A spacecraft formation attitude cooperative control method coupled with flywheel dynamics

Abstract

The present application relates to the field of spacecraft control technology and provides a method for coordinated attitude control of a spacecraft formation coupled with flywheel dynamics. The method comprises: obtaining a Hamiltonian energy function based on the angular kinetic energy of the spacecraft and the angular kinetic energy of the flywheel, and calculating the navigator's estimated state based on the attitude dynamics and kinematic equations; constructing the PH equation of the target spacecraft formation based on all Hamiltonian energy functions and the attitude dynamics and kinematic equations; constructing the expected Hamiltonian function of the target spacecraft formation based on the attitude dynamics and kinematic equations of all spacecraft and the navigator's estimated state of all spacecraft; calculating the system controller equation of the target spacecraft formation using the IDA-PBC algorithm based on the PH equation and the expected Hamiltonian function, and obtaining the control law equation of the spacecraft based on the system controller equation; and controlling the spacecraft using the control law equation of the spacecraft. The method of the present application can improve the rationality of spacecraft formation control.

Description

Technical Field

[0001] The present application relates to the field of spacecraft control technology, and in particular to a spacecraft formation attitude collaborative control method coupled with flywheel dynamics. Background Art

[0002] Coordinated attitude control of spacecraft formations involves ensuring that the attitudes of all spacecraft maintain a relative orientation or ultimate alignment through control. Its importance in formation missions such as synthetic aperture imaging, gravity field measurement, and three-dimensional stereoscopic imaging has attracted considerable attention. Currently, a variety of approaches exist for studying coordinated attitude control of spacecraft. For example, to address the requirement of maintaining attitude alignment among multiple spacecraft during formation rotation maneuvers, existing research has proposed control laws that combine three actions: reducing attitude errors, maintaining attitude consistency, and rotating around a specified axis, as well as passive dynamic control laws that do not require angular velocity information. Existing research has also proposed decentralized control mechanisms for spacecraft based on virtual structures to maintain strict relative position and attitude configuration during formation maneuvers.

[0003] Momentum exchange actuators, particularly flywheels, are environmentally friendly and energy-efficient spacecraft attitude control devices and have been extensively studied in single-spacecraft control. For example, the coplanar dual flywheel-single jet configuration stabilizes the spacecraft's angular velocity through the dual flywheel combination, minimizing fuel consumption when maneuvering to the desired attitude. However, existing studies on spacecraft attitude cooperative control mostly simplify the spacecraft as rigid bodies and fail to consider the role of momentum exchange actuators. A few studies on attitude cooperative control have considered the role of flywheels, such as the study of the attitude cooperative control of a formation of flexible spacecraft with asymmetric actuator configurations. An integral sliding mode adaptive control law and a robust, anti-windup distributed attitude cooperative controller were designed to enable the attitude and angular velocity to accurately track the desired time-varying commands within a finite time. However, these studies failed to consider the coupling between the flywheel and spacecraft dynamics in the control law design, hindering the realization of high-precision distributed cooperative control of the attitude of spacecraft formations. Consequently, existing spacecraft cooperative control methods suffer from the problem of low rationality in attitude control of spacecraft formations. Summary of the Invention

[0004] The present application provides a spacecraft formation attitude collaborative control method coupled with flywheel dynamics, which can solve the problem of low rationality of attitude control of spacecraft formation.

[0005] In a first aspect, an embodiment of the present application provides a method for collaborative attitude control of a spacecraft formation coupled with flywheel dynamics, the method comprising:

[0006] Obtain the current angular velocity, attitude, and flywheel angular velocity of each spacecraft in the target spacecraft formation, and construct the attitude dynamics and kinematics equations for each spacecraft based on the angular velocity, attitude, and flywheel angular velocity of each spacecraft. For spacecraft using flywheels, the attitude dynamics and kinematics equations are used to describe the spacecraft's attitude information, flywheel information, and control information.

[0007] For each spacecraft, the Hamiltonian energy function is obtained based on the spacecraft's angular velocity and the angular velocity of the flywheel. The navigator's estimated state is then calculated based on the attitude dynamics and kinematic equations of all spacecraft. The Hamiltonian energy function is used to describe the spacecraft's angular kinetic energy and the flywheel's angular kinetic energy at the current moment, and the navigator's estimated state is used to describe the spacecraft's desired state.

[0008] The PH equation of the target spacecraft formation is constructed based on the Hamiltonian energy function and attitude dynamics and kinematics equations of all spacecraft. The PH equation is used to describe the relationship between the system controller of the target spacecraft formation and the attitudes of all spacecraft.

[0009] The expected Hamiltonian function of the target spacecraft formation is constructed based on the attitude dynamics and kinematic equations of all spacecraft and the navigator-estimated states of all spacecraft. The expected Hamiltonian function is used to describe the attitude error of each spacecraft and the relative attitude error between every two spacecraft.

[0010] According to the PH equation and the expected Hamiltonian function, the system controller equation of the target spacecraft formation is calculated using the IDA-PBC algorithm, and the control law equation of each spacecraft is obtained based on the system controller equation.

[0011] For each spacecraft, the control law equation of the spacecraft is used to control the spacecraft.

[0012] In a second aspect, an embodiment of the present application provides a spacecraft formation attitude coordinated control device coupled with flywheel dynamics, comprising:

[0013] An acquisition module is used to obtain the current angular velocity, attitude, and flywheel angular velocity of each spacecraft in the target spacecraft formation, and to construct the attitude dynamics and kinematics equations of each spacecraft based on the angular velocity, attitude, and flywheel angular velocity of each spacecraft. For spacecraft using flywheels, the attitude dynamics and kinematics equations are used to describe the spacecraft's attitude information, flywheel information, and control information.

[0014] The first calculation module is used to obtain the Hamiltonian energy function of each spacecraft based on the angular velocity of the spacecraft and the angular velocity of the flywheel, and calculate the navigator estimated state of the spacecraft based on the attitude dynamics and kinematic equations of all spacecraft. The Hamiltonian energy function is used to describe the angular kinetic energy of the spacecraft and the angular kinetic energy of the flywheel at the current moment, and the navigator estimated state is used to describe the expected state of the spacecraft.

[0015] The first building block is used to construct the PH equation of the target spacecraft formation based on the Hamiltonian energy function and attitude dynamics and kinematic equations of all spacecraft; the PH equation is used to describe the relationship between the system controller of the target spacecraft formation and the attitudes of all spacecraft;

[0016] The second building block is used to construct the expected Hamiltonian function of the target spacecraft formation based on the attitude dynamics and kinematic equations of all spacecraft and the navigator-estimated states of all spacecraft. The expected Hamiltonian function is used to describe the attitude error of each spacecraft and the relative attitude error between every two spacecraft.

[0017] The second calculation module is used to calculate the system controller equation of the target spacecraft formation using the IDA-PBC algorithm according to the PH equation and the expected Hamiltonian function, and obtain the control law equation of each spacecraft based on the system controller equation;

[0018] The control module is used to control each spacecraft using the control law equation of the spacecraft.

[0019] In a third aspect, an embodiment of the present application provides a terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the method for collaborative control of spacecraft formation attitudes coupled with flywheel dynamics is implemented.

[0020] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for collaborative control of spacecraft formation attitudes coupled with flywheel dynamics.

[0021] The above solution of the present application has the following beneficial effects:

[0022] In an embodiment of the present application, the angular velocity, attitude and angular velocity of the flywheel of each spacecraft in the target spacecraft formation at the current moment are obtained, and the attitude dynamics and kinematic equations of each spacecraft are constructed based on the angular velocity, attitude and angular velocity of the flywheel of each spacecraft. Then, for each spacecraft, the Hamiltonian energy function of the spacecraft is obtained based on the angular velocity of the spacecraft and the angular velocity of the flywheel, and the navigator estimated state of the spacecraft is calculated based on the attitude dynamics and kinematic equations of all spacecraft. Then, the PH equation of the target spacecraft formation is constructed based on the Hamiltonian energy function and the attitude dynamics and kinematic equations of all spacecraft. Then, based on the attitude dynamics and kinematic equations of all spacecraft and the navigator estimated state of all spacecraft, the expected Hamiltonian function of the target spacecraft formation is constructed. Then, based on the PH equation and the expected Hamiltonian function, the system controller equation of the target spacecraft formation is calculated using the IDA-PBC algorithm, and the control law equation of each spacecraft is obtained based on the system controller equation. Finally, for each spacecraft, the control law equation of the spacecraft is used to control the spacecraft. Among them, the attitude dynamics and kinematic equations are constructed according to the flywheel angular momentum of the spacecraft, so that the dynamic information of the flywheel is coupled into the attitude dynamics and kinematic equations, thereby improving the accuracy and rationality of the equations in describing the spacecraft state. The navigator's estimated state obtained based on accurate and reasonable attitude dynamics and kinematic equations is highly accurate, which can provide the spacecraft with an accurate expected state, thereby improving the accuracy of the expected Hamiltonian function. The rationality of the spacecraft control law equation obtained according to the highly accurate expected Hamiltonian function is improved, thereby improving the rationality of the attitude control of the spacecraft formation, and can make the error convergence speed faster and the configuration more stable.

[0023] Other beneficial effects of the present application will be described in detail in the subsequent specific implementation section. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0025] Figure 1 A flow chart of a method for coordinated control of spacecraft formation attitude coupled with flywheel dynamics provided in one embodiment of the present application;

[0026] Figure 2 A schematic diagram of the topological structure of a spacecraft formation provided in one embodiment of the present application;

[0027] Figure 3A schematic diagram of a spacecraft attitude trajectory provided in one embodiment of the present application;

[0028] Figure 4 A snapshot of the spacecraft attitude error provided by an embodiment of the present application;

[0029] Figure 5 A steady-state diagram of the spacecraft attitude error provided in one embodiment of the present application;

[0030] Figure 6 This is a snapshot of the spacecraft output torque provided by an embodiment of the present application;

[0031] Figure 7 A steady-state diagram of the spacecraft output torque provided in one embodiment of the present application;

[0032] Figure 8 A snapshot of the spacecraft relative attitude error provided in an embodiment of the present application;

[0033] Figure 9 A steady-state diagram of the spacecraft relative attitude error provided in one embodiment of the present application;

[0034] Figure 10 A schematic diagram of the structure of a spacecraft formation attitude cooperative control device coupled with flywheel dynamics provided in one embodiment of the present application;

[0035] Figure 11 A schematic diagram of the structure of a terminal device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0036] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0037] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or collections thereof.

[0038] It will also be understood that the term "and / or" used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0039] As used in this specification and the appended claims, the term "if" can be interpreted as "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "upon determination" or "in response to determining" or "upon detection of [described condition or event]" or "in response to detecting [described condition or event]," depending on the context.

[0040] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0041] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0042] In response to the problem of low rationality of the attitude control of existing spacecraft formations, an embodiment of the present application provides a spacecraft formation attitude collaborative control method coupled with flywheel dynamics. The spacecraft formation attitude collaborative control method obtains the angular velocity, attitude and angular velocity of the flywheel of each spacecraft in the target spacecraft formation at the current moment, and constructs the attitude dynamics and kinematic equations of each spacecraft based on the angular velocity, attitude and angular velocity of the flywheel of each spacecraft. Then, for each spacecraft, the Hamiltonian energy function of the spacecraft is obtained based on the angular velocity of the spacecraft and the angular velocity of the flywheel, and the attitude dynamics and kinematic equations of all spacecraft are calculated. The navigator of the spacecraft estimates the state, and then constructs the PH equation of the target spacecraft formation based on the Hamiltonian energy function, attitude dynamics and kinematic equations of all spacecraft. Then, based on the attitude dynamics and kinematic equations of all spacecraft and the navigator's estimated state of all spacecraft, the expected Hamiltonian function of the target spacecraft formation is constructed. Then, based on the PH equation and the expected Hamiltonian function, the IDA-PBC algorithm is used to calculate the system controller equation of the target spacecraft formation, and based on the system controller equation, the control law equation of each spacecraft is obtained. Finally, for each spacecraft, the control law equation of the spacecraft is used to control the spacecraft separately. Among them, the attitude dynamics and kinematic equations are constructed according to the flywheel angular momentum of the spacecraft, so that the dynamic information of the flywheel is coupled into the attitude dynamics and kinematic equations, thereby improving the accuracy and rationality of the equations in describing the spacecraft state. The navigator's estimated state obtained based on accurate and reasonable attitude dynamics and kinematic equations is highly accurate, which can provide the spacecraft with an accurate expected state, thereby improving the accuracy of the expected Hamiltonian function. The rationality of the spacecraft control law equation obtained according to the highly accurate expected Hamiltonian function is improved, thereby improving the rationality of the attitude control of the spacecraft formation, and can make the error convergence speed faster and the configuration more stable.

[0043] Next, an exemplary description is given of the spacecraft formation attitude collaborative control method coupled with flywheel dynamics provided in this application.

[0044] like Figure 1 As shown, the spacecraft formation attitude coordinated control method coupled with flywheel dynamics provided by the present application includes the following steps:

[0045] Step 11: Obtain the current angular velocity, attitude, and flywheel angular velocity of each spacecraft in the target spacecraft formation, and construct the attitude dynamics and kinematics equations of each spacecraft based on the angular velocity, attitude, and flywheel angular velocity of each spacecraft.

[0046] The above-mentioned spacecraft is a spacecraft using a flywheel, that is, a rigid body spacecraft under the action of a flywheel group (three flywheels are distributed on the three inertia axes of the spacecraft's body coordinate system). The attitude dynamics and kinematic equations are used to describe the spacecraft's attitude information, flywheel information and control information.

[0047] In some embodiments of the present application, the angular velocity, attitude, and angular velocity of the flywheel of the spacecraft may be acquired through the control system of the spacecraft.

[0048] Specifically, the posture dynamics and kinematics equations are:

[0049]

[0050] Among them, q i represents the attitude error quaternion of the i-th spacecraft, i = 1, 2, ..., n, n represents the number of spacecraft in the target spacecraft formation, q i1 Represents the first element of the attitude error, q i2 Represents the second element of the attitude error, q i3 Represents the third element of the attitude error, q i4 Represents the fourth element of attitude error, represents the direction angle of the i-th spacecraft, e1 represents the component of the unit vector e in the horizontal axis direction, e2 represents the component of the unit vector e in the vertical axis direction, e3 represents the component of the unit vector e in the vertical axis direction, Ω(q i ) represents the matrix composed of attitude quaternions, P i represents the angular momentum of the i-th spacecraft, P i =Iω i , I represents the moment of inertia matrix, ω i represents the angular velocity of the i-th spacecraft, represents the derivative of the attitude error quaternion of the i-th spacecraft, represents the derivative of the angular momentum of the i-th spacecraft, u i represents the flywheel output torque of the i-th spacecraft, u i =[u i1 ,u i2 ,u i3 ] T ,u i1 represents the flywheel output torque component of the i-th spacecraft along the first coordinate axis, u i2 represents the flywheel output torque component of the i-th spacecraft along the second coordinate axis, u i3 represents the flywheel output torque component of the i-th spacecraft along the third coordinate axis, Q i represents the angular velocity of the flywheel of the i-th spacecraft, represents the derivative of the angular velocity of the flywheel of the i-th spacecraft, F i represents the moment of inertia matrix of the flywheel of the i-th spacecraft, θ i represents the rotation angle of the flywheel of the i-th spacecraft, θ i =[θ i1 ,θ i2 ,θ i3 ] T ,θ i1 represents the rotation angle of the flywheel of the i-th spacecraft along the first coordinate axis, θ i2 represents the rotation angle of the flywheel of the i-th spacecraft along the second coordinate axis, θ i3 represents the rotation angle of the flywheel of the i-th spacecraft along the third coordinate axis, represents the angular velocity of the flywheel of the i-th spacecraft, P i +Q i =BP i0 , P i0 represents the initial angular momentum of the system, B represents the system transformation matrix, ω i * Represents the angular velocity component matrix of the i-th spacecraft:

[0051]

[0052] Among them, ω i1 represents the angular velocity component of the i-th spacecraft along the first coordinate axis, ω i2 represents the angular velocity component of the i-th spacecraft along the second coordinate axis, ω i3 represents the angular velocity component of the i-th spacecraft along the third coordinate axis.

[0053] It should be noted that the first, second, and third coordinate axes are all coordinate axes in the body coordinate system of the spacecraft. The system transformation matrix B is specifically:

[0054]

[0055] For example, computer software such as MATLAB can be used to construct the attitude dynamics and kinematics equations of the spacecraft.

[0056] It is worth mentioning that the attitude dynamics and kinematics equations are constructed based on the flywheel angular momentum of the spacecraft, so that the dynamic information of the flywheel is coupled into the attitude dynamics and kinematics equations, thereby improving the accuracy and rationality of the equations in describing the spacecraft state.

[0057] In step 12, for each spacecraft, the Hamiltonian energy function of the spacecraft is obtained according to the angular velocity of the spacecraft and the angular velocity of the flywheel, and the navigator estimated state of the spacecraft is calculated according to the attitude dynamics and kinematic equations of all spacecraft.

[0058] The Hamiltonian energy function described above describes the spacecraft's angular kinetic energy and the flywheel's angular kinetic energy at the current moment. Specifically, the spacecraft's angular kinetic energy is calculated based on the spacecraft's angular velocity, attitude, and the flywheel's angular velocity at the current moment, as well as the relationships between the various parameters reflected in the attitude dynamics and kinematic equations. The navigator's estimated state describes the spacecraft's desired state.

[0059] In some embodiments of the present application, the steps of obtaining the Hamiltonian energy function of the spacecraft based on the angular velocity of the spacecraft and the angular velocity of the flywheel, and calculating the navigator estimated state of the spacecraft based on the attitude dynamics and kinematic equations of all spacecraft are specifically as follows:

[0060] The first step is to obtain the Hamiltonian energy function of the spacecraft based on the angular velocity of the spacecraft and the angular velocity of the flywheel.

[0061] Specifically, the above Hamiltonian energy function is:

[0062]

[0063] Among them, H i (x i ) represents the Hamiltonian function value of the i-th spacecraft, x i represents the state of the i-th spacecraft, x i =(q i , P i , Q i ) T , I i represents the moment of inertia matrix of the i-th spacecraft.

[0064] In the second step, the navigator-estimated states of the spacecraft are calculated based on the attitude dynamics and kinematic equations of all spacecraft.

[0065] Specifically, through the formula:

[0066]

[0067] Calculate the navigator estimated state x of the i-th spacecraft i R .

[0068] in, represents the derivative of the navigator's estimated state of the i-th spacecraft, b iirepresents the communication relationship between the i-th spacecraft and the pilot spacecraft in the target spacecraft formation, λ represents the degree of dependence between the i-th spacecraft and the pilot spacecraft, and x R Indicates the state of the pilot spacecraft, x R =(q R , P R , Q R ) T ,q R Represents the attitude error quaternion of the pilot spacecraft, P R represents the angular momentum of the pilot spacecraft, Q R is the angular velocity of the pilot spacecraft's flywheel, represents the state derivative of the pilot spacecraft, a ij represents the connection relationship between the i-th spacecraft and the j-th spacecraft, represents the derivative of the navigator's estimated state of the jth spacecraft, x j R represents the navigator estimated state of the j-th spacecraft, i = 1, 2, ..., n, and n represents the number of spacecraft in the target spacecraft formation.

[0069] It should be noted that when there is a communication relationship between the i-th spacecraft and the pilot spacecraft, b ii ≠0, when there is no communication relationship between the i-th spacecraft and the pilot spacecraft, b ii = 0, when there is a connection between the i-th spacecraft and the j-th spacecraft, a ij ≠0, when there is no connection between the i-th spacecraft and the j-th spacecraft, a ij = 0. When the i-th spacecraft is the pilot spacecraft, the pilot estimated state is not calculated using the above calculation formula, and the pilot estimated state of the pilot spacecraft is the preset expected state.

[0070] For example, the above steps can be executed using computer software such as MATLAB to obtain the Hamiltonian energy function and the navigator estimated state.

[0071] It is worth mentioning that the navigator's estimated state obtained based on accurate and reasonable attitude dynamics and kinematic equations is highly accurate and can provide the spacecraft with an accurate expected state.

[0072] Step 13: Construct the PH equation of the target spacecraft formation based on the Hamiltonian energy function and attitude dynamics and kinematic equations of all spacecraft.

[0073] The above PH equation is used to describe the relationship between the system controller and the attitudes of all spacecraft in the target spacecraft formation.

[0074] In some embodiments of the present application, the steps of constructing the PH equation of the target spacecraft formation based on the Hamiltonian energy function and attitude dynamics and kinematic equations of all spacecraft are specifically as follows:

[0075] The first step is to construct the Hamiltonian energy function of the formation system of the target spacecraft formation based on the Hamiltonian energy function of all spacecraft.

[0076] Specifically, the Hamiltonian energy function of the formation system is:

[0077]

[0078] in, represents the Hamiltonian energy function value of the formation system, X represents the state of all spacecraft in the target spacecraft formation, x i ∈X,I n represents the n-order identity matrix, represents the Kronecker product, and N represents the parameter matrix:

[0079]

[0080] Among them, 0 3×3 represents a zero matrix with three rows and three columns, 0 3×4 Represents a zero matrix with three rows and four columns, 0 4×3 represents a zero matrix with four rows and three columns, 0 4×4 represents a zero matrix with four rows and four columns, I represents the moment of inertia matrix of all spacecraft, and F represents the moment of inertia matrix of the flywheel of all spacecraft.

[0081] It should be noted that, according to the characteristics of the PH control system, that is, a system composed of multiple PH systems is still a PH system, it can be deduced that the Hamiltonian energy function of the formation system of a spacecraft formation composed of multiple spacecraft can be obtained by the accumulation of the Hamiltonian energy functions of all spacecraft.

[0082] In the second step, the PH equation of the target spacecraft formation is obtained based on the Hamiltonian energy function of the formation system and the attitude dynamics and kinematic equations of all spacecraft.

[0083] Specifically, the pH equation is:

[0084]

[0085] in, represents the derivatives of the states of all spacecraft in the target spacecraft formation, J represents the interconnection matrix, J = diag[J1, J2, ..., J n ], J1 represents the interconnection matrix of the first spacecraft, J2 represents the interconnection matrix of the second spacecraft, and J n represents the interconnection matrix of the nth spacecraft, represents the partial derivative of the Hamiltonian energy function of the formation system, I n represents the n-order identity matrix, G represents the first constant matrix, U represents the system controller of the target spacecraft formation, U=diag[u1,u2,...,u n ], u1 represents the flywheel output torque of the first spacecraft, u2 represents the flywheel output torque of the second spacecraft, u n represents the flywheel output torque of the nth spacecraft, and Y represents the spacecraft output.

[0086] It should be noted that the interconnection matrix between the first constant matrix G and the i-th spacecraft is:

[0087] G=[0 4×3 I3I3] T

[0088]

[0089] Among them, Ω(q i ) represents the value of the relationship matrix between the attitude and angular velocity of the i-th spacecraft, ω i * represents the angular velocity component matrix of the i-th spacecraft, F represents the moment of inertia matrix of the flywheels of all spacecraft, P i * represents the angular momentum component matrix of the spacecraft.

[0090] For example, the PH equation of the target spacecraft formation can be obtained by running the above steps using computer software such as MATLAB.

[0091] Step 14: construct the expected Hamiltonian function of the target spacecraft formation based on the attitude dynamics and kinematic equations of all spacecraft and the navigator-estimated states of all spacecraft.

[0092] The above expected Hamiltonian function is used to describe the attitude error of each spacecraft and the relative attitude error between every two spacecraft.

[0093] Specifically, the expected Hamiltonian function is:

[0094]

[0095] in, represents the expected Hamiltonian function value, represents the attitude error between the state of the i-th spacecraft and the state estimated by the navigator of the i-th spacecraft, represents the relative attitude error between the state of the i-th spacecraft and the state of the j-th spacecraft, and M and N both represent weight coefficient matrices:

[0096]

[0097] For example, the expected Hamiltonian function of the target spacecraft formation can be constructed using computer software such as Matlab.

[0098] It is worth mentioning that the accuracy of the expected Hamiltonian function constructed based on the accurate expected state of the spacecraft provided by the navigator's estimated state is improved, which enables the accurate description of the attitude error of each spacecraft and the relative attitude error between every two spacecraft, further improving the accuracy of the error description of the spacecraft formation and the robustness of the expected Hamiltonian function.

[0099] Step 15: According to the PH equation and the expected Hamiltonian function, the IDA-PBC algorithm is used to calculate the system controller equation of the target spacecraft formation, and the control law equation of each spacecraft is obtained based on the system controller equation.

[0100] Interconnection and Damping Assignment-Passivity-Based Control (IDA-PBC) is a method specifically designed for designing control laws for PH systems. It uses state feedback to modify the system's interconnection and damping matrices, thereby configuring a positive energy function that can function as a Lyapunov function for a closed-loop system. The system transformed using the IDA-PBC algorithm remains a PH system, and the control law can be solved by configuring the desired interconnection and damping matrices. The IDA-PBC algorithm can transform the spacecraft formation attitude error system into a passive output form, improving the system's robustness.

[0101] In some embodiments of the present application, the steps of calculating the system controller equation of the target spacecraft formation using the IDA-PBC algorithm based on the PH equation and the expected Hamiltonian function, and obtaining the control law equation of each spacecraft based on the system controller equation are specifically as follows:

[0102] In the first step, a matching equation is constructed based on the expected Hamiltonian function and the PH equation.

[0103] Specifically, the matching equation is:

[0104]

[0105] Among them, I n represents the n-order identity matrix, represents the Kronecker product, G ⊥ represents the second constant matrix, J represents the interconnection matrix, represents the partial derivative of the Hamiltonian energy function of the formation system, J dDenotes the system expected interconnection matrix, D d represents the system's expected damping matrix, represents the partial derivative of the expected Hamiltonian function, and X represents the state system of the target spacecraft formation.

[0106] In the second step, the matching equation is solved to obtain the relationship matrix between the attitude and angular velocity of each spacecraft.

[0107] Specifically, according to G ⊥ G=0, and G ⊥ Full rank, G is acceptable ⊥ =[I4 0 4×3 0 4×3 ], and let J d and D d The elements in are:

[0108]

[0109]

[0110] in, represents the component matrix of the first row and first column of the desired interconnection matrix of the i-th spacecraft, represents the component matrix of the first row and second column of the desired interconnection matrix of the i-th spacecraft, represents the component matrix of the first row and third column of the desired interconnection matrix of the i-th spacecraft, represents the component matrix of the second row and second column of the desired interconnection matrix of the i-th spacecraft, represents the component matrix of the second row and third column of the desired interconnection matrix of the i-th spacecraft, represents the component matrix of the third row and third column of the desired interconnection matrix of the i-th spacecraft, represents the component matrix of the first row and first column of the desired damping matrix of the i-th spacecraft, represents the component matrix of the first row and third column of the desired damping matrix of the i-th spacecraft, represents the component matrix of the second row and second column of the desired damping matrix of the i-th spacecraft, represents the component matrix in the third row and third column of the desired damping matrix of the i-th spacecraft.

[0111] Substituting the above parameters into the matching equation and solving it, we get the relationship matrix between the attitude and angular velocity of the spacecraft:

[0112]

[0113] Among them, Ω(q i ) represents the value of the relationship matrix between the attitude and angular velocity of the i-th spacecraft, ω irepresents the angular velocity of the i-th spacecraft, represents the difference in attitude error quaternion between the i-th spacecraft and the j-th spacecraft, represents the component matrix of the first row and first column of the desired interconnection matrix of the i-th spacecraft, The first row and first column of the desired damping matrix of the i-th spacecraft is represented by the component matrix, M 11 Represents the element in the first row and first column of the weight coefficient matrix M, N 11 Represents the element in the first row and first column of the weight coefficient matrix N, l ii represents the sum of all connection relationships of the i-th spacecraft, The component matrix of the first row and second column of the expected interconnection matrix of the i-th spacecraft, M 22 Represents the element in the second row and second column of the weight coefficient matrix M, N 22 Represents the element in the second row and second column of the weight coefficient matrix N, represents the difference in angular momentum between the i-th spacecraft and the j-th spacecraft, represents the component matrix of the first row and third column of the desired interconnection matrix of the i-th spacecraft, The first row and third column of the desired damping matrix of the i-th spacecraft is represented by the component matrix, M 33 Represents the element in the third row and third column of the weight coefficient matrix M, N 33 Represents the element in the third row and third column of the weight coefficient matrix N, represents the difference in angular velocity of the flywheel between the i-th spacecraft and the j-th spacecraft.

[0114] It should be noted that according to q i 、ω i and θ i The arbitrariness of , the conditions for satisfying the above relationship are: ω id =0, N 22 =0 3×3 , M 11 =N 11 =I4,M 22 =I3,M 33 =N 33 =I3.

[0115] In the third step, the system controller equations of the target spacecraft formation are constructed based on the relationship matrix of all spacecraft.

[0116] Specifically, the system controller equation of the target spacecraft formation is:

[0117]

[0118] Where U represents the system controller of the target spacecraft formation, J d represents the system expected interconnection matrix, J id ∈J d , J id represents the expected interconnection matrix of the i-th spacecraft, D d Denotes the system's desired damping matrix, D id ∈D d , D id represents the expected damping matrix of the i-th spacecraft:

[0119]

[0120] Among them, 0 3×3 represents a zero matrix with three rows and three columns, 0 3×4 Represents a zero matrix with three rows and four columns, 0 4×3 represents a zero matrix with four rows and three columns, 0 4×4 represents a zero matrix with four rows and four columns, k d1 represents the first damping coefficient, k d2 represents the second damping coefficient.

[0121] The fourth step is to obtain the control law equations of each spacecraft based on the system controller equations.

[0122] Specifically, the system controller equation of the target spacecraft formation is derived to obtain the control law equation of each spacecraft. The control law equation is:

[0123]

[0124] Among them, u i represents the flywheel output torque of the i-th spacecraft, represents the attitude error element of the i-th spacecraft, represents the angular momentum error of the i-th spacecraft, represents the angular velocity error of the flywheel of the i-th spacecraft, k d Represents the interconnection coefficient.

[0125] For example, the above steps can be executed using computer software such as MATLAB to obtain the control law equation for each spacecraft in the target spacecraft formation.

[0126] It is worth mentioning that the accuracy of the system controller equation obtained based on the expected Hamiltonian function with high accuracy is improved, and the robustness is increased, thereby improving the rationality and accuracy of the spacecraft control law equation.

[0127] Step 16: For each spacecraft, control the spacecraft using the control law equation of the spacecraft.

[0128] Specifically, for each spacecraft, the angular momentum of the spacecraft at its current position, the angular velocity of the flywheel and other relevant data are substituted into the control law equation of the spacecraft to obtain the target flywheel output torque of the spacecraft, and the flywheel of the spacecraft is controlled according to the target flywheel output torque.

[0129] For example, the target flywheel output torque can be input into the control system of the spacecraft flywheel, and the control system controls the flywheel according to the target control law to adjust the attitude of the spacecraft.

[0130] It is worth mentioning that the attitude dynamics and kinematics equations are constructed based on the flywheel angular momentum of the spacecraft, so that the dynamic information of the flywheel is coupled into the attitude dynamics and kinematics equations, thereby improving the accuracy and rationality of the equations in describing the spacecraft state. The navigator's estimated state obtained based on accurate and reasonable attitude dynamics and kinematics equations is highly accurate, which can provide the spacecraft with an accurate expected state, thereby improving the accuracy of the expected Hamiltonian function. The rationality of the spacecraft control law equation obtained based on the highly accurate expected Hamiltonian function is improved, thereby improving the rationality of the attitude control of the spacecraft formation.

[0131] Next, the attitude control method of the spacecraft formation of the present application is exemplified.

[0132] A five-spacecraft formation is used as the target spacecraft formation. Each spacecraft has a flywheel on each axis, forming a flywheel cluster. The control objective is to control each spacecraft in the formation from an initial attitude to the same desired attitude under the influence of a bounded environmental disturbance torque. The spacecraft parameters and environmental disturbance torque are shown in Table 1.

[0133]

[0134] Table 1

[0135] In the simulation example, the distributed control of the spacecraft formation adopts a fixed directed topology connection, and the fourth spacecraft is the pilot spacecraft, such as Figure 2 As shown, the spacecraft are numbered 1, 2, 3, 4, and 5, polygons represent spacecraft, and lines with arrows represent the connection relationship between spacecraft.

[0136] Initial attitude of each spacecraft and expected posture for:

[0137]

[0138] Among them, t d represents the desired phase, t d =5,Δ i =10(i-1), i=1, 2,...,5.

[0139] The above spacecraft formation is simulated and controlled by adopting the attitude cooperative control method of this application, the method provided by this application but removing the flywheel related terms in the formula, and the virtual structure control method respectively, and the damping coefficient k is used. d =6, interconnection coefficient k d =1, the simulation results are shown in Table 2.

[0140]

[0141] Table 2

[0142] Among them, Eq1, Eq2, Eq3, and Eq4 are attitude error quaternions.

[0143] It can be seen that under the control considering the flywheel dynamics, that is, the control method of the present application, the attitude error convergence time of the spacecraft is faster.

[0144] The spacecraft's attitude trajectory is as follows Figure 3 As shown in the figure, the horizontal axis represents time (Time), the unit is second (s), and the vertical axis represents Figure 3 (a) is the change curve of the first component q1 in the spacecraft attitude quaternion, Figure 3 (b) is the variation curve of the second component q2 in the spacecraft attitude quaternion, Figure 3 (c) is the variation curve of the third component q3 in the spacecraft attitude quaternion, Figure 3 (d) is the variation curve of the fourth component q4 in the spacecraft attitude quaternion, the solid line S i The i-th spacecraft controlled by the method of this application, i=1, 2, ..., 5, the dotted line Sn i The point line Sc is the i-th spacecraft controlled without considering the flywheel. i The virtual structure control method is used to control the i-th spacecraft. As can be seen from the figure, the control method of the present application can track the desired attitude more quickly and maintain stability.

[0145] The instantaneous graph of the spacecraft's attitude error is as follows: Figure 4 As shown, the steady-state diagram is Figure 5 As shown, Figure 4 and Figure 5 The horizontal axis represents time (Tim e ), the unit is seconds (s), Figure 4 (a) and Figure 5 (a) represents the variation curve of the first dimension of the attitude error Eq1, Figure 4 (b) and Figure 5 (b) represents the variation curve of the second dimension of the attitude error Eq2, Figure 4 (c) and Figure 5(c) represents the variation curve of the third dimension of the attitude error Eq3, Figure 4 (d) and Figure 5 (d) represents the change curve of the fourth dimension of the attitude error Eq4, and Figure 4 and Figure 5 Middle solid line SS i The dashed line Sn-Sn is the attitude error curve of the i-th spacecraft under the control of the method of this application. i is the attitude error curve of the i-th spacecraft under the control method without considering the flywheel, and the dotted line Sc-Sc i is the attitude error curve of the i-th spacecraft under the control of the virtual structure control method.

[0146] The instantaneous diagram of the spacecraft's output torque is as follows: Figure 6 As shown, the steady-state diagram is Figure 7 As shown, Figure 6 and Figure 7 The horizontal axis represents time (Tim e ), the unit is seconds (s), the vertical axis represents the value of output torque, the unit is Nm, Figure 6 (a) and Figure 7 (a) represents the curve of the change of the flywheel output torque on the horizontal axis, Figure 6 (b) and Figure 7 (b) shows the change curve of flywheel output torque on the vertical axis, Figure 6 (c) and Figure 7 (c) represents the curve of the change of the flywheel output torque of the vertical axis, and Figure 6 and Figure 7 In the middle, the solid line S i The dashed line Sn is the i-th spacecraft controlled by the method of this application. i The point line Sc is the i-th spacecraft controlled without considering the flywheel. i is the i-th spacecraft controlled by the virtual structure control method.

[0147] The instantaneous graph of the spacecraft's relative attitude error is as follows: Figure 8 As shown, the steady-state diagram is Figure 9 As shown, Figure 8 and Figure 9 The horizontal axis represents time (Tim e ), the unit is seconds (s), the vertical axis represents the value of the relative attitude error, Figure 8 (a) and Figure 9 (a) represents the variation curve of the first dimension of relative attitude error Eq1, Figure 8 (b) and Figure 9 (b) represents the variation curve of the second dimension of relative attitude error Eq2, Figure 8 (c) and Figure 9 (c) represents the variation curve of the third dimension of relative attitude error Eq3, Figure 8(d) and Figure 9 (d) represents the variation curve of the fourth dimension of the relative attitude error Eq4, and Figure 8 and Figure 9 In the figure, the five solid lines represent the relative attitude errors between the spacecraft under the control of the method of the present application, which are the relative attitude error curves S1-S4 between the 1st spacecraft and the 4th spacecraft, the relative attitude error curves S2-S4 between the 2nd spacecraft and the 4th spacecraft, the relative attitude error curves S3-S4 between the 3rd spacecraft and the 4th spacecraft, the relative attitude error curves S4-S4 between the 4th spacecraft and the 4th spacecraft, and the relative attitude error curves S5-S4 between the 5th spacecraft and the 4th spacecraft; the five dotted lines represent the relative attitude errors between the spacecraft under the control method without considering the flywheel, which are the relative attitude error curves Sn1-Sn4 between the 1st spacecraft and the 4th spacecraft, the relative attitude error curves Sn2-Sn4 between the 2nd spacecraft and the 4th spacecraft, the relative attitude error curves Sn3-Sn4 between the 3rd spacecraft and the 4th spacecraft, The relative attitude error curve Sn3-Sn4 between the spacecraft and the fourth spacecraft, the relative attitude error curve Sn4-Sn4 between the fourth spacecraft and the fourth spacecraft, and the relative attitude error curve Sn5-Sn4 between the fifth spacecraft and the fourth spacecraft; the five dotted lines represent the relative attitude errors between spacecraft under the control of the virtual structure control method, namely the relative attitude error curve Sc1-Sc4 between the first spacecraft and the fourth spacecraft, the relative attitude error curve Sc2-Sc4 between the second spacecraft and the fourth spacecraft, the relative attitude error curve Sc3-Sc4 between the third spacecraft and the fourth spacecraft, the relative attitude error curve Sc4-Sc4 between the fourth spacecraft and the fourth spacecraft, and the relative attitude error curve Sc5-Sc4 between the fifth spacecraft and the fourth spacecraft.

[0148] It can be seen that under the control of the attitude collaborative control method considering the flywheel of the spacecraft provided in this application, the convergence speed of the spacecraft's attitude error and relative attitude error is faster than the other two methods, and the accuracy and robustness of the spacecraft's attitude control are high.

[0149] The following is an exemplary description of the spacecraft formation device coupled with flywheel dynamics provided by the present application.

[0150] like Figure 10 As shown, an embodiment of the present application provides a spacecraft formation attitude collaborative control device coupled with flywheel dynamics. The spacecraft formation attitude collaborative control device 1000 coupled with flywheel dynamics includes:

[0151] Acquisition module 1001 is used to obtain the current angular velocity, attitude, and flywheel angular velocity of each spacecraft in the target spacecraft formation, and construct the attitude dynamics and kinematics equations for each spacecraft based on the angular velocity, attitude, and flywheel angular velocity of each spacecraft. For spacecraft using flywheels, the attitude dynamics and kinematics equations are used to describe the spacecraft's attitude information, flywheel information, and control information.

[0152] A first calculation module 1002 is configured to obtain, for each spacecraft, a Hamiltonian energy function based on the spacecraft's angular velocity and the angular velocity of its flywheel, and calculate the navigator-estimated state of the spacecraft based on the attitude dynamics and kinematic equations of all spacecraft. The Hamiltonian energy function is used to describe the angular kinetic energy of the spacecraft and the angular kinetic energy of the flywheel at a current moment, and the navigator-estimated state is used to describe the desired state of the spacecraft.

[0153] The first construction module 1003 is used to construct the PH equation of the target spacecraft formation based on the Hamiltonian energy function and the attitude dynamics and kinematics equations of all spacecraft; the PH equation is used to describe the relationship between the system controller of the target spacecraft formation and the attitudes of all spacecraft;

[0154] The second construction module 1004 is configured to construct an expected Hamiltonian function for the target spacecraft formation based on the attitude dynamics and kinematics equations of all spacecraft and the navigator-estimated states of all spacecraft. The expected Hamiltonian function is used to describe the attitude error of each spacecraft and the relative attitude error between every two spacecraft.

[0155] The second calculation module 1005 is configured to calculate the system controller equation of the target spacecraft formation using the IDA-PBC algorithm according to the PH equation and the expected Hamiltonian function, and obtain the control law equation of each spacecraft based on the system controller equation;

[0156] The control module 1006 is used to control each spacecraft using the control law equation of the spacecraft.

[0157] It should be noted that the information interaction, execution process, etc. between the above-mentioned devices / units are based on the same concept as the method embodiment of this application. Their specific functions and technical effects can be found in the method embodiment section and will not be repeated here.

[0158] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0159] like Figure 11 As shown, an embodiment of the present application provides a terminal device, and the terminal device D10 of this embodiment includes: at least one processor D100 ( Figure 11 Only one processor is shown in the figure), a memory D101, and a computer program D102 stored in the memory D101 and executable on the at least one processor D100, wherein the processor D100 implements the steps of any of the above method embodiments when executing the computer program D102.

[0160] Specifically, when the processor D100 executes the computer program D102, it obtains the angular velocity, attitude and angular velocity of the flywheel of each spacecraft in the target spacecraft formation at the current moment, and constructs the attitude dynamics and kinematic equations of each spacecraft based on the angular velocity, attitude and angular velocity of the flywheel of each spacecraft. Then, for each spacecraft, the Hamiltonian energy function of the spacecraft is obtained based on the angular velocity of the spacecraft and the angular velocity of the flywheel, and the navigator estimated state of the spacecraft is calculated based on the attitude dynamics and kinematic equations of all spacecraft. Then, the PH equation of the target spacecraft formation is constructed based on the Hamiltonian energy function and the attitude dynamics and kinematic equations of all spacecraft. Then, based on the attitude dynamics and kinematic equations of all spacecraft and the navigator estimated state of all spacecraft, the expected Hamiltonian function of the target spacecraft formation is constructed. Then, based on the PH equation and the expected Hamiltonian function, the system controller equation of the target spacecraft formation is calculated using the IDA-PBC algorithm, and the control law equation of each spacecraft is obtained based on the system controller equation. Finally, for each spacecraft, the control law equation of the spacecraft is used to control the spacecraft. Among them, the attitude dynamics and kinematic equations are constructed according to the flywheel angular momentum of the spacecraft, so that the dynamic information of the flywheel is coupled into the attitude dynamics and kinematic equations, thereby improving the accuracy and rationality of the equations in describing the spacecraft state. The navigator's estimated state obtained based on accurate and reasonable attitude dynamics and kinematic equations is highly accurate, which can provide the spacecraft with an accurate expected state, thereby improving the accuracy of the expected Hamiltonian function. The rationality of the spacecraft control law equation obtained according to the highly accurate expected Hamiltonian function is improved, thereby improving the rationality of the attitude control of the spacecraft formation, and can make the error convergence speed faster and the configuration more stable.

[0161] The processor D100 may be a central processing unit (CPU), or may be another general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. A general-purpose processor may be a microprocessor or any conventional processor.

[0162] In some embodiments, the memory D101 may be an internal storage unit of the terminal device D10, such as a hard disk or memory of the terminal device D10. In other embodiments, the memory D101 may also be an external storage device of the terminal device D10, such as a plug-in hard disk, a smart memory card (SMC, SmartMedia Card), a secure digital (SD, Secure Digital) card, a flash card, etc. equipped on the terminal device D10. Furthermore, the memory D101 may also include both an internal storage unit of the terminal device D10 and an external storage device. The memory D101 is used to store an operating system, an application program, a boot loader (BootLoader), data, and other programs, such as the program code of the computer program. The memory D101 may also be used to temporarily store data that has been output or is to be output.

[0163] An embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps in the above-mentioned various method embodiments can be implemented.

[0164] An embodiment of the present application provides a computer program product. When the computer program product is run on a terminal device, the terminal device can implement the steps in the above-mentioned method embodiments when executing the computer program product.

[0165] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present application implements all or part of the process steps in the above-mentioned method embodiments by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When executed by a processor, the computer program can implement the steps of each of the above-mentioned method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file, or some intermediate form. The computer-readable medium can at least include: any entity or device capable of carrying the computer program code to the apparatus / terminal device for the method / terminal device for the coordinated attitude control of spacecraft formations coupled with flywheel dynamics, a recording medium, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signals, telecommunication signals, and software distribution media. Examples include USB flash drives, mobile hard drives, magnetic disks, or optical disks. In some jurisdictions, based on legislation and patent practice, computer-readable media cannot be electric carrier signals or telecommunication signals.

[0166] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0167] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0168] The above is a preferred embodiment of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles described in the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for coordinated control of spacecraft formation attitude coupled with flywheel dynamics, characterized in that: include: Obtaining the current angular velocity, attitude, and flywheel angular velocity of each spacecraft in the target spacecraft formation, and constructing attitude dynamics and kinematics equations for each spacecraft based on the angular velocity, attitude, and flywheel angular velocity of each spacecraft; wherein the spacecraft utilizes a flywheel, and the attitude dynamics and kinematics equations are used to describe the attitude information, flywheel information, and control information of the spacecraft; For each spacecraft, respectively, a Hamiltonian energy function is obtained based on the angular velocity of the spacecraft and the angular velocity of the flywheel, and a navigator-estimated state of the spacecraft is calculated based on the attitude dynamics and kinematic equations of all spacecraft; the Hamiltonian energy function is used to describe the angular kinetic energy of the spacecraft and the angular kinetic energy of the flywheel at a current moment, and the navigator-estimated state is used to describe the desired state of the spacecraft; Constructing a PH equation for the target spacecraft formation based on the Hamiltonian energy function and attitude dynamics and kinematics equations of all spacecraft; the PH equation is used to describe the relationship between the system controller of the target spacecraft formation and the attitudes of all spacecraft; constructing an expected Hamiltonian function for the target spacecraft formation based on attitude dynamics and kinematic equations of all spacecraft and navigator-estimated states of all spacecraft; the expected Hamiltonian function is used to describe the attitude error of each spacecraft and the relative attitude error between every two spacecraft; According to the PH equation and the desired Hamiltonian function, the system controller equation of the target spacecraft formation is calculated using the IDA-PBC algorithm, and the control law equation of each spacecraft is obtained based on the system controller equation; For each of the spacecraft, the control law equation of the spacecraft is used to control the spacecraft.

2. The spacecraft formation attitude coordinated control method according to claim 1, characterized in that: The posture dynamics and kinematics equations are: Among them, q i represents the attitude error quaternion of the i-th spacecraft, i = 1, 2, ..., n, n represents the number of spacecraft in the target spacecraft formation, q i1 Represents the first element of the attitude error, q i2 Represents the second element of the attitude error, q i3 Represents the third element of the attitude error, q i4 Represents the fourth element of attitude error, represents the direction angle of the i-th spacecraft, e1 represents the component of the unit vector e in the horizontal axis direction, e2 represents the component of the unit vector e in the vertical axis direction, e3 represents the component of the unit vector e in the vertical axis direction, Ω(q i ) represents the matrix composed of attitude quaternions, P i represents the angular momentum of the i-th spacecraft, P i =Iω i , I represents the moment of inertia matrix, ω i represents the angular velocity of the i-th spacecraft, represents the derivative of the attitude error quaternion of the i-th spacecraft, represents the derivative of the angular momentum of the i-th spacecraft, u i represents the flywheel output torque of the i-th spacecraft, u i =[u i1 ,u i2 ,u i3 ] T ,u i1 represents the flywheel output torque component of the i-th spacecraft along the first coordinate axis, u i2 represents the flywheel output torque component of the i-th spacecraft along the second coordinate axis, u i3 represents the flywheel output torque component of the i-th spacecraft along the third coordinate axis, Q i represents the angular velocity of the flywheel of the i-th spacecraft, represents the derivative of the angular velocity of the flywheel of the i-th spacecraft, F i represents the moment of inertia matrix of the flywheel of the i-th spacecraft, θ i represents the rotation angle of the flywheel of the i-th spacecraft, θ i =[θ i1 ,θ i2 ,θ i3 ] T ,θ i1 represents the rotation angle of the flywheel of the i-th spacecraft along the first coordinate axis, θ i2 represents the rotation angle of the flywheel of the i-th spacecraft along the second coordinate axis, θ i3 represents the rotation angle of the flywheel of the i-th spacecraft along the third coordinate axis, represents the angular velocity of the flywheel of the i-th spacecraft, P i +Q i =BP i0 , P i0 represents the initial angular momentum of the system, B represents the system transformation matrix, ω i * Represents the angular velocity component matrix of the i-th spacecraft: Among them, ω i1 represents the angular velocity component of the i-th spacecraft along the first coordinate axis, ω i2 represents the angular velocity component of the i-th spacecraft along the second coordinate axis, ω i3 represents the angular velocity component of the i-th spacecraft along the third coordinate axis.

3. The spacecraft formation attitude coordinated control method according to claim 2, characterized in that: The Hamiltonian energy function is: Among them, H i (x i ) represents the Hamiltonian function value of the i-th spacecraft, x i represents the state of the i-th spacecraft, x i =(q i ,P i ,Q i ) T , I i represents the moment of inertia matrix of the i-th spacecraft.

4. The spacecraft formation attitude coordinated control method according to claim 1, characterized in that: The calculating the navigator estimated state of the spacecraft according to the attitude dynamics and kinematic equations of all spacecraft includes: By formula: Calculate the navigator estimated state of the i-th spacecraft in, represents the derivative of the navigator's estimated state of the i-th spacecraft, b ii represents the communication relationship between the i-th spacecraft and the pilot spacecraft in the target spacecraft formation, λ represents the degree of dependence between the i-th spacecraft and the pilot spacecraft, and x R Indicates the state of the pilot spacecraft, x R =(q R ,P R ,Q R ) T ,q R represents the attitude error quaternion of the pilot spacecraft, P R represents the angular momentum of the pilot spacecraft, Q R represents the angular velocity of the flywheel of the pilot spacecraft, represents the state derivative of the pilot spacecraft, a ij represents the connection relationship between the i-th spacecraft and the j-th spacecraft, represents the derivative of the navigator's estimated state of the j-th spacecraft, represents the navigator estimated state of the j-th spacecraft, i=1, 2, ..., n, and n represents the number of spacecraft in the target spacecraft formation.

5. The spacecraft formation attitude coordinated control method according to claim 3, characterized in that: The PH equation of the target spacecraft formation is constructed based on the Hamiltonian energy function and attitude dynamics and kinematic equations of all spacecraft, including: Constructing a Hamiltonian energy function of a formation system of the target spacecraft formation according to the Hamiltonian energy functions of all spacecraft; The PH equation of the target spacecraft formation is obtained based on the Hamiltonian energy function of the formation system and the attitude dynamics and kinematic equations of all spacecraft.

6. The spacecraft formation attitude coordinated control method according to claim 5, characterized in that: The Hamiltonian energy function of the formation system is: in, represents the Hamiltonian energy function value of the formation system, X represents the state of all spacecraft in the target spacecraft formation, x i ∈X,I n represents the n-order identity matrix, represents the Kronecker product, Represents the parameter matrix: Among them, 0 3×3 represents a zero matrix with three rows and three columns, 0 3×4 Represents a zero matrix with three rows and four columns, 0 4×3 represents a zero matrix with four rows and three columns, 0 4×4 represents a zero matrix with four rows and four columns, I represents the moment of inertia matrix of all spacecraft, and F represents the moment of inertia matrix of the flywheel of all spacecraft; The pH equation is: in, represents the derivative of the states of all spacecraft in the target spacecraft formation, J represents the interconnection matrix, J = diag[J1, J2, ..., J n ], J1 represents the interconnection matrix of the first spacecraft, J2 represents the interconnection matrix of the second spacecraft, and J n represents the interconnection matrix of the nth spacecraft, represents the partial derivative of the Hamiltonian energy function of the formation system, I n represents the n-order identity matrix, G represents the first constant matrix, U represents the system controller of the target spacecraft formation, U=diag[u1,u2,...,u n ], u1 represents the flywheel output torque of the first spacecraft, u2 represents the flywheel output torque of the second spacecraft, u n represents the flywheel output torque of the n-th spacecraft, and Y represents the spacecraft output.

7. The spacecraft formation attitude coordinated control method according to claim 4, characterized in that: The expected Hamiltonian function is: in, represents the expected Hamiltonian function value, represents the attitude error between the state of the i-th spacecraft and the navigator-estimated state of the i-th spacecraft, represents the relative attitude error between the state of the i-th spacecraft and the state of the j-th spacecraft, and M and N both represent weight coefficient matrices.

8. The spacecraft formation attitude coordinated control method according to claim 7, characterized in that: The system controller equation of the target spacecraft formation is calculated using the IDA-PBC algorithm according to the PH equation and the expected Hamiltonian function, including: Constructing a matching equation according to the expected Hamiltonian function and the PH equation; Solving the matching equation to obtain a relationship matrix between the attitude and angular velocity of each spacecraft; The system controller equation of the target spacecraft formation is constructed based on the relationship matrix of all spacecraft.

9. The spacecraft formation attitude coordinated control method according to claim 8, characterized in that: The matching equation is: Among them, I n represents the n-order identity matrix, represents the Kronecker product, G ⊥ represents the second constant matrix, J represents the interconnection matrix, represents the partial derivative of the Hamiltonian energy function of the formation system, J d Denotes the system expected interconnection matrix, D d represents the system's expected damping matrix, represents the partial derivative of the desired Hamiltonian function, and X represents the state system of the target spacecraft formation; The relationship matrix between the attitude and angular velocity of each spacecraft is: Among them, Ω(q i ) represents the value of the relationship matrix between the attitude and angular velocity of the i-th spacecraft, ω i represents the angular velocity of the i-th spacecraft, represents the difference in attitude error quaternion between the i-th spacecraft and the j-th spacecraft, represents the component matrix of the first row and first column of the desired interconnection matrix of the i-th spacecraft, The first row and first column component matrix of the desired damping matrix of the i-th spacecraft is represented by M 11 Represents the element in the first row and first column of the weight coefficient matrix M, N 11 Represents the element in the first row and first column of the weight coefficient matrix N, l ii represents the sum of all connection relationships of the i-th spacecraft, The component matrix of the first row and second column of the desired interconnection matrix of the i-th spacecraft, M 22 Represents the element in the second row and second column of the weight coefficient matrix M, N 22 Represents the element in the second row and second column of the weight coefficient matrix N, represents the difference in angular momentum between the i-th spacecraft and the j-th spacecraft, represents the component matrix of the first row and third column of the desired interconnection matrix of the i-th spacecraft, The first row and third column component matrix of the desired damping matrix of the i-th spacecraft is represented by M 33 Represents the element in the third row and third column of the weight coefficient matrix M, N 33 Represents the element in the third row and third column of the weight coefficient matrix N, represents the difference in angular velocity of the flywheel between the i-th spacecraft and the j-th spacecraft; The system controller equation of the target spacecraft formation is: Wherein, U represents the system controller of the target spacecraft formation, J d represents the system expected interconnection matrix, J id ∈J d , J id represents the expected interconnection matrix of the i-th spacecraft, D d Denotes the system's desired damping matrix, D id ∈D d , D id represents the expected damping matrix of the i-th spacecraft: Among them, 0 3×3 represents a zero matrix with three rows and three columns, 0 3×4 Represents a zero matrix with three rows and four columns, 0 4×3 represents a zero matrix with four rows and three columns, 0 4×4 represents a zero matrix with four rows and four columns, k d1 represents the first damping coefficient, k d2 represents the second damping coefficient.

10. The spacecraft formation attitude coordinated control method according to claim 9, characterized in that: The control law equation of each of the spacecraft is: Among them, u i represents the flywheel output torque of the i-th spacecraft, represents the attitude error element of the i-th spacecraft, represents the angular momentum error of the i-th spacecraft, represents the angular velocity error of the flywheel of the i-th spacecraft, k d Represents the interconnection coefficient.

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