parameters. The estimation error curve of the relative attitude is as shown in Figure 2 . The convergence time is about 20 seconds, and the steady-state error is less than 2 degrees. The estimation error curve of the relative angular velocity is as shown in Figure 3 . The convergence time is about 30 seconds, and the steady-state error is less than 0.3 degrees / second. Figure 4 and Figure 5 respectively give the estimation error curves of the relative position and relative linear velocity, and their convergence times are both less than 100 seconds. The steady-state error of the relative position is less than 0.04 m, and the steady-state error of the relative linear velocity is less than 0.002 m / s.

[0077] Through the above steps, it is possible to achieve accurate estimation of the six-degree-of-freedom relative pose of the failed spacecraft under non-inertial observation and severe pose coupling.

[0078] The content not described in detail in the specification of the present invention belongs to the prior art well-known to those skilled in the art.

Claims

1. A method for estimating the relative pose of a failed spacecraft based on dual algebra, characterized in that, It includes the following steps: S1: Establish a six-degree-of-freedom relative motion and dynamics model of the failed spacecraft under dual-algebra description; S2: Utilize the six-degree-of-freedom relative motion and dynamics model of the failed spacecraft, and through the matrix vectorization operator, derive the analytical forms of the state equation and the observation equation, build an extended multiplicative Kalman filter, and establish a non-linear analytical formula between the system state and the measurement; S3: According to the non-linear analytical formula between the system state and the measurement, introduce the unscented transform, design the adaptive laws of the process noise covariance and the measurement noise covariance, and realize the accurate real-time pose estimation of the failed spacecraft during proximity operations.

2. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 1, characterized in that, The S1 includes: （1） （2） Among them, is the pose dual quaternion of the service spacecraft system relative to the failed spacecraft system, is the derivative with respect to its relative time; is the dual angular velocity of the service spacecraft system relative to the failed spacecraft system, and is expressed in the service spacecraft system; is the dual unit; is the dual angular velocity of the service spacecraft system relative to the inertial system, and is expressed in the service spacecraft system; is the dual angular velocity of the failed spacecraft system relative to the inertial system, and is expressed in the failed spacecraft system; is the derivative with respect to relative time; is the dual torque and is Gaussian noise; is the dual inertia of the failed spacecraft, defined as , is the 3×3 identity matrix, is the mass of the failed spacecraft, is the moment of inertia of the failed spacecraft, is the principal axis moment of inertia, is the product of inertia; considering the unobservability of the actual moment of inertia of the failed spacecraft in the visual navigation mission, the moment of inertia ratio is also estimated as a state variable.

3. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 2, wherein, In the above S1, is a dual cosine matrix. For any unit dual quaternion , is a dual number, is a three-dimensional dual vector, and its corresponding dual cosine matrix is defined as . For the three-dimensional dual vectors in different coordinate systems in space, it has the following coordinate transformation properties: （4） wherein, is the conjugate dual quaternion of , the superscript represents the conjugate of the quaternion, and represents the cross product matrix.

4. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 1, wherein In the S2, the determined state equation is: （5） The state quantity is , are the process noises of the state quantity, where denotes taking the vector part of this physical quantity, is 's vector part, is 's vector part, and the error dual quaternion is defined as , the error dual angular velocity is defined as , and the error moment of inertia ratio is defined as ; denotes the moment ; denotes the measurement value of at the moment ; is the measurement vector at the moment ; is the measurement matrix at the moment ; is the measurement noise at the moment .

5. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 4, characterized in that, In the S2, the Jacobian matrices in the state equation are as follows: （10） （11） （12） （13） Among them, and are the real part and the dual part of respectively, is the Kronecker product, and the matrix vectorization operator is defined as ; the matrix truncation function removes the first and fifth rows and the first and fifth columns of the 8th-order matrix , and only retains the 6th-order matrix of the corresponding vector part.

6. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 5, wherein In the above S2, the left multiplication matrix of the dual quaternion is defined as: （15） where the quaternion is defined as , represents the scalar part, represents the vector part; , , is an arbitrary three-dimensional vector; the superscript T represents the transpose of a matrix.

7. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 6, characterized in that In S2, the pose measurement of the failed spacecraft is obtained by taking images with a camera installed on the servicing spacecraft and performing calculations. , the pseudo-measurement is the pose dual quaternion of the failed spacecraft, so the observation matrix is (16) Among them, represents the moment ; is the measurement matrix at the moment .

8. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 1, characterized in that In the S3, after introducing the unscented transform, the obtained adaptive law of the measurement noise covariance is: （17） wherein, is the measurement noise covariance estimate; is the measurement innovation sequence, defined as ; is the residual covariance matrix.

9. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 8, wherein In S3, the definition formula is given through unscented transformation (19) Among them, is a loop variable, is the residual, defined as ; is sampling points, is the system dimension, is the weight corresponding to the sampling point. Each sampling point is obtained by the Sigma sampling function through the state estimate at the current moment and the error covariance is calculated; represents the moment, represents the size of the moving window, is a loop variable.

10. The method for estimating the relative pose of a failed spacecraft based on dual algebra according to claim 9, characterized in that, In the S3, the adaptive law design of the process noise covariance is: （23） （24） Among them, is the estimated value of the process noise covariance, is the preset prior process noise covariance, is the adaptive adjustment coefficient, is the numerator of the adaptive adjustment coefficient, the denominator of the adaptive adjustment coefficient, represents taking the trace of the matrix, is the prediction residual ; and the state error adjustment factor , the process noise adjustment factor , and the innovation adjustment factor are determined by real-time iteration of the unscented transform and filter update; the measurement residual covariance , the filter gain , the optimal state error covariance , the prior state error covariance , and the innovation matrix are estimated by the moving window method.

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