Data-driven spacecraft adaptive feedback gain attitude control method
Through the data-driven spacecraft adaptive feedback gain attitude control method, the existing takeover control method has solved the problem of poor control effect and large computing resources on space non-cooperation goals, and real-time and efficient processing of on-orbit tasks are achieved.
Patent Information
- Application Number
- CN202410400912.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-03
- Publication Date
- 2025-08-08
AI Technical Summary
The existing takeover control method has poor control effect on non-cooperational goals in space, cannot meet the real-time requirements of on-orbit tasks, and requires a large number of satellite-on-board computing resources.
Using a data-driven spacecraft adaptive feedback gain attitude control method, the spacecraft adaptive feedback gain attitude control law is designed by establishing a combined spacecraft attitude dynamic equation that considers model uncertainty, and using Gaussian process regression model and logarithmic edge likelihood function to calculate hyperparameters.
It realizes the real-time requirements of on-orbit tasks, reduces the computing resource requirements for satellite-based computers, and is highly robust to measuring noise and external interference, which can effectively support the efficient processing of on-orbit tasks.
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Abstract
Description
Technical Field
[0001] The present invention relates to the field of combined spacecraft attitude control, and in particular to a data-driven spacecraft adaptive feedback gain attitude control method. Background Art
[0002] With the rapid development of space technology, on-orbit servicing missions are becoming increasingly diverse and complex. Effective attitude takeover and control of targets by servicing spacecraft is the foundation for subsequent on-orbit refueling, on-orbit maintenance, debris removal, and other missions.
[0003] Takeover control technology for traditional cooperative targets is currently well established and has been deployed in orbit. However, for takeover control of non-cooperative targets in space, the resulting combined spacecraft is a complex, nonlinear system with numerous parameters, high coupling, and uncertain overall structure and mass characteristics. Conventional takeover control methods generally fall into two categories: identification-first, then control, and adaptive control that accounts for model uncertainty.
[0004] However, the precise identification of the moment of inertia requires that the entire assembly be free-floating in space without any external torque input, making it unsuitable for mission scenarios involving target attitude maneuvers. Furthermore, adaptive control methods typically assume, during their demonstration, that model uncertainties and external interference have upper bounds to ensure the stability of the closed-loop system. This is an overly conservative assumption for attitude takeover missions involving assembled spacecraft. Furthermore, parametric approaches to model uncertainty based on neural networks and fuzzy rules suffer from complex structures and a reliance on model information for basis function selection. Consequently, the control effectiveness of existing takeover control methods remains poor. Furthermore, existing takeover control methods struggle to meet the real-time requirements of on-orbit missions and require significant computational resources from onboard computers. In summary, takeover control missions for non-cooperative space targets with complex structures, unknown mass characteristics, and unclear attitude maneuverability are extremely challenging and require urgent solutions. Summary of the Invention
[0005] The purpose of the present invention is to solve the problems of poor control effect of existing takeover control methods, inability to meet the real-time requirements of on-orbit mission control, and large computing resources required by on-board computers, and to propose a data-driven spacecraft adaptive feedback gain attitude control method.
[0006] The technical solution adopted by the present invention to solve the above technical problems is:
[0007] A data-driven spacecraft adaptive feedback gain attitude control method, the method specifically comprising the following steps:
[0008] Step 1: Establish the attitude dynamics equation of the combined spacecraft considering the model uncertainty;
[0009] Step 2: Based on the unknown parts of the attitude dynamics equation of the combined spacecraft, a Gaussian process regression model is established according to the input and output data of the combined spacecraft on orbit, and then the logarithmic marginal likelihood function is obtained according to the Gaussian process regression model;
[0010] Step 3: Approximate the posterior probability density to a Gaussian distribution and calculate the hyperparameters based on the log-marginal likelihood function.
[0011] Step 4: Design the spacecraft adaptive feedback gain attitude control law based on the hyperparameters calculated in step 2.
[0012] Furthermore, the specific process of step one is:
[0013] The attitude dynamics of the combined spacecraft described by quaternions are:
[0014]
[0015]
[0016] Where Q=[q0,q T ] T ∈R 4 is the unit quaternion of the attitude and orientation of the combined spacecraft body coordinate system relative to the inertial coordinate system; I3 is the third-order unit matrix; q × :R 3 →R 3×3 is the cross product of vector q; ω∈R 3 is the attitude angular velocity of the combined spacecraft body coordinate system relative to the inertial coordinate system; is the first derivative of q; is the first-order derivative of q0; J c ∈R 3×3 is the moment of inertia matrix of the combined spacecraft; is the first derivative of ω; × is the cross product of vector ω; u∈R 3 is the attitude control torque; τ d ∈R 3 is the disturbance torque on the combined spacecraft;
[0017] definition J c0 ∈R 3×3 is the prior moment of inertia of the combined spacecraft; is the unknown equivalent moment of inertia caused by capturing the target spacecraft;
[0018] Then the attitude dynamics of the combined spacecraft considering model uncertainty is:
[0019]
[0020]
[0021] Among them, d(ω,u) is the intermediate variable;
[0022] The combined spacecraft attitude dynamics equation considering model uncertainty can be written into the following compact form:
[0023]
[0024] Where: x=[q T ,ω T ] T ∈R 6 is the system state; G=[0 3×3 ,I3] T ∈R 6×3 is the transformation matrix; f(x,u) is the known part of the model, is the unknown part of the model;
[0025]
[0026] Furthermore, the intermediate variable d(ω,u) is:
[0027]
[0028] in, is an intermediate variable.
[0029] Furthermore, the intermediate variable for:
[0030]
[0031] The superscript -1 represents the inverse of the matrix.
[0032] Furthermore, the specific process of step 2 is as follows:
[0033] Step 2.1. Describe the Gaussian process regression model as:
[0034]
[0035] in, R is a real number, x represents the attitude angle and angular velocity, u represents the attitude control torque, is the prior mean, is a semi-positive definite covariance function, Represents the output value of the Gaussian process;
[0036] Step 2: Given a training set containing N sets of Gaussian process input data and output data Y=[y1,…,y N ]∈R N×3}, where the i-th output data in the training set i=1,…,N, ε is the mean 0 and the standard deviation is σ ε Independent and identically distributed Gaussian white noise;
[0037] Then the function The Gaussian prior distribution P(Δ) and model likelihood function P(Y|Δ) are:
[0038]
[0039]
[0040] in, is a Gaussian distribution, K N ∈R N×N For the training set The symmetric and semi-positive covariance matrix of N is the identity matrix;
[0041]
[0042] Step 2 and 3: Known training set The analytical form of the posterior probability density P(Δ|D) under the condition is:
[0043]
[0044] Among them, P(Y|Δ,D) is the training set The model likelihood function under the condition, P(Y) is the marginal likelihood function of the output data Y;
[0045] According to formula (5), the test point is The probability density of is:
[0046]
[0047] Where, is the joint probability density distribution;
[0048]
[0049] Where: as well as
[0050] Substituting equations (5) and (7) into equation (6), we get the test point Function value Δ * The posterior distribution of is:
[0051]
[0052] in, is the posterior mean function, is the variance function;
[0053]
[0054]
[0055] Then, by maximizing the log-marginal likelihood function of formula (11), we can obtain the optimal hyperparameter set:
[0056]
[0057] Furthermore, the semi-positive definite covariance function is:
[0058]
[0059] Where: is the signal variance, R ≥0 represents a real number greater than or equal to 0, the diagonal matrix Λ=diag(λ), is the variance scale vector, is an element in the variance scale vector, the superscript -1 represents the inverse of the matrix, and the superscript T represents the transpose of the matrix.
[0060] Furthermore, the specific process of step three is:
[0061] Step 3. Approximate the posterior probability density P(Δ|D) to the Gaussian distribution q(Δ, Δ u )=P(Δ|Δ u )q(Δ u ), Δ u Represents the output data of the pseudo data set, then maximize the lower bound of the evidence of lnP(Y):
[0062]
[0063] Where F(q)=∫q(Δ u )∫P(Δ|Δ u )lnP(Y|Δ)dΔdΔ u ;
[0064] make Then the Gaussian distribution q(Δ, Δ u ) has the analytical form of ELBO:
[0065]
[0066] Among them, m u and S u is the variational parameter, For pseudo input and training input The covariance matrix between M is the covariance matrix of the pseudo input itself, tr(·) represents the trace of the matrix;
[0067]
[0068] Step 3.2: Calculate the variational parameter m for equation (14) u and S u The partial derivative is set to 0 to obtain the optimal posterior distribution q * (Δ u );
[0069] Step 3. Set the optimal posterior distribution q * (Δ u ) into formula (14) and we get:
[0070]
[0071] The pseudo input point position is obtained by maximizing formula (16) and hyperparameters
[0072] Furthermore, the specific process of step 4 is as follows:
[0073] Step 4.1. According to the approximate posterior distribution q(Δ,Δ u ), the marginal distribution of the function Δ is obtained as:
[0074]
[0075] in, is the mean function, is the variance function, q(Δ u ) represents Δ u Variational distribution of test points The mean function and variance function at are:
[0076]
[0077] Step 4.2: Define the function About Nuclear The reproducing kernel Hilbert space norm of is bounded, that is, The model error At least with probability (1-δ)3 Tight set All are all bounded, that is:
[0078]
[0079] Where: δ is a positive real number less than 1, β=[β1,β2,β3] T ∈R 3 ;
[0080]
[0081] Where: γ j is the jth information gain, that is K represents the j-th dimension N matrix;
[0082] Define the nominal part of the spacecraft moment of inertia matrix J c0 Satisfy λ min (J c0 )<λ J , where λ J is a known constant, λ min (·) is the matrix J c0 The minimum eigenvalue of ; define the bounded feedback gain function K p (∑ Δ ) and K p (∑ Δ ) satisfies formula (21):
[0083]
[0084] Where: k p1 、k p2 、k d1 and k d2 All are positive numbers;
[0085] Then the spacecraft adaptive feedback gain attitude control law is:
[0086]
[0087] The beneficial effects of the present invention are:
[0088] The magnitude of the feedback control gain of the present invention can be adaptively varied with the confidence of the GP model, and the system state can achieve eventual uniformly bounded convergence to a neighborhood near the equilibrium point in a probabilistic sense, thus ensuring the control effect. Furthermore, compared to existing methods, the control strategy proposed by the present invention can avoid the time-consuming process of precise on-orbit model identification, while having strong robustness to measurement noise, external interference, and active target attitude maneuvers, effectively supporting the efficient processing of on-orbit missions and meeting the real-time requirements of on-orbit mission control. Furthermore, the method of the present invention has a low computational complexity, which reduces the requirements for computing resources of the onboard computer. BRIEF DESCRIPTION OF THE DRAWINGS
[0089] Figure 1 Schematic diagram of the geometric configuration of the combined spacecraft of the present invention;
[0090] Figure 2 GP model response curve and 95% confidence interval diagram under the PD control law of the present invention;
[0091] Figure 3 It is the quaternion diagram of the service spacecraft attitude under the action of two control laws;
[0092] Figure 4 The attitude angular velocity diagram of the service spacecraft under the action of two control laws;
[0093] The unit of the vertical axis is rad·s -1 ;
[0094] Figure 5 The attitude control torque diagram of the service spacecraft under the action of two control laws is shown;
[0095] The unit of the ordinate is N·m;
[0096] Figure 6 This is the standard GPR model response diagram after the attitude heavy maneuver of the present invention. DETAILED DESCRIPTION
[0097] Specific implementation method 1: This implementation method provides a data-driven spacecraft adaptive feedback gain attitude control method, which specifically includes the following steps:
[0098] Step 1: Establish the attitude dynamics equation of the combined spacecraft considering the model uncertainty;
[0099] Step 2: Based on the unknown parts of the attitude dynamics equation of the combined spacecraft, a Gaussian process regression model is established according to the input and output data of the combined spacecraft on orbit, and then the logarithmic marginal likelihood function is obtained according to the Gaussian process regression model;
[0100] Step 3: Approximate the posterior probability density to a Gaussian distribution and calculate the hyperparameters based on the log-marginal likelihood function.
[0101] Step 4: Design the spacecraft adaptive feedback gain attitude control law based on the hyperparameters calculated in step 2.
[0102] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the specific process of step 1 is as follows:
[0103] The attitude dynamics of the combined spacecraft described by quaternions are:
[0104]
[0105]
[0106] Where Q=[q0,q T ] T ∈R 4 is the unit quaternion of the attitude and orientation of the combined spacecraft body coordinate system relative to the inertial coordinate system; I3 is the third-order unit matrix; q × :R 3 →R 3×3 is the cross product of vector q; ω∈R 3 is the attitude angular velocity of the combined spacecraft body coordinate system relative to the inertial coordinate system; is the first derivative of q; is the first-order derivative of q0; J c ∈R 3×3 is the moment of inertia matrix of the combined spacecraft; is the first derivative of ω; × is the cross product of vector ω; u∈R 3 is the attitude control torque; τ d ∈R 3 is the disturbance torque on the combined spacecraft;
[0107] definition J c0 ∈R 3×3 is the prior moment of inertia of the combined spacecraft; is the unknown equivalent moment of inertia caused by capturing the target spacecraft;
[0108] Then the attitude dynamics of the combined spacecraft considering model uncertainty is:
[0109]
[0110]
[0111] Among them, d(ω,u) is the intermediate variable;
[0112] Further considering the additional moment of inertia caused by the attitude maneuver of the target spacecraft and the relative motion between the service spacecraft and the target spacecraft, the attitude dynamics equation of the combined spacecraft considering the model uncertainty is written into the following compact form:
[0113]
[0114] Where: x=[q T ,ω T ] T ∈R 6 is the system state; G=[0 3×3 ,I3] T ∈R 6×3 is the transformation matrix; f(x,u) is the known part of the model, namely the "prior model"; is the unknown part of the model (including parameter uncertainty generated after capturing the target, target spacecraft attitude maneuvering and other uncertainties);
[0115]
[0116] Other steps and parameters are the same as those in the first embodiment.
[0117] Specific embodiment three: This embodiment differs from the specific embodiment two in that the intermediate variable d(ω,u) is:
[0118]
[0119] in, is an intermediate variable.
[0120] Other steps and parameters are the same as those in the second embodiment.
[0121] Specific embodiment 4: This embodiment differs from specific embodiment 3 in that the intermediate variable for:
[0122]
[0123] The superscript -1 represents the inverse of the matrix.
[0124] Other steps and parameters are the same as those in the third embodiment.
[0125] Specific embodiment 5: This embodiment differs from specific embodiment 4 in that the specific process of step 2 is as follows:
[0126] Step 2.1. Describe the Gaussian process regression model as:
[0127]
[0128] in, R is a real number, x represents the attitude angle and angular velocity (system state), u represents the attitude control torque (system input), is the prior mean (usually assumed to be zero, indicating that no prior knowledge is given for the unknown function Δ(x, u)), is a semi-positive covariance function (characterizing any two data points correlation between Represents the output value of the Gaussian process;
[0129] Step 2: Given a training set containing N sets of Gaussian process input data and output data Y=[y1,…,y N ]∈R N×3}, where the i-th output data in the training set i=1,…,N, ε is the mean 0 and the standard deviation is σ ε Independent and identically distributed Gaussian white noise;
[0130] Then the function The Gaussian prior distribution P(Δ) and model likelihood function P(Y|Δ) are:
[0131]
[0132]
[0133] in, is a Gaussian distribution, K N ∈R N×N For the training set The symmetric and semi-positive covariance matrix of N is the identity matrix;
[0134]
[0135] Step 2 and 3: Known training set The analytical form of the posterior probability density P(Δ|D) under the condition is:
[0136]
[0137] Among them, P(Y|Δ,D) is the training set The model likelihood function under the condition, P(Y) is the marginal likelihood function of the output data Y;
[0138] According to formula (5), the test point is The probability density of is:
[0139]
[0140] Where, is the joint probability density distribution;
[0141]
[0142] Where: as well as
[0143] Substituting equations (5) and (7) into equation (6), we get the test point Function value Δ * The posterior distribution of is:
[0144]
[0145] in, is the posterior mean function, is the variance function;
[0146]
[0147]
[0148] Then, by maximizing the log-marginal likelihood function of formula (11), we can obtain the optimal hyperparameter set:
[0149]
[0150] Other steps and parameters are the same as those in the fourth embodiment.
[0151] Specific embodiment 6: This embodiment differs from specific embodiment 5 in that the semi-positive definite covariance function is:
[0152]
[0153] Where: is the signal variance, R ≥0 represents a real number greater than or equal to 0, the diagonal matrix Λ=diag(λ), is the variance scale vector, is an element in the variance scale vector, the superscript -1 represents the inverse of the matrix, and the superscript T represents the transpose of the matrix.
[0154] Other steps and parameters are the same as those in the fifth embodiment.
[0155] Taking into account the global approximation characteristics of any continuous function, the present invention selects a covariance function in the form of a square exponential kernel determined by autocorrelation.
[0156] Specific embodiment seven: This embodiment differs from specific embodiment six in that the specific process of step three is as follows:
[0157] Step 3. Approximate the posterior probability density P(Δ|D) to a Gaussian distribution q(Δ, Δ u )=P(Δ|Δ u )q(Δu ) , Δ u Represents the output data of the pseudo data set, then maximize the lower bound of the evidence of lnP(Y):
[0158]
[0159] Where F(q)=∫q(Δ u )∫P(Δ|Δ u )lnP(Y|Δ)dΔdΔ u ;
[0160] make Then the Gaussian distribution q(Δ, Δ u ) has the analytical form of ELBO:
[0161]
[0162] Among them, m u and S u is the variational parameter, For pseudo input and training input The covariance matrix between M is the covariance matrix of the pseudo input itself, tr(·) represents the trace of the matrix;
[0163]
[0164] Step 3.2: Calculate the variational parameter m for equation (14) u and S u The partial derivative is set to 0 to obtain the optimal posterior distribution q * (Δ u );
[0165] Step 3. Set the optimal posterior distribution q * (Δ u ) into formula (14) and we get:
[0166]
[0167] The pseudo input point position is obtained by maximizing formula (16) and hyperparameters
[0168] Other steps and parameters are the same as those in the sixth embodiment.
[0169] Specific embodiment eight: This embodiment differs from specific embodiment seven in that the specific process of step four is as follows:
[0170] Step 4.1. According to the approximate posterior distribution q(Δ,Δ u ), the marginal distribution of the function Δ is obtained as:
[0171]
[0172] in, is the mean function, is the variance function, q(Δ u ) represents Δ u Variational distribution of test points The mean function and variance function at are:
[0173]
[0174] For any predefined compact set The reproducing kernel Hilbert space (RKHS) of the global kernel function is Given any positive real number ∈ and any continuous function Then there exists a function So that ||f c -f H ||≤∈;
[0175] The global kernel function can approximate any continuous function with arbitrary precision; on the other hand, the norm in assumption 1 It characterizes the smoothness of the function Δ, and its boundedness indicates that the selected kernel function is appropriate. Therefore, for any continuous function Δ, there exists a function in RKHS that is arbitrarily close to it;
[0176] Step 4.2: Define the function About Nuclear The reproducing kernel Hilbert space norm of is bounded, that is, The model error At least with probability (1-δ) 3 Tight set All are all bounded, that is:
[0177]
[0178] Where: δ is a positive real number less than 1, β=[β1,β2,β3] T ∈R 3 ;
[0179]
[0180] Where: γ j is the jth information gain, that is K represents the j-th dimension N matrix;
[0181] Define the nominal part of the spacecraft moment of inertia matrix J c0 Satisfy λ min (J c0 )<λ J , where λ J is a known constant, λ min (·) is the matrix J c0 The minimum eigenvalue of ; define the bounded feedback gain function K p (∑ Δ ) and K p (∑ Δ ) satisfies formula (21):
[0182]
[0183] Where: k p1 、k p2 、k d1 and k d2 All are positive numbers;
[0184] Then the spacecraft adaptive feedback gain attitude control law is:
[0185]
[0186] Other steps and parameters are the same as those in the seventh embodiment.
[0187] Theorem 1: Consider the attitude dynamics of the combined spacecraft described in step 1 with unknown dynamic models and the target's possible attitude maneuverability, as well as the definition in step 4, where the dynamics of the unknown model part It is obtained by Gaussian process learning of formula (1). If the control law design has the form shown in formula (22), the attitude quaternion and attitude angular velocity of the combined spacecraft are calculated with probability (1-δ) 3 Uniformly eventually bounded and converges to the compact sets Ω1 and Ω2.
[0188] Uniformly eventually bounded convergence is defined as follows: for bounded initial conditions, if there exists a continuous and positive definite Lyapunov function V(x) such that:
[0189]
[0190] Where: for function; c1 and c2 are positive constants. Then the system state x(t) is uniform and eventually converges to a bounded state.
[0191] Substituting the control law of Equation (22) into the combined spacecraft attitude dynamics equation considering model uncertainty, the closed-loop system is obtained:
[0192]
[0193] Consider the Lyapunov candidate function V as:
[0194]
[0195] Where: v is a positive constant. Then we can find the derivative of V along time:
[0196]
[0197] Then according to the Cauchy-Schwartz inequality, we can get:
[0198]
[0199] Further combining formulas (19) and (20), the following formula holds:
[0200]
[0201] Where: M l =diag[vk p1 ,-(k d1 -1 / 2v)λ J ]. According to the definition of V:
[0202] V≤x T M s x≤λ max (M s )||x|| 2 (29)
[0203] in,
[0204] Combined with the boundedness of q and ω, we have We can get:
[0205]
[0206] Where:
[0207] In order to further study the convergence characteristics of the system state, the function is defined here Then formula (30) can be rewritten as an inequality about L:
[0208]
[0209] Where: According to the principle of comparability, we have:
[0210]
[0211] Where: s2=λ min (M l ) / (2λ max (M s )). When t→∞, we can get:
[0212]
[0213] According to the definition of V, V≤2(k p2 +vk d2 )(1-q0), then:
[0214]
[0215] We can further obtain the upper bound of the quaternion vector part q as:
[0216]
[0217] On the other hand, according to We can get:
[0218]
[0219] That is, the system states q and ω can eventually converge to the compact sets Ω1 and Ω2. The proof is complete.
[0220] The control law of formula (22) mainly consists of two parts: the first part is variable gain feedback control, whose feedback gain changes with the GP (Gaussian Process, GP) prediction variance (i.e., the confidence level of model learning). If the error between the current GP model and the true model is large, the feedback control will give a larger control input to stabilize the system, effectively improving the robustness of the algorithm; the second part is "semi" feedforward control, where the definition of "semi" means that the uncertainty of the system is determined by the GP prediction mean. Compensation is also a function of the system state and is therefore not traditional feedforward control.
[0221] Simulation analysis
[0222] Training and validation of GP models
[0223] To construct the training data set, the combined spacecraft should be stimulated by appropriate input signals. The present invention adopts the data collection scenario of controlled tracking under the PD control law. The initial attitude quaternion of the service spacecraft is Qs0 =[0.85,0.32,-0.30,0.27] T , the initial attitude angular velocity is ω s0 =[0.05,-0.05,-0.03] T rad / s. The feedback gain matrix of PD control is selected as K p =0.2J c0 , K d =0.5J c0 And the desired angular velocity is ω sd =[0.01sin0.6t,-0.01sin0.5t,-0.02sin0.8t]rad / s. The geometric configuration of the combined spacecraft is as follows: Figure 1 As shown, the excitation signal is continuously applied to the assembly for 50 seconds, and data is collected at a frequency of 10 Hz. Stored in training set Considering the sensor measurement process, the GP training output data is distributed as Gaussian white noise pollution. Assume that the nominal moment of inertia of the combined spacecraft is selected as J c0 =diag[600,405,600]kg·m 2 After data collection is completed, the initial hyperparameters θ0 = {1 11 , 1 11 , 1 11 For sparse GP, the pseudo dataset size M = 50, and its initial value is in the training set The conjugate gradient descent method is used to maximize Equation (11) and Equation (16) respectively to obtain the optimal hyperparameters θ of the standard GP and sparse GP (i.e., SVGP, representing the method of the present invention) * The response curves of the two GP model regressions are as follows: Figure 2 As shown, the shaded area represents the 95% confidence interval at the predicted mean, the scattered points are the measurement data contaminated by noise, and the vertical coordinates Δ1, Δ2, and Δ3 represent It can be seen that both GP models can fit the unknown function well under noise interference. The error between the predicted mean and the true value is kept at 10 -2 Magnitude.
[0224] Table 1 also shows a quantitative comparison of the learning performance of standard GP and SVGP (in bold) on datasets of varying sizes, in terms of training time and regression error. Since the computational effort during the training phase is cubically correlated with the dataset size, as the dataset size increases from 500 to 2000, the training time required for standard GP increases significantly from 6.31 seconds to 303.78 seconds. However, the training time for the sparse GP model only increases from 1.56 seconds to 3.64 seconds, while maintaining a comparable mean squared error to standard GP. In practical applications, dataset size is a trade-off between computational effort and regression accuracy.
[0225] Table 1 Relationship between GP training time, regression accuracy and dataset capacity
[0226]
[0227] The active attitude control law of the target spacecraft is selected as the PD form:
[0228] u t =-K pt qx e -K dt ω t (37)
[0229] Where: K pt =0.02Jt;K dt =0.05Jt; q td is the representation of the initial attitude quaternion vector part of the target spacecraft body coordinate system relative to the inertial coordinate system in the target spacecraft body coordinate system. According to the geometric configuration of the spacecraft in the simulation environment, let q td =[-0.251,0.0235,0.084] T .
[0230] The initial Euler angle of the service spacecraft is [5,0,-20]°, and the initial attitude angular velocity is ω s0 =[0.01,0.02,0.01] T rad / s. In the first 50 seconds of the simulation, a PD-type excitation torque is applied to the combined spacecraft to construct a training data set for the Gaussian process. Its feedback gain is: K p0 =0.1J c0 , K d0 =0.3J c0 When the simulation is running for 50 seconds, The sparse GP model is trained on , and the control law is updated to Equation (22) at the same time. In the formula, the feedback gain functions are selected as:
[0231]
[0232] At the same time, in order to verify the generalization performance and control effect of the GP-based learning control algorithm in the untrained area, after the system is stabilized, the combined spacecraft attitude is required to re-maneuver to the new attitude pointing to Q s =[0.963,0.10,-0.15,0.20] T . Note that the attitude points away from the initial training set. The attitude quaternion, angular velocity and control torque curves of the service spacecraft under the two control laws are as follows: Figure 3 、 Figure 4 and Figure 5 As shown, the vertical coordinate {q s1 ,q s2 ,q s3}、{ω sx ,ω sy ,ω sz} and {u x ,u y ,u z} respectively represent the three-axis components of the corresponding vector.
[0233] It can be seen that when the target has an active attitude maneuvering torque in the form of PD control as shown in Equation (37) and under the influence of unknown model uncertainty, both control algorithms can achieve the goal of attitude stabilization. Figure 3 and Figure 4 The proposed sparse GP-based learning control law significantly improves both dynamic response and steady-state error compared to the baseline control law, ultimately enabling state convergence to a smaller set. This is primarily due to the introduction of a GP model compensation mechanism, which effectively compensates for the target attitude maneuvering torque and the unknown model components within the control law.
[0234] The standard GP model response after attitude heavy maneuver is as follows Figure 6 As shown in the figure, when the combined spacecraft attitude maneuvers to an area outside the training set, the GP prediction variance (represented by the shaded 95% confidence interval) increases significantly, indicating that there is a large error between the current GP predicted mean and the actual unknown function value. This also makes it possible to appropriately increase the feedback gain of the GP-based learning control algorithm proposed in this invention to further resist the negative impact of model errors.
[0235] Feedback gain function K p (∑ Δ ) and K d (∑ Δ ) contains the prior knowledge of the combined spacecraft system model, namely the nominal moment of inertia J c0It is reasonably selected based on the service spacecraft parameters and combined with engineering experience. In actual on-orbit missions, when the target spacecraft is captured by the service spacecraft, the service spacecraft will usually try to increase the feedback gain to output a larger control torque to achieve attitude takeover of the entire combined spacecraft, but this approach may lead to poor control effects or unnecessary energy consumption. Thanks to the probabilistic modeling characteristics of GP, it is possible to predict the mean at the test point and obtain the corresponding prediction variance, which allows us to quantify the accuracy of the prediction results. Therefore, based on the GP-based attitude takeover learning control algorithm proposed in the present invention, when the state of the combined spacecraft system is in the trained area, the feedback gain can always be maintained at a low level; once an unknown external situation occurs, such as the target undergoes attitude maneuvers or the mission requires the attitude to be re-maneuvered to a new equilibrium point, the GP prediction variance ∑ Δ will increase significantly, resulting in a corresponding increase in the feedback gain, so that the combined spacecraft can be stabilized again.
[0236] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.
Claims
1. A data-driven spacecraft adaptive feedback gain attitude control method, characterized in that: The method specifically comprises the following steps: Step 1: Establish the attitude dynamics equation of the combined spacecraft considering the model uncertainty; Step 2: Based on the unknown parts of the attitude dynamics equation of the combined spacecraft, a Gaussian process regression model is established according to the input and output data of the combined spacecraft on orbit, and then the logarithmic marginal likelihood function is obtained according to the Gaussian process regression model; Step 3: Approximate the posterior probability density to a Gaussian distribution and calculate the hyperparameters based on the log-marginal likelihood function. Step 4: Design the spacecraft adaptive feedback gain attitude control law based on the hyperparameters calculated in step 2.
2. A data-driven spacecraft adaptive feedback gain attitude control method according to claim 1, characterized in that: The specific process of step one is: The attitude dynamics of the combined spacecraft described by quaternions are: Where Q=[q0,q T ] T ∈R 4 is the unit quaternion of the attitude and orientation of the combined spacecraft body coordinate system relative to the inertial coordinate system; I3 is the third-order unit matrix; q × :R 3 →R 3×3 is the cross product of vector q; ω∈R 3 is the attitude angular velocity of the combined spacecraft body coordinate system relative to the inertial coordinate system; is the first derivative of q; is the first-order derivative of q0; J c ∈R 3×3 is the moment of inertia matrix of the combined spacecraft; is the first derivative of ω; × is the cross product of vector ω; u∈R 3 is the attitude control torque; τ d ∈R 3 is the disturbance torque on the combined spacecraft; definition J c0 ∈R 3×3 is the prior moment of inertia of the combined spacecraft; is the unknown equivalent moment of inertia caused by capturing the target spacecraft; Then the attitude dynamics of the combined spacecraft considering model uncertainty is: Among them, d(ω,u) is the intermediate variable; The combined spacecraft attitude dynamics equation considering model uncertainty can be written into the following compact form: Where: x=[q T ,ω T ] T ∈R 6 is the system state; G=[0 3×3 ,I3] T ∈R 6×3 is the transformation matrix; f(x,u) is the known part of the model, is the unknown part of the model; 3. The data-driven spacecraft adaptive feedback gain attitude control method according to claim 2, characterized in that: The intermediate variable d(ω,u) is: in, is an intermediate variable.
4. The data-driven spacecraft adaptive feedback gain attitude control method according to claim 3, characterized in that: The intermediate variable for: The superscript -1 represents the inverse of the matrix.
5. The data-driven spacecraft adaptive feedback gain attitude control method according to claim 4, characterized in that: The specific process of step 2 is: Step 2.
1. Describe the Gaussian process regression model as: in, R is a real number, x represents the attitude angle and angular velocity, u represents the attitude control torque, is the prior mean, is a semi-positive definite covariance function, Represents the output value of the Gaussian process; Step 2: Given a training set containing N sets of Gaussian process input data and output data Among them, the i-th output data in the training set ε is the mean of 0 and the standard deviation of σ ε Independent and identically distributed Gaussian white noise; Then the function The Gaussian prior distribution P(Δ) and model likelihood function P(Y|Δ) are: in, is a Gaussian distribution, K N ∈R N×N For the training set The symmetric and semi-positive covariance matrix of N is the identity matrix; Step 2 and 3: Known training set The analytical form of the posterior probability density P(Δ|D) under the condition is: Among them, P(Y|Δ,D) is the training set The model likelihood function under the condition, P(Y) is the marginal likelihood function of the output data Y; According to formula (5), the test point is The probability density of is: Where, is the joint probability density distribution; Where: as well as Substituting equations (5) and (7) into equation (6), we get the test point Function value Δ * The posterior distribution of is: in, is the posterior mean function, is the variance function; Then, by maximizing the log-marginal likelihood function of formula (11), we can obtain the optimal hyperparameter set:
6. A data-driven spacecraft adaptive feedback gain attitude control method according to claim 5, characterized in that: The semi-positive definite covariance function is: Where: is the signal variance, R ≥0 represents a real number greater than or equal to 0, the diagonal matrix Λ=diag(λ), is the variance scale vector, is an element in the variance scale vector, the superscript -1 represents the inverse of the matrix, and the superscript T represents the transpose of the matrix.
7. The data-driven spacecraft adaptive feedback gain attitude control method according to claim 6, characterized in that: The specific process of step three is: Step 3. Approximate the posterior probability density P(Δ|D) to the Gaussian distribution q(Δ, Δ u )=P(Δ|Δ u )q(Δ u ), Δ u Represents the output data of the pseudo data set, then maximize the lower bound of the evidence of lnP(Y): where \(F(q)=\int_{q}(\Delta u )\int_{P(\Delta|\Delta u )}\ln P(Y|\Delta)d\Delta d\Delta u ;\ make Then the Gaussian distribution q(Δ, Δ u ) has the analytical form of ELBO: Among them, m u and S u is the variational parameter, For pseudo input and training input The covariance matrix between M is the covariance matrix of the pseudo input itself, tr(·) represents the trace of the matrix; Step 3.2: Calculate the variational parameter m for equation (14) u and S u The partial derivative is set to 0 to obtain the optimal posterior distribution q * (Δ u ); Step 3. Set the optimal posterior distribution q * (Δ u ) into formula (14) and we get: The pseudo input point position is obtained by maximizing formula (16) and hyperparameters 8. The data-driven spacecraft adaptive feedback gain attitude control method according to claim 7, characterized in that: The specific process of step 4 is as follows: Step 4.
1. According to the approximate posterior distribution q(Δ,Δ u ), the marginal distribution of the function Δ is obtained as: in, is the mean function, is the variance function, q(Δ u ) represents Δ u Variational distribution of test points The mean function and variance function at are: Step 4.2: Define the function About Nuclear The reproducing kernel Hilbert space norm of is bounded, that is, The model error At least with probability (1-δ) 3 Tight set All are all bounded, that is: Where: δ is a positive real number less than 1, β=[β1,β2,β3] T ∈R 3 ; Where: γ j is the jth information gain, that is K represents the j-th dimension N matrix; Define the nominal part of the spacecraft moment of inertia matrix J c0 Satisfy λ min (J c0 )<λ J , where λ J is a known constant, λ min (·) is the matrix J c0 The minimum eigenvalue of ; define the bounded feedback gain function K p (∑ Δ ) and K p (∑ Δ ) satisfies formula (21): Where: k p1 、k p2 、k d1 and k d2 All are positive numbers; Then the spacecraft adaptive feedback gain attitude control law is: