A spacecraft attitude and orbit integrated control method based on twistor

Abstract

The present invention belongs to the field of aerospace control technology, and specifically relates to a method for spacecraft attitude and orbit integrated control based on twistor, comprising the following steps: S1: establishing a first-order state space model of spacecraft attitude and orbit integrated based on twistor, S2: according to the HOFA system method, eliminating and raising the order of the established first-order state space model of spacecraft attitude and orbit integrated to obtain a HOFA system model of spacecraft attitude and orbit integrated, S3: designing a HOFA controller based on the HOFA system model of spacecraft attitude and orbit integrated, S4: according to the parametric design method, applying the HOFA controller to the attitude and orbit integrated model of the spacecraft to obtain a stable linear closed loop with arbitrarily configured closed-loop poles. The present invention solves the complex nonlinear problems faced by spacecraft attitude and orbit control under the traditional first-order state space method, converts the closed-loop system into a linear closed loop with arbitrarily configured poles, and avoids the unit constraint problem of the dual quaternion.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace control technology, and in particular relates to a method for integrating attitude and orbit control of a spacecraft based on torsion. Background Art

[0002] The attitude and orbit control of spacecraft is an important part of aerospace engineering. It involves the stability, reliability, safety and mission efficiency of spacecraft. The attitude and orbit motion of spacecraft is a nonlinear coupling system with six degrees of freedom. The establishment and solution of its dynamic and kinematic equations is a challenging problem.

[0003] At present, many methods have been proposed to describe and control the attitude and orbital motion of spacecraft. One of the commonly used methods is to model and control the attitude and orbital motion of spacecraft separately, that is, to express the attitude motion of spacecraft with Euler angles, quaternions or modified Rodrigues parameters, and to express the orbital motion of spacecraft with Kepler orbital elements or position and velocity in orbital coordinate system, and then design attitude controller and orbital controller respectively to achieve the attitude and orbital control objectives of spacecraft. The advantage of this method is that it is simple and easy to implement, but the disadvantage is that it ignores the coupling effect between the attitude and orbital motion of spacecraft, which may lead to the reduction of control performance and waste of control resources;

[0004] Another method is to integrate the attitude and orbital motion of the spacecraft into modeling and control, that is, to express the attitude and orbital motion of the spacecraft with a unified mathematical model, and then design an integrated controller to achieve the attitude and orbital integrated control goal of the spacecraft. The advantage of this method is that it fully considers the coupling effect between the attitude and orbital motion of the spacecraft, which can improve the control performance and control efficiency, but the disadvantage is that the design of the mathematical model and controller is relatively complex, requiring more computing resources and control knowledge;

[0005] Recently, inspired by the concept of full drive in the physical sense (the degrees of freedom of motion are the same as the degrees of freedom of control), the high-order full drive (HOFA) system method has been proposed. A series of papers published by Duan Guangren et al. fully demonstrated the unique advantages of the HOFA system method in dealing with nonlinear control problems. The key to the HOFA system method is how to transform the system into a HOFA system. Different from the traditional method of transforming all system equations into a first-order state space model, the HOFA system method focuses on how to transform the original system into a HOFA form, and proposes a new method to solve the control problem from a different perspective. Then, based on the transformed HOFA system, the desired linear closed-loop system can be obtained as needed.

[0006] The existing technology is based on the HOFA system method, which realizes the attitude and orbit control of the spacecraft through a carefully designed controller. However, the spacecraft attitude and orbit integrated model used in this technology is not based on twistors, and does not have the advantages of describing the spacecraft attitude and orbit based on twistor integration;

[0007] Therefore, based on the advantages of twistors in describing the attitude and orbital motion of spacecraft, it is necessary to propose a twistor-based integrated control method for spacecraft attitude and orbit. Summary of the invention

[0008] The purpose of the present invention is to provide a torsion-based spacecraft attitude and orbit integrated control method, which solves the complex nonlinear problems faced by spacecraft attitude and orbit control under the traditional first-order state space method, transforms the closed-loop system into a linear closed-loop whose poles can be arbitrarily configured, and avoids the unit constraint problem of the dual quaternion.

[0009] The technical solution adopted by the present invention is as follows:

[0010] A method for spacecraft attitude and orbit integrated control based on twistor, comprising the following steps:

[0011] S1: Establish a first-order state space model of spacecraft attitude and orbit integration based on twistor;

[0012] S2: According to the HOFA system method, the first-order state space model of spacecraft attitude and orbit integration is eliminated and upgraded to obtain the HOFA system model of spacecraft attitude and orbit integration;

[0013] S3: Design the HOFA controller based on the spacecraft attitude and orbit integrated HOFA system model;

[0014] S4: According to the parametric design method, the HOFA controller is applied to the attitude-orbit integrated model of the spacecraft to obtain a stable linear closed loop with arbitrarily configured closed-loop poles, and the specific values ​​of the parameter matrix in the HOFA controller are confirmed;

[0015] S5: Substitute the HOFA controller into the HOFA system model to obtain a desired linear closed-loop system.

[0016] In S1:

[0017] Define the geocentric inertial coordinate system as O I -X I Y I Z I , the center of the earth is the origin of the coordinate system and its value is O I , the positive direction of the X-axis points to the vernal equinox along the intersection of the ecliptic plane and the equatorial plane, the Z-axis points to the North Pole, and the Y-axis forms a right-handed coordinate system with the X and Z axes;

[0018] Define the desired coordinate system O D -X D Y D Z D , the expected coordinate system is consistent with the LVLH coordinate system, and the coordinate origin O D is the desired position of the spacecraft center of mass, X D The axis coincides with the radial vector from the center of the Earth to the desired location, Z D The Y axis is consistent with the direction of orbital angular momentum. D The axis forms a right-handed orthogonal coordinate system with the other two axes;

[0019] Define the body coordinate system O B -X B Y B Z B , where the coordinate origin O B At the center of mass of the spacecraft, the three axes coincide with the principal axes of inertia of the spacecraft;

[0020] The calculation formula of the spacecraft attitude and orbit torque is:

[0021]

[0022] Among them, p BD =[p1,p2,p3] T is the Rodriguez parameter corrected by the spacecraft body coordinate system relative to the desired coordinate system, is the projection of the position vector of the spacecraft body coordinate system relative to the desired coordinate system in the body coordinate system, b1, b2, b3, b5, b6, b7 are specific elements of the twistor, and ε is the dual unit;

[0023] Π BD The calculation formula is:

[0024]

[0025] Among them, ||p BD || 2 is the square of the second norm of the Rodriguez parameter corrected by the spacecraft body coordinate system relative to the desired coordinate system, and I3 is a three-by-three identity matrix;

[0026] and The calculation formula is:

[0027]

[0028] Among them, p1, p2, and p3 are specific elements of the modified Rodriguez parameters of the body coordinate system relative to the desired coordinate system.

[0029] In the S1, the velocity spinor of the spacecraft is established, and the calculation formula of the velocity spinor is:

[0030]

[0031] in, is the angular velocity of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, is the angular velocity of the spacecraft body coordinate system relative to the inertial coordinate system expressed in the body coordinate system, is the angular velocity of the spacecraft's desired coordinate system relative to the inertial coordinate system expressed in the desired coordinate system, is the position vector of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, is the position vector of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, The position vector of the desired coordinate system of the spacecraft relative to the inertial coordinate system is expressed in the desired coordinate system;

[0032] And the calculation formula of the conversion relationship between the velocity spinors of the spacecraft is:

[0033]

[0034] The first-order state space model of spacecraft attitude and orbit integration based on twistor is:

[0035]

[0036] Among them, B BD is the twist of the body coordinate system relative to the desired coordinate system, The velocity spinor of the body coordinate system relative to the desired coordinate system is expressed in the body coordinate system. is the velocity spinor of the body coordinate system relative to the inertial coordinate system expressed in the body coordinate system, The velocity spinor of the desired coordinate system relative to the inertial coordinate system is expressed in the desired coordinate system. is the dual gravity acting on the spacecraft, is the dual control force on the spacecraft, M is the dual inertia matrix of the spacecraft, M -1 is the inverse matrix of the spacecraft dual inertia matrix;

[0037] The dual gravity The calculation formula is:

[0038]

[0039] in, is the gravity gradient force on the spacecraft, is the gravity gradient torque on the spacecraft;

[0040] The dual inertia matrix M and the inverse matrix M -1 The calculation formula is:

[0041]

[0042] Among them, 03 is a three-by-three zero matrix, 0 3×1 and 0 1×3 are the zero matrices of corresponding dimensions, J is the moment of inertia matrix of the spacecraft, m is the mass of the spacecraft, and I3 is the three-by-three unit matrix.

[0043] In S2, the HOFA system method is used to transform the torsion-based spacecraft attitude and orbit integrated first-order state space model established in S1 into a HOFA model through elimination and order raising;

[0044] The derivative of the dynamic expression based on the twistor is:

[0045]

[0046] Substituting the twistor-based dynamics into the following formula, we get:

[0047]

[0048] The matrix formula is:

[0049] D=[1+B BD ][1-B BD ] ∨

[0050] Then the above formula is:

[0051]

[0052] Substituting the dynamic equation based on twistor into the above formula, we can get:

[0053]

[0054] Substituting the conversion relationship between the velocity spinors of the spacecraft into the equation, we can obtain:

[0055]

[0056] Considering the kinematic equation based on the twistor, we can get:

[0057]

[0058] Substituting it into the above formula, we can get:

[0059]

[0060] Among them, the specific expansion of matrix D is:

[0061]

[0062] in:

[0063]

[0064]

[0065] According to the definition of matrix D and the above derivation process, the HOFA system model of the spacecraft attitude and orbit integrated motion is obtained by eliminating elements and raising the order of the spacecraft attitude and orbit integrated state space model.

[0066] In S3, based on the spacecraft attitude and orbit integrated HOFA system model obtained in S2, a HOFA controller is designed, and the specific design formula is:

[0067]

[0068] in, is a column vector consisting of the spacecraft torsion with the real part and the dual part exchanged and the first-order derivative of the torsion, is the dual operator to be designed, and its calculation formula is:

[0069]

[0070] is the parameter augmentation matrix to be designed, and its specific form is:

[0071]

[0072] Among them, A0, A1, is the parameter matrix to be designed.

[0073] In S4, based on the parametric design method, the parameter matrix of the HOFA controller proposed in S3 is designed, and the design steps are as follows:

[0074] Define parameter matrices F1 and F2, A 0～1 =[A0 A1], Then the matrix Φ(A 0～1 )and The relationship is:

[0075]

[0076] The further formula is:

[0077]

[0078] Among them, Z and is a real matrix, then V, Specifically:

[0079]

[0080] Z and The formula for the selection criteria is:

[0081]

[0082] Where det is the value of the corresponding determinant.

[0083] In S5, the HOFA controller is introduced into the HOFA system model, and the following is obtained:

[0084]

[0085] Let B BD =a BD +εb BD , written in first-order state space form, the above formula is:

[0086]

[0087] Then, the designed HOFA controller obtains a linear closed-loop system, the poles of which are consistent with the matrix F and have the same eigenvalues.

[0088] The parameter matrix F and for:

[0089]

[0090] The parameter matrix Z and for:

[0091]

[0092] Then the matrix can be obtained as:

[0093]

[0094] According to the parametric design method, the parameter matrix to be designed can be obtained as follows:

[0095]

[0096] Assuming the mass of the spacecraft is 100 kg, the moment of inertia matrix is:

[0097]

[0098] The technical effects achieved by the present invention are:

[0099] The present invention provides a spacecraft attitude and orbit integrated control method based on a high-order all-drive system method, which solves the complex nonlinear problems faced by spacecraft attitude and orbit control under the traditional first-order state space method, and transforms the closed-loop system into a linear closed loop whose poles can be arbitrarily configured. At the same time, since the present invention adopts a spacecraft attitude and orbit integrated model established by twistors and designs a controller, it also avoids the unit constraint problem of dual quaternions. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 It is a schematic diagram of the process of the present invention;

[0101] Figure 2 is a graph showing a change in relative attitude of a spacecraft in the present invention;

[0102] Figure 3 is a curve diagram of the relative angular velocity change of the spacecraft in the present invention;

[0103] Figure 4 is a curve diagram of the relative position change of the spacecraft in the present invention;

[0104] Figure 5 is a graph showing a change in relative speed of a spacecraft in the present invention;

[0105] Figure 6 is a curve diagram of the change of the control torque of the spacecraft in the present invention;

[0106] Figure 7 It is a curve diagram of the change of the control force of the spacecraft in the present invention. DETAILED DESCRIPTION

[0107] In order to make the purpose and advantages of the present invention more clearly understood, the present invention is specifically described below in conjunction with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present invention, and does not strictly limit the scope of protection of the specific claims of the present invention.

[0108] like Figure 1-7 As shown, a method for integrated control of spacecraft attitude and orbit based on twistor comprises the following steps:

[0109] S1: Establish a first-order state space model of spacecraft attitude and orbit integration based on twistor;

[0110] Define the geocentric inertial coordinate system as O I -X I Y I Z I , the center of the earth is the origin of the coordinate system and its value is O I , the positive direction of the X-axis points to the vernal equinox along the intersection of the ecliptic plane and the equatorial plane, the Z-axis points to the North Pole, and the Y-axis forms a right-handed coordinate system with the X and Z axes;

[0111] Define the desired coordinate system O D -X D Y D Z D , the expected coordinate system is consistent with the LVLH coordinate system, and the coordinate origin O D is the desired position of the spacecraft center of mass, X D The axis coincides with the radial vector from the center of the Earth to the desired location, Z D The Y axis is consistent with the direction of orbital angular momentum. D The axis forms a right-handed orthogonal coordinate system with the other two axes;

[0112] Define the body coordinate system O B -X B Y B Z B , where the coordinate origin O B At the center of mass of the spacecraft, the three axes coincide with the principal axes of inertia of the spacecraft;

[0113] The calculation formula of the spacecraft attitude and orbit torque is:

[0114]

[0115] Among them, p BD =[p1,p2,p3] T is the Rodriguez parameter corrected by the spacecraft body coordinate system relative to the desired coordinate system, is the projection of the position vector of the spacecraft body coordinate system relative to the desired coordinate system in the body coordinate system, b1, b2, b3, b5, b6, b7 are specific elements of the twistor, and ε is the dual unit;

[0116] Π BD The calculation formula is:

[0117]

[0118] Among them, ||p BD || 2 is the square of the second norm of the Rodriguez parameter corrected by the spacecraft body coordinate system relative to the desired coordinate system, and I3 is a three-by-three identity matrix;

[0119] and The calculation formula is:

[0120]

[0121] Among them, p1, p2, and p3 are specific elements of the modified Rodriguez parameters of the body coordinate system relative to the desired coordinate system.

[0122] The velocity spinor of the spacecraft is established in S1, and the calculation formula of the velocity spinor is:

[0123]

[0124] in, is the angular velocity of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, is the angular velocity of the spacecraft body coordinate system relative to the inertial coordinate system expressed in the body coordinate system, is the angular velocity of the spacecraft's desired coordinate system relative to the inertial coordinate system expressed in the desired coordinate system, is the position vector of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, is the position vector of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, The position vector of the desired coordinate system of the spacecraft relative to the inertial coordinate system is expressed in the desired coordinate system;

[0125] And the calculation formula for the conversion relationship between the velocity spinor of the spacecraft is:

[0126]

[0127] The first-order state space model of spacecraft attitude and orbit integration based on twistor is:

[0128]

[0129] Among them, B BD is the twist of the body coordinate system relative to the desired coordinate system, The velocity spinor of the body coordinate system relative to the desired coordinate system is expressed in the body coordinate system. is the velocity spinor of the body coordinate system relative to the inertial coordinate system expressed in the body coordinate system, The velocity spinor of the desired coordinate system relative to the inertial coordinate system is expressed in the desired coordinate system. is the dual gravity acting on the spacecraft, is the dual control force on the spacecraft, M is the dual inertia matrix of the spacecraft, M -1 is the inverse matrix of the spacecraft dual inertia matrix;

[0130] Dual Gravity The calculation formula is:

[0131]

[0132] in, is the gravity gradient force on the spacecraft, is the gravity gradient torque on the spacecraft;

[0133] Dual inertia matrix M and inverse matrix M-1 The calculation formula is:

[0134]

[0135] Among them, 03 is a three-by-three zero matrix, 0 3×1 and 0 1×3 are the zero matrices of corresponding dimensions, J is the moment of inertia matrix of the spacecraft, m is the mass of the spacecraft, and I3 is the three-by-three unit matrix.

[0136] S2: According to the HOFA system method, the first-order state space model of spacecraft attitude and orbit integration is eliminated and upgraded to obtain the HOFA system model of spacecraft attitude and orbit integration;

[0137] Using the HOFA system method, the twistor-based spacecraft attitude and orbit integrated first-order state space model established in S1 is transformed into the HOFA model through elimination and order raising.

[0138] The derivative of the dynamic expression based on the twistor is:

[0139]

[0140] Substituting the twistor-based dynamics into the following formula, we get:

[0141]

[0142] The matrix formula is:

[0143] D=[1+B BD ][1-B BD ] ∨

[0144] Then the above formula is:

[0145]

[0146] Substituting the dynamic equation based on twistor into the above formula, we can get:

[0147]

[0148] Substituting the conversion relationship between the spacecraft velocity spinors, we can obtain:

[0149]

[0150] Considering the kinematic equation based on the twistor, we can get:

[0151]

[0152] Substituting it into the above formula, we can get:

[0153]

[0154] Among them, the specific expansion of matrix D is:

[0155]

[0156] in:

[0157]

[0158] According to the definition of matrix D and the above derivation process, the HOFA system model of the spacecraft attitude and orbit integrated motion is obtained by eliminating and raising the order of the spacecraft attitude and orbit integrated state space model. It should be noted that the core of the HOFA system method is to establish the HOFA system model. As long as the HOFA system model is obtained, a controller can be easily designed to compensate for nonlinear dynamics and a linear closed-loop system can be built to achieve arbitrary pole configuration.

[0159] S3: Based on the spacecraft attitude-orbit integrated HOFA system model obtained in S2, the HOFA controller is designed. The specific design formula is:

[0160]

[0161] in, is a column vector consisting of the spacecraft torsion with the real part and the dual part exchanged and the first-order derivative of the torsion, is the dual operator to be designed, and its calculation formula is:

[0162]

[0163] is the parameter augmentation matrix to be designed, and its specific form is:

[0164]

[0165] Among them, A0, A1, is the parameter matrix to be designed. By reasonably designing the parameter matrix, the system closed loop can be arbitrarily configured while satisfying system stability.

[0166] S4: According to the parametric design method, the HOFA controller is applied to the attitude-orbit integrated model of the spacecraft to obtain a stable linear closed loop with arbitrarily configured closed-loop poles, and the specific values ​​of the parameter matrix in the HOFA controller are confirmed;

[0167] Based on the parametric design method, the parameter matrix of the HOFA controller proposed by S3 is designed.

[0168] The design steps are:

[0169] Define parameter matrices F1 and F2, A 0～1 =[A0 A1], Then the matrix Φ(A 0～1 )and The relationship is:

[0170]

[0171] The further formula is:

[0172]

[0173] Among them, Z and is a real matrix, then V, Specifically:

[0174]

[0175] Z and The formula for the selection criteria is:

[0176]

[0177] Where det is the value of the corresponding determinant.

[0178] S5: Substitute the HOFA controller into the HOFA system model to obtain the desired linear closed-loop system.

[0179] By bringing the HOFA controller into the HOFA system model, we can obtain:

[0180]

[0181] Let B BD =a BD +εb BD , written in first-order state space form, the above formula is:

[0182]

[0183] Then, the designed HOFA controller obtains a linear closed-loop system whose poles are related to the matrix F and The eigenvalues ​​of are the same. Based on the linear system theory, the stability of the closed-loop system can be easily derived.

[0184] The above analysis shows that the spacecraft attitude-orbit integrated control method proposed in this invention can eventually obtain a linear closed-loop system. The poles of the closed-loop system can be determined by designing the matrices F and The eigenvalues ​​of can be configured arbitrarily, which is difficult to achieve using the traditional first-order state space method. At the same time, the present invention establishes a spacecraft attitude and orbital motion model based on twistors, avoiding the unit constraint problem associated with dual quaternion modeling.

[0185] The parameter matrix F and for:

[0186]

[0187] The parameter matrix Z and for:

[0188]

[0189] Then the matrix can be obtained as:

[0190]

[0191] According to the parametric design method, the parameter matrix to be designed can be obtained as follows:

[0192]

[0193] Assuming the mass of the spacecraft is 100kg, the moment of inertia matrix is:

[0194]

[0195] According to the simulation curve diagram, the present application effectively realizes the integrated control of the spacecraft attitude and orbit, obtains a closed-loop linear system that can be arbitrarily configured, and solves the nonlinear problem of the first-order state space method.

[0196] The above is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. The structures, devices and operating methods not specifically described and explained in the present invention shall be implemented according to the conventional means in the art unless otherwise specified and limited.

Claims

1. A method for integrated attitude and orbit control of a spacecraft based on twistor, characterized in that: The following steps are involved: S1: Establish a first-order state space model of spacecraft attitude and orbit integration based on twistor; S2: According to the HOFA system method, the first-order state space model of spacecraft attitude and orbit integration is eliminated and upgraded to obtain the HOFA system model of spacecraft attitude and orbit integration; S3: Design the HOFA controller based on the spacecraft attitude and orbit integrated HOFA system model; In S3, based on the spacecraft attitude and orbit integrated HOFA system model obtained in S2, the HOFA controller is designed, and the specific design formula is: in, is a column vector consisting of the spacecraft torsion with the real part and the dual part exchanged and the first-order derivative of the torsion, is the dual operator to be designed, and its calculation formula is: is the parameter augmentation matrix to be designed, and its specific form is: Among them, A0, A1, is the parameter matrix to be designed; S4: According to the parametric design method, the HOFA controller is applied to the attitude-orbit integrated model of the spacecraft to obtain a stable linear closed loop with arbitrarily configured closed-loop poles, and the specific values ​​of the parameter matrix in the HOFA controller are confirmed; S5: Substitute the HOFA controller into the HOFA system model to obtain a desired linear closed-loop system.

2. The method for integrated control of spacecraft attitude and orbit based on torsion according to claim 1, characterized in that: In S1: Define the geocentric inertial coordinate system as O I -X I Y I Z I , the center of the earth is the origin of the coordinate system I , the positive direction of the X-axis points to the vernal equinox along the intersection of the ecliptic plane and the equatorial plane, the Z-axis points to the North Pole, and the Y-axis forms a right-handed coordinate system with the X and Z axes; Define the desired coordinate system O D -X D Y D Z D , the expected coordinate system is consistent with the LVLH coordinate system, and the coordinate origin O D is the desired position of the spacecraft center of mass, X D The axis coincides with the radial vector from the center of the Earth to the desired location, Z D The Y axis is consistent with the direction of orbital angular momentum. D The axis forms a right-handed orthogonal coordinate system with the other two axes; Define the body coordinate system O B -X B Y B Z B , where the coordinate origin O B At the center of mass of the spacecraft, the three axes coincide with the principal axes of inertia of the spacecraft; The calculation formula of the spacecraft attitude and orbit torque is: Among them, p BD =[p1,p2,p3] T is the Rodriguez parameter corrected by the spacecraft body coordinate system relative to the desired coordinate system, is the projection of the position vector of the spacecraft body coordinate system relative to the desired coordinate system in the body coordinate system, b1, b2, b3, b5, b6, b7 are specific elements of the twistor, and ε is the dual unit; Π BD The calculation formula is: Among them, ||p BD || 2 is the square of the second norm of the Rodriguez parameter corrected by the spacecraft body coordinate system relative to the desired coordinate system, and I3 is a three-by-three identity matrix; and The calculation formula is: Among them, p1, p2, and p3 are specific elements of the modified Rodriguez parameters of the body coordinate system relative to the desired coordinate system.

3. The method for integrated attitude and orbit control of a spacecraft based on torsion according to claim 2, characterized in that: In the S1, the velocity spinor of the spacecraft is established, and the calculation formula of the velocity spinor is: in, is the angular velocity of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, is the angular velocity of the spacecraft body coordinate system relative to the inertial coordinate system expressed in the body coordinate system, is the angular velocity of the spacecraft's desired coordinate system relative to the inertial coordinate system expressed in the desired coordinate system, is the position vector of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, is the position vector of the spacecraft body coordinate system relative to the desired coordinate system expressed in the body coordinate system, The position vector of the desired coordinate system of the spacecraft relative to the inertial coordinate system is expressed in the desired coordinate system; And the calculation formula of the conversion relationship between the velocity spinors of the spacecraft is: The first-order state space model of spacecraft attitude and orbit integration based on twistor is: Among them, B BD is the twist of the body coordinate system relative to the desired coordinate system, The velocity spinor of the body coordinate system relative to the desired coordinate system is expressed in the body coordinate system. is the velocity spinor of the body coordinate system relative to the inertial coordinate system expressed in the body coordinate system, The velocity spinor of the desired coordinate system relative to the inertial coordinate system is expressed in the desired coordinate system. is the dual gravity acting on the spacecraft, is the dual control force on the spacecraft, M is the dual inertia matrix of the spacecraft, M -1 is the inverse matrix of the spacecraft dual inertia matrix; The dual gravity The calculation formula is: in, is the gravity gradient force on the spacecraft, is the gravity gradient torque on the spacecraft; The dual inertia matrix M and the inverse matrix M -1 The calculation formula is: Among them, 03 is a three-by-three zero matrix, 0 3×1 and 0 1×3 are the zero matrices of corresponding dimensions, J is the moment of inertia matrix of the spacecraft, m is the mass of the spacecraft, and I3 is the three-by-three unit matrix.

4. The method for integrated control of spacecraft attitude and orbit based on torsion according to claim 3, characterized in that: In S2, the HOFA system method is used to transform the torsion-based spacecraft attitude and orbit integrated first-order state space model established in S1 into a HOFA model through elimination and order raising; The derivative of the dynamic expression based on the twistor is: Substituting the twistor-based dynamics into the following formula, we get: The matrix formula is: D=[1+B BD ][1-B BD ] ∨ Then the above formula is: Substituting the dynamic equation based on twistor into the above formula, we can get: Substituting the conversion relationship between the velocity spinors of the spacecraft into the equation, we can obtain: Considering the kinematic equation based on the twistor, we can get: Substituting it into the above formula, we can get: Among them, the specific expansion of matrix D is: in: According to the definition of matrix D and the above derivation process, the HOFA system model of the spacecraft attitude and orbit integrated motion is obtained by eliminating elements and raising the order of the spacecraft attitude and orbit integrated state space model.

5. The method for integrated control of spacecraft attitude and orbit based on twistor according to claim 1, characterized in that: In S4, based on the parametric design method, the parameter matrix of the HOFA controller proposed in S3 is designed, and the design steps are as follows: Define parameter matrices F1 and F2, A 0～1 =[A0 A1], Then the matrix Φ(A 0～1 )and The relationship is: The further formula is: Among them, Z and is a real matrix, then V, Specifically: Z and The formula for the selection criteria is: Where det is the value of the corresponding determinant.

6. The method for integrated control of spacecraft attitude and orbit based on torsion according to claim 3, characterized in that: In S5, the HOFA controller is introduced into the HOFA system model, and the following is obtained: Let B BD =a BD +εb BD , written in first-order state space form, the above formula is: Then, the designed HOFA controller obtains a linear closed-loop system, the poles of which are consistent with the matrix F and have the same eigenvalues.

7. The method for integrated control of spacecraft attitude and orbit based on torsion according to claim 6, characterized in that: The parameter matrix F and for: The parameter matrix Z and for: Then the matrix can be obtained as: According to the parametric design method, the parameter matrix to be designed can be obtained as follows: Assuming the mass of the spacecraft is 100 kg, the moment of inertia matrix is:

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