Real-time planning method for spacecraft attitude maneuver path based on flywheel under multiple constraints

Abstract

The application discloses a spacecraft attitude maneuver path real-time planning method based on a flywheel under multiple constraints, which comprises the following steps: state-dependent decomposition is performed on integrated spacecraft kinematics and dynamics equations containing a flywheel working principle; a performance-power optimization index is designed, and a spacecraft attitude path planning problem of performance-power comprehensive optimization under multiple constraints is constructed; a state-dependent penalty function and a continuous saturation function are designed to process spacecraft angular velocity constraints, flywheel speed saturation constraints and flywheel output torque constraints, the constructed spacecraft attitude path planning problem of performance-power comprehensive optimization under multiple constraints is converted into an augmented state-dependent optimization problem; and a solution of the converted augmented state-dependent optimization problem is obtained by solving a state Riccati equation in real time. The method avoids numerical reconstruction and solvability judgment of attitude dynamics state-dependent decomposition, and realizes real-time planning of a spacecraft attitude maneuver path based on a flywheel under multiple constraints.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft control technology, and in particular relates to a real-time planning method for a spacecraft attitude maneuvering path based on a flywheel under multiple constraints. Background Art

[0002] A wide range of space missions, such as Earth observation and laser communications, place increasingly stringent demands on spacecraft attitude and orientation. First, the most fundamental and crucial goal is to achieve reliable, high-performance attitude control. Second, for safety reasons, spacecraft must consider multiple physical engineering constraints, including angular velocity saturation, flywheel rotational speed saturation, and flywheel output torque saturation. Flywheel assembly operation consumes electrical energy, an extremely precious on-orbit resource. Therefore, designing a flywheel-based real-time spacecraft attitude maneuver path planning method that optimizes performance and energy consumption under multiple constraints, while maintaining the available onboard computing resources, is a highly practical and pressing engineering challenge.

[0003] Regarding the current multi-constraint optimal attitude maneuvering path planning method, Chinese invention patent CN201910707553.3 considers the power limitation during spacecraft attitude maneuvers, establishes performance-energy consumption evaluation indicators, and uses nonlinear model predictive control methods to achieve spacecraft attitude maneuvering path planning and control. However, this method does not consider the spacecraft angular velocity constraints, and the nonlinear model predictive control method cannot achieve real-time planning with existing onboard computing resources. Chinese invention patent CN202110774673.2 considers multiple engineering constraints such as saturation constraints and attitude pointing constraints. The performance indicators can be selected as time optimization, energy optimization, or angular velocity optimization according to requirements. Spacecraft attitude maneuvering path planning is achieved based on polynomial planning methods. However, this method cannot achieve real-time planning with existing onboard computing resources and does not consider energy constraints.

[0004] Regarding the current multi-constrained optimal attitude maneuver path planning methods, it can be concluded that the existing results mainly include the following two problems: First, the design of the existing attitude maneuver path planning strategy does not take into account the optimal performance-power comprehensive performance; Second, the existing attitude maneuver path planning strategy cannot achieve real-time planning under the existing onboard computing resources. Summary of the Invention

[0005] In order to meet the physical constraints existing in the process of on-orbit spacecraft attitude maneuvering, balance the requirements between performance and power, and realize real-time planning under the existing on-board computing resources, the present invention provides a flywheel-based spacecraft attitude maneuvering path real-time planning method under multiple constraints. It covers the entire attitude maneuvering space through the state-dependent decomposition form of the integrated spacecraft dynamic equation, avoids the numerical reconstruction and solvability judgment of the state-dependent decomposition, and further increases the computing efficiency; in addition, the state-dependent penalty function and continuous saturation function designed by the present invention transform the multi-constraint optimization problem into an augmented state-dependent optimization problem, so that the flywheel-based spacecraft can realize the real-time planning of the attitude maneuvering path with the optimal performance-power comprehensive under multiple constraints.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A real-time planning method for a spacecraft attitude maneuvering path based on a flywheel under multiple constraints includes the following steps:

[0008] S1: State-dependent decomposition of the kinematic and dynamic equations of an integrated spacecraft with a flywheel operating principle;

[0009] S2: Design performance-power optimization indicators and construct a spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints;

[0010] S3: Design a state-dependent penalty function and a continuous saturation function to handle spacecraft angular velocity constraints, flywheel speed saturation constraints, and flywheel output torque constraints, thereby transforming the multi-constrained performance-power optimization spacecraft attitude path problem into an augmented state-dependent optimization problem.

[0011] S4: By solving the state Riccati equation in real time, the solution of the augmented state-dependent optimization problem transformed in step S3 is obtained, thereby realizing real-time planning of the spacecraft attitude maneuvering path under constraints.

[0012] Furthermore, the specific process of step S1 is as follows:

[0013] The kinematic and dynamic equations of the integrated spacecraft including the flywheel working principle are established as follows:

[0014]

[0015]

[0016]

[0017]

[0018] in, is the error quaternion describing the spacecraft attitude, where qe0 is the scalar part of the error quaternion, representing the Euler angle, q ev =[q e1 ,q e2 ,q e3 ] T is the three-dimensional vector part of the quaternion, q e1 ,q e2 ,q e3 Represent the three-dimensional directions of the Euler axes and satisfy the constraints The superscript T indicates the vector transpose; ω = [ω1, ω2, ω3] T ∈R 3 is the angular velocity of the spacecraft, ω1, ω2, ω3 represent the angular velocity of the spacecraft along three axes respectively; J s =diag(J s1 ,J s2 ,J s3 )∈R 3×3 is the spacecraft inertia matrix, J s1 ,J s2 ,J s3 Represents the spacecraft's three-axis inertia; Ω=[Ω1,Ω2,Ω3,Ω4] T ∈R 4 is the flywheel speed, Ω1, Ω2, Ω3, Ω4 represent the speed of each flywheel in the flywheel assembly relative to its own shaft; J rw =diag(J rw1 ,J rw2 ,J rw3 ,J rw4 )∈R 4×4 is the flywheel combination inertia matrix, J rw1 ,J rw2 ,J rw3 ,J rw4 Represents the inertia of each flywheel in the flywheel combination, and the superscript -1 represents the inverse of the matrix; τ rw =[τ rw1 ,τ rw2 ,τ rw3 ,τ rw4 ]∈R 4 is the flywheel execution torque, τ rw1 ,τ rw2 ,τ rw3 ,τ rw4 Respectively represent the execution torque of each flywheel in the flywheel combination;

[0019] q ev The skew antisymmetric matrix is ​​as follows:

[0020]

[0021] ω × is the skew antisymmetric matrix of ω, and its specific form is as follows:

[0022]

[0023] A rw is the projection matrix of the flywheel combination, and its specific form is as follows:

[0024]

[0025] Define the state variable x = [q v ,ω,Ω] T , the state-dependent decomposition of the integrated spacecraft kinematics and dynamics equations is performed, and its specific form is as follows:

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] x∈Δ3={q ev =0 3×1 &ω≠0 3×1};

[0032]

[0033]

[0034] Among them, Δ1(q), Δ2(q), Δ3(q), and Δ4(q) represent different neighborhoods with different state-dependent decomposition forms, and satisfy I3 is the 3rd order identity matrix; 0 3×3 , 0 4×4 , 0 3×4 and 0 4×3 They represent the 3rd-order zero matrix, the 4th-order zero matrix, the 3-row 4-column zero matrix, and the 4-row 3-column zero matrix respectively; α1 to α5 are constant matrices; J a =52.4600.

[0035] Formula (8)-Formula (11) can be written in the following compact form:

[0036]

[0037] Where x = [q v ,ω,Ω] Tis the state variable, is the first-order derivative of x; A x ={A x1 ,A x2 ,A x3 ,A x4} and B x is the state dependency matrix and has the following form:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Furthermore, the specific process of step S2 is as follows:

[0044] Design performance-power optimization indicators are as follows:

[0045] J=J1+kJ2 (13)

[0046]

[0047]

[0048] Among them, J is the performance-electricity evaluation index, J1 is the performance evaluation index, and J2 is the electric energy evaluation index; Q q ∈R 3×3 , Q ω ∈R 3×3 , K∈R 4×4 、R c ∈R 4×4 、R f ∈R 4×4 are weight matrices, and k is a weight constant. In particular, R f =K=βI4, where R is the armature resistance of the flywheel DC motor, K T is the torque constant of the flywheel DC motor, β is the flywheel viscous friction coefficient, and I4 is the fourth-order unit matrix.

[0049] Consider the following physical constraints during spacecraft attitude maneuvers:

[0050] (1) Sensor measurement constraints: To ensure that the spacecraft angular velocity is within the sensor measurement range, the spacecraft angular velocity must meet the following constraints:

[0051]

[0052] in, is the maximum angular velocity allowed for the spacecraft.

[0053] (2) Flywheel constraints: Due to the limitations of the flywheel hardware structure, the flywheel rotation speed and driving torque meet the following saturation constraints:

[0054]

[0055]

[0056] in, They are the maximum allowable flywheel rotation speed and the maximum flywheel execution torque respectively.

[0057] Subject to the above constraints, the spacecraft kinematic and dynamic equations after state-dependent decomposition are considered to construct a spacecraft attitude path planning problem with optimal performance-power under multiple constraints:

[0058]

[0059] Among them, P0 is the spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints.

[0060] Furthermore, the specific process of step S3 is as follows:

[0061] In order to deal with the spacecraft angular velocity constraint and the flywheel speed constraint, the spacecraft angular velocity state dependent penalty function matrix Q is designed respectively. ωc and the flywheel rotation speed state-dependent penalty function matrix Q Ωc :

[0062]

[0063]

[0064] in, is the angular velocity state-dependent penalty function, is the flywheel rotation speed state dependent penalty function. For any variable a and its upper bound The corresponding state-dependent penalty function has the following form:

[0065]

[0066] Where k1, k2, and k3 are constants for designers to choose, ln is the logarithmic function with e as the base, and exp is the exponential function with the natural constant e as the base.

[0067] Based on the above state-dependent penalty function matrix, the problem P0 is expanded to:

[0068]

[0069] Among them, P1 is the spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints after the first augmentation; is the first augmentation optimization indicator; Q x and N s are all weight matrices and have the following form:

[0070]

[0071] To handle input constraints, we first design a continuous saturation input constraint function

[0072]

[0073] Among them, tanh is the tangent function.

[0074] Substitute formula (24) into P1 to replace τ rw , the multi-constraint optimization problem P1 can be written as:

[0075]

[0076] Among them, P2 is the equivalent form of problem P1, that is, the spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints after the second augmentation. Optimize the index for the second augmentation.

[0077] Further introduce integral auxiliary control variables Then problem P2 can be further expanded into an augmented state-dependent optimization problem:

[0078]

[0079] Among them, P3 is the augmented state-dependent optimization problem, For the third augmented state dependency optimization indicator, For the augmented state, and is the augmented state dependency matrix,

[0080]

[0081] and is an augmented weight matrix that satisfies:

[0082]

[0083]

[0084] Furthermore, the specific process of step S4 is as follows:

[0085] Solve the following state Riccati equation in real time:

[0086]

[0087] Among them, P x is the unique solution of the state Riccati equation, and the matrix is ​​symmetric and positive definite;

[0088] Obtain the solution to the augmented state-dependent optimization problem:

[0089]

[0090] Beneficial effects of the present invention:

[0091] 1) The state-dependent decomposition form of the integrated spacecraft dynamics equation proposed in this invention covers the entire attitude maneuver space, avoiding the numerical reconstruction and solvability judgment of the state-dependent decomposition, and further improving the computational efficiency;

[0092] 2) The present invention transforms the flywheel-based spacecraft attitude maneuvering path planning problem considering performance-energy consumption indicators under multiple constraints into an augmented state-dependent optimization problem through the designed state-dependent penalty function matrix and continuous saturation function. The corresponding solution is obtained by solving the state Riccati equation in real time, so that the flywheel-based spacecraft can achieve real-time planning of the performance-electricity comprehensive optimal attitude maneuvering path under multiple constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 This is a flow chart of the real-time planning method for a spacecraft attitude maneuvering path based on a flywheel under multiple constraints of the present invention;

[0094] Figure 2 A diagram showing the change trajectory of the spacecraft error quaternion according to an embodiment of the present invention;

[0095] Figure 3 This is a diagram showing the actual angular velocity change trajectory of a spacecraft according to an embodiment of the present invention;

[0096] Figure 4 This is a diagram showing the actual rotation speed change trajectory of the flywheel according to an embodiment of the present invention;

[0097] Figure 5 This is a diagram showing the actual torque change trajectory of the flywheel according to an embodiment of the present invention. DETAILED DESCRIPTION

[0098] The present invention will be further described below with reference to the accompanying drawings and examples. It should be understood that the examples described below are intended to facilitate understanding of the present invention and do not have any limiting effect on the present invention.

[0099] The present invention provides a real-time planning method for a flywheel-based spacecraft attitude maneuvering path under multiple constraints, comprising: first, performing state-dependent decomposition on the integrated spacecraft kinematic and dynamic equations containing the flywheel working principle; then, designing performance-electric energy optimization indicators, and constructing a spacecraft attitude path planning problem with the best performance-electric energy under multiple constraints; designing a state-dependent penalty function and a continuous saturation function to handle the spacecraft angular velocity constraint, the flywheel speed saturation constraint, and the flywheel output torque constraint, thereby converting the constructed spacecraft attitude path problem with the best performance-electric energy under multiple constraints into an augmented state-dependent optimization problem; finally, by solving the state Riccati equation in real time, obtaining the solution of the converted augmented state-dependent optimization problem, thereby realizing real-time planning of the spacecraft attitude maneuvering path under multiple constraints.

[0100] like Figure 1 As shown, the present invention specifically includes the following steps:

[0101] S1: State-dependent decomposition of the kinematic and dynamic equations of an integrated spacecraft with a flywheel operating principle.

[0102] The kinematic and dynamic equations of the integrated spacecraft including the flywheel working principle are established as follows:

[0103]

[0104]

[0105]

[0106]

[0107] in, is the error quaternion describing the spacecraft attitude, where q e0 is the scalar part of the error quaternion, representing the Euler angle, q ev =[q e1 ,q e2 ,q e3 ] T is the three-dimensional vector part of the quaternion, q e1 ,q e2 ,q e3 Represent the three-dimensional directions of the Euler axes and satisfy the constraints The superscript T indicates the vector transpose; ω = [ω1, ω2, ω3] T ∈R 3 is the angular velocity of the spacecraft, ω1, ω2, ω3 represent the angular velocity of the spacecraft along three axes respectively; J s =diag(J s1 ,J s2 ,J s3 )∈R 3×3is the spacecraft inertia matrix, J s1 ,J s2 ,J s3 Represents the spacecraft's three-axis inertia; Ω=[Ω1,Ω2,Ω3,Ω4] T ∈R 4 is the flywheel speed, Ω1, Ω2, Ω3, Ω4 represent the speed of each flywheel in the flywheel assembly relative to its own shaft; J rw =diag(J rw1 ,J rw2 ,J rw3 ,J rw4 )∈R 4×4 is the flywheel combination inertia matrix, J rw1 ,J rw2 ,J rw3 ,J rw4 Represents the inertia of each flywheel in the flywheel combination, and the superscript -1 represents the inverse of the matrix; τ rw =[τ rw1 ,τ rw2 ,τ rw3 ,τ rw4 ]∈R 4 is the flywheel execution torque, τ rw1 ,τ rw2 ,τ rw3 ,τ rw4 Respectively represent the execution torque of each flywheel in the flywheel combination;

[0108] q ev The skew antisymmetric matrix is ​​as follows:

[0109]

[0110] ω × is the skew antisymmetric matrix of ω, and its specific form is as follows:

[0111]

[0112] A rw is the projection matrix of the flywheel combination, and its specific form is as follows:

[0113]

[0114] In this embodiment, the value is q e (0) = [-0.3620, -0.4356, 0.6597, 0.4940] T ,ω(0)=0 3×1 (rad / s), J s =diag(59.22,40.56,57.60)(kg·m 2),Ω=0 4×1 (rad / s), J rw =0.012I4(kg·m 2 ).

[0115] Define the state variable x = [q v ,ω,Ω] T , the state-dependent decomposition of the integrated spacecraft kinematics and dynamics equations is performed, and its specific form is as follows:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] x∈Δ3={q ev =0 3×1 &ω≠0 3×1};

[0122]

[0123]

[0124] Among them, Δ1(q), Δ2(q), Δ3(q), and Δ4(q) represent different neighborhoods with different state-dependent decomposition forms, and satisfy I3 is the 3rd order identity matrix; 0 3×3 , 0 4×4 , 0 3×4 and 0 4×3 Respectively represent the 3rd order zero matrix, 4th order zero matrix, 3 rows and 4 columns zero matrix and 4 rows and 3 columns zero matrix; α1 to α5 are constant matrices for designers to choose. In this embodiment, the value is α1 = 0.1J a , α2=10 -3 J a , α3=10 -4 J a , α4=10 -3 J a ,α5=1,J a =52.4600.

[0125] Formula (8)-Formula (11) can be written in the following compact form:

[0126]

[0127] Where x = [q v ,ω,Ω] T is the state variable, is the first-order derivative of x, A x ={A x1 ,A x2 ,A x3 ,A x4} and B x is the state dependency matrix and has the following form:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] S2: Design performance-power optimization indicators and construct a spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints.

[0134] Design performance-power optimization indicators are as follows:

[0135] J=J1+kJ2 (13)

[0136]

[0137]

[0138] Among them, J is the performance-electricity evaluation index, J1 is the performance evaluation index, and J2 is the electric energy evaluation index; Q q ∈R 3×3 , Q ω ∈R 3×3 , K∈R 4×4 、R c ∈R 4×4 、R f ∈R 4×4 are weight matrices, and k is a weight constant. In particular, R f =K=βI4, where R is the armature resistance of the flywheel DC motor, K T is the flywheel DC motor torque constant, β is the flywheel viscous friction coefficient, and I4 is the 4th order unit matrix. q =I3, R=1.8(Ω),K T =0.0696(N·m / A), β=4.3×10 -5(N·m / (rad / s)).

[0139] Consider the following physical constraints during spacecraft attitude maneuvers:

[0140] (1) Sensor measurement constraints: To ensure that the spacecraft angular velocity is within the sensor measurement range, the spacecraft angular velocity must meet the following constraints:

[0141]

[0142] in, is the maximum angular velocity allowed for the spacecraft.

[0143] (2) Flywheel constraints: Due to the limitations of the flywheel hardware structure, the flywheel rotation speed and driving torque meet the following saturation constraints:

[0144]

[0145]

[0146] in, are the maximum allowable flywheel rotation speed and the maximum flywheel execution torque respectively.

[0147] Subject to the above constraints, the spacecraft kinematic and dynamic equations after state-dependent decomposition are considered to construct a spacecraft attitude path planning problem with optimal performance-power under multiple constraints:

[0148]

[0149] Among them, P0 is the spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints.

[0150] S3: Design a state-dependent penalty function and a continuous saturation function to handle the spacecraft angular velocity constraints, flywheel speed saturation constraints, and flywheel output torque constraints, thereby transforming the spacecraft attitude path planning problem with the optimal performance-power combination under multiple constraints into an augmented state-dependent optimization problem.

[0151] In order to deal with the spacecraft angular velocity constraint and the flywheel speed constraint, the spacecraft angular velocity state dependent penalty function matrix Q is designed respectively. ωc and the flywheel rotation speed state-dependent penalty function matrix Q Ωc :

[0152]

[0153]

[0154] in, is the angular velocity state-dependent penalty function, is the flywheel rotation speed state dependent penalty function. For any variable a and its upper bound The corresponding state-dependent penalty function has the following form:

[0155]

[0156] Among them, k1, k2, k3 are constants for designers to choose, ln is the logarithmic function with e as the base, and exp is the exponential function with the natural constant e as the base. In this embodiment, the value of k1 is 5×10 2 , k2=10 3 , k3=0.95.

[0157] Based on the above state-dependent penalty function matrix, the problem P0 is expanded to:

[0158]

[0159] Among them, P1 is the spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints after the first augmentation; is the first augmentation optimization indicator; Q x and N s are all weight matrices and have the following form:

[0160]

[0161] To handle input constraints, we first design a continuous saturation input constraint function

[0162]

[0163] Among them, tanh is the tangent function.

[0164] Substitute formula (24) into P1 to replace τ rw , the multi-constraint optimization problem P1 can be written as:

[0165]

[0166] Among them, P2 is the equivalent form of problem P1, that is, the spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints after the second augmentation. Optimize the index for the second augmentation.

[0167] Further introduce integral auxiliary control variables Then problem P2 can be further expanded into an augmented state-dependent optimization problem:

[0168]

[0169] Among them, P3 is the augmented state-dependent optimization problem, For the third augmented state dependency optimization indicator, For the augmented state, and is the augmented state dependency matrix,

[0170]

[0171] and is an augmented weight matrix that satisfies:

[0172]

[0173]

[0174] S4: By solving the state Riccati equation in real time, the solution of the augmented state-dependent optimization problem transformed in step S3 is obtained, thereby realizing real-time planning of the spacecraft attitude maneuvering path under constraints.

[0175] Solve the following state Riccati equation in real time:

[0176]

[0177] Among them, P x is the unique solution of the state Riccati equation, and the matrix is ​​symmetric and positive definite;

[0178] Obtain the solution to the augmented state-dependent optimization problem:

[0179]

[0180] In summary, the present invention can complete the real-time planning of the spacecraft attitude maneuvering path based on the flywheel under multiple constraints through the above steps.

[0181] The spacecraft attitude error quaternion, angular velocity, flywheel rotation speed and flywheel execution torque obtained by the method of the present invention are as follows: Figures 2 to 5 As shown. Figure 2 It can be seen that the error quaternion converges to its nearest equilibrium point, given by Figure 3 , Figure 4 , Figure 5 It can be seen that the physical constraints are fully met during the spacecraft attitude maneuver and the spacecraft attitude path planning task is successfully completed.

[0182] Any matters not described in detail in this specification are prior art known to those skilled in the art. Furthermore, those skilled in the art will appreciate that variations and improvements to the embodiments of the present invention may be made without departing from the inventive concept of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A real-time planning method for spacecraft attitude maneuvering path based on flywheel under multiple constraints, characterized by: The steps include: S1: Perform state-dependent decomposition of the kinematic and dynamic equations of the integrated spacecraft with the flywheel working principle, which covers the entire attitude maneuver space; S2: Designing a performance-power optimization index. This index not only considers the optimal path-energy consumption, but also specifically considers power consumption, to achieve the goal of optimal performance-power. Design performance-power optimization indicators are as follows: (13) (14) (15) in, is the performance-electricity evaluation index, is the performance evaluation index, It is an indicator of electric energy evaluation; 、 、 、 、 are all weight matrices, is the weight constant, , , is the armature resistance of the flywheel DC motor, is the torque constant of the flywheel DC motor, is the flywheel viscous friction coefficient, is the 4th-order identity matrix; is the three-dimensional vector part of the quaternion, Represent the three-dimensional directions of the Euler axes and satisfy the constraints , the superscript T indicates vector transpose; is the angular velocity of the spacecraft, They represent the three-axis angular velocity of the spacecraft respectively; t represents time; is the flywheel execution torque, Respectively represent the execution torque of each flywheel in the flywheel combination; is the flywheel speed, Respectively represent the speed of each flywheel in the flywheel combination relative to its own shaft; S3: Design a state-dependent penalty function and a continuous saturation function to handle spacecraft angular velocity constraints, flywheel speed saturation constraints, and flywheel output torque constraints. This transforms the multi-constrained performance-power optimization spacecraft attitude path planning problem into an augmented state-dependent optimization problem. S4: By solving the state Riccati equation in real time, the solution of the augmented state-dependent optimization problem transformed in step S3 is obtained, thereby realizing real-time planning of the spacecraft attitude maneuvering path under constraints.

2. The method for real-time planning of a spacecraft attitude maneuvering path based on a flywheel under multiple constraints according to claim 1, characterized in that: The specific process of step S1 is as follows: The kinematic and dynamic equations of the integrated spacecraft including the flywheel working principle are established as follows: (1) (2) (3) (4) in, is the error quaternion describing the spacecraft attitude, where is the scalar part of the error quaternion, representing the Euler rotation; is the spacecraft inertia matrix, They represent the spacecraft's three-axis inertia respectively; is the flywheel combination inertia matrix, Represents the inertia of each flywheel in the flywheel combination, and the superscript represents the inverse of a matrix; for The skew antisymmetric matrix is ​​as follows: (5) for The skew antisymmetric matrix is ​​as follows: (6) is the projection matrix of the flywheel combination, and its specific form is as follows: (7) Defining state variables , the state-dependent decomposition of the integrated spacecraft kinematics and dynamics equations is performed, and its specific form is as follows: (8) (9) (10) (11) in, 、 、 、 Respectively represent different neighborhoods of different state dependency decomposition forms, and satisfy ; is the 3rd-order identity matrix; 、 、 and They represent 3rd-order zero matrix, 4th-order zero matrix, 3-row 4-column zero matrix and 4-row 3-column zero matrix respectively; ~ is a constant matrix; Formula (8)-Formula (11) can be written in the following compact form: (12) in, is the state variable, for The first derivative of and is the state dependency matrix and has the following form: ， ， ， , 。 3. The method for real-time planning of a spacecraft attitude maneuvering path based on a flywheel under multiple constraints according to claim 2, characterized in that: In step S2, the following physical constraints are considered during the spacecraft attitude maneuvering process: (1) Sensor measurement constraints: To ensure that the spacecraft angular velocity is within the sensor measurement range, the spacecraft angular velocity must meet the following constraints: (16) in, is the maximum angular velocity allowed for the spacecraft; (2) Flywheel constraints: Due to the limitations of the flywheel hardware structure, the flywheel rotation speed and driving torque meet the following saturation constraints: (17) (18) in, are the maximum allowable flywheel rotation speed and the maximum flywheel execution torque respectively; Subject to the above constraints, the spacecraft kinematic and dynamic equations after state-dependent decomposition are considered to construct a spacecraft attitude path planning problem with optimal performance-power under multiple constraints: (19) in, This paper is about the spacecraft attitude path planning problem with optimal performance-power combination under multiple constraints.

4. The method for real-time planning of a spacecraft attitude maneuvering path based on a flywheel under multiple constraints according to claim 3 is characterized in that: The specific process of step S3 is as follows: In order to deal with the spacecraft angular velocity constraint and the flywheel speed constraint, the spacecraft angular velocity state dependent penalty function matrix is ​​designed respectively and the flywheel rotation speed state-dependent penalty function matrix : (20) (21) in, is the angular velocity state-dependent penalty function, is the flywheel rotation speed state-dependent penalty function; For any variable and its upper bound , and its corresponding state-dependent penalty function has the following form: (22) in, is a constant, ln is a logarithmic function with e as the base, and exp is an exponential function with the natural constant e as the base; Based on the above state-dependent penalty function matrix, the problem Expanded to: (23) in, This is the spacecraft attitude path planning problem with optimal performance-power combination under multiple constraints after the first augmentation; Optimize the metrics for the first augmentation; and are all weight matrices and have the following form: ， To handle input constraints, we first design a continuous saturation input constraint function : (24) Among them, tanh is the tangent function; Substituting formula (24) into To replace , the multi-constraint optimization problem Written as: (25) in, For the problem The equivalent form of the second augmentation is the spacecraft attitude path planning problem with optimal performance-power comprehensiveness under multiple constraints. Optimize the metrics for the second augmentation; Introducing integral auxiliary control variables , then the problem Further expanded to the augmented state-dependent optimization problem: (26) in, To augment the state-dependent optimization problem, For the third augmented state dependency optimization indicator, For the augmented state, and is the augmented state dependency matrix, , ， and is an augmented weight matrix that satisfies: ， 。 5. The method for real-time planning of a spacecraft attitude maneuvering path based on a flywheel under multiple constraints according to claim 4 is characterized in that: The specific process of step S4 is: Solve the following state Riccati equation in real time: (27) in, is the unique solution of the state Riccati equation, and the matrix is ​​symmetric and positive definite; Obtain the solution to the augmented state-dependent optimization problem: (28)。

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