Robust adaptive dynamic planning method for spacecraft attitude control

Abstract

The invention relates to a robust adaptive dynamic planning method for spacecraft attitude control, and belongs to the technical field of spacecraft control. According to the method, the neural network identifier is designed, online identification and reconstruction are carried out on unknown dynamic items caused by inertia parameter uncertainty in spacecraft attitude dynamics, the attitude tracking optimal control law based on adaptive dynamics is constructed on the basis, and under the condition that inertia parameter uncertainty exists, the attitude tracking optimal control law is optimized. The balance between tracking precision and control energy consumption is realized, and the applicability of the attitude control method in complex space tasks is improved.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft control technology, specifically relating to a robust adaptive dynamic programming method for spacecraft attitude control. Background Technology

[0002] With the continuous development of aerospace science and technology, spacecraft attitude control has become one of the key fundamental technologies in space missions such as Earth observation, satellite surveillance, rendezvous and docking, formation flying, and on-orbit servicing. In various space missions, spacecraft need to achieve precise attitude adjustment or stable maintenance according to mission requirements, and their attitude control performance directly affects the accuracy of mission execution and the reliability of system operation.

[0003] As the complexity of space missions continues to increase, the operating conditions faced by spacecraft attitude control systems are becoming increasingly diverse. On the one hand, influenced by factors such as the complexity of the spacecraft structure, configuration changes, and thruster fuel consumption, inertial parameters such as the moment of inertia may change during on-orbit operation, leading to uncertainties in the attitude dynamics model. On the other hand, spacecraft on-orbit resources are limited, and the attitude control system needs to reasonably constrain control energy consumption while meeting control accuracy requirements to ensure the long-term stable operation of the spacecraft. Therefore, there is an urgent need for an attitude control method that can achieve high-precision tracking control while optimizing control energy consumption under conditions of parameter uncertainty, in order to meet the attitude control requirements of complex space missions. Summary of the Invention

[0004] The purpose of this invention is to overcome the problem that existing spacecraft attitude control methods struggle to balance attitude tracking performance and control energy consumption under conditions of parameter uncertainty, and to propose a robust adaptive dynamic programming method for spacecraft attitude control. This invention designs a neural network identifier to identify and reconstruct unknown dynamic terms in spacecraft attitude dynamics caused by inertial parameter uncertainties online. Based on this, it constructs an optimal attitude tracking control law based on adaptive dynamics, achieving a balance between tracking accuracy and control energy consumption even in the presence of inertial parameter uncertainties, thus improving the applicability of attitude control methods in complex space missions.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A robust adaptive dynamic programming method for spacecraft attitude control includes the following steps:

[0007] Step S1: Based on attitude quaternions, establish the kinematic and dynamic model of the spacecraft attitude tracking error;

[0008] Step S2: Introduce sliding mode variables to transform the attitude error dynamics system, and express it as a nonlinear affine system containing unknown dynamic terms;

[0009] Step S3: For nonlinear affine dynamic systems, design a neural network identifier and construct a corresponding neural network weight adaptive update law to identify and reconstruct unknown dynamic terms in attitude dynamics online.

[0010] Step S4: Based on the completion of dynamic reconstruction, construct a cost function that includes attitude tracking error and control input according to the principle of optimality, and design the optimal control law for spacecraft attitude tracking accordingly.

[0011] Step S5: Based on the adaptive dynamic programming method, a first-order filter is introduced to construct the weight update law of the evaluation network, thereby realizing the online estimation of the optimal control law.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] (1) The neural network identifier designed in this invention can identify and reconstruct unknown dynamic terms in spacecraft attitude dynamics caused by factors such as uncertainty of inertial parameters online, effectively reducing the impact of model uncertainty on attitude tracking performance.

[0014] (2) The cost function constructed in this invention includes both attitude tracking error and control input, enabling a reasonable balance between tracking accuracy and control energy consumption during attitude control.

[0015] (3) The present invention uses an adaptive dynamic programming algorithm with a single evaluation network to estimate the optimal control law, avoiding the dual network structure of alternating training of the action network and the evaluation network, simplifying the controller implementation process and reducing the computational complexity of the system. Attached Figure Description

[0016] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0017] Figure 1 This is a flowchart of the attitude tracking control method according to Embodiment 1 of the present invention;

[0018] Figure 2 This is a graph showing the sliding mode variable identification error in Embodiment 1 of the present invention.

[0019] Figure 3 This is a graph showing the attitude tracking error in Embodiment 1 of the present invention.

[0020] Figure 4 This is a graph showing the angular velocity error in one embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments:

[0022] like Figure 1 As shown, a robust adaptive dynamic programming method for spacecraft attitude control includes the following steps:

[0023] Step S1: Based on attitude quaternions, establish the kinematic and dynamic model of the spacecraft attitude tracking error;

[0024] Step S2: Introduce sliding mode variables to transform the attitude error dynamics system, and express it as a nonlinear affine system containing unknown dynamic terms;

[0025] Step S3: For nonlinear affine dynamic systems, design a neural network identifier and construct a corresponding neural network weight adaptive update law to identify and reconstruct unknown dynamic terms in attitude dynamics online.

[0026] Step S4: Based on the completion of dynamic reconstruction, construct a cost function that includes attitude tracking error and control input according to the principle of optimality, and design the optimal control law for spacecraft attitude tracking accordingly.

[0027] Step S5: Based on the adaptive dynamic programming method, a first-order filter is introduced to construct the weight update law of the evaluation network, thereby realizing the online estimation of the optimal control law.

[0028] Step S1 further includes:

[0029] The attitude kinematics and dynamics of spacecraft based on quaternions can be described as follows:

[0030]

[0031] in, It is a unit quaternion representing the attitude of a spacecraft. and These are its scalar and vector parts, respectively; It is the body coordinate system F b The following represents the angular velocity; The inertia matrix; To control the input torque; It is a three-dimensional identity matrix; (·) × Represents the antisymmetric matrix of a vector.

[0032] Define attitude tracking error in As desired, q d conjugate, This is a quaternion multiplication operation, from which we can obtain

[0033] Furthermore, the kinematics of the spacecraft attitude tracking error are obtained:

[0034]

[0035] in, For angular velocity error, For the desired angular velocity, Indicates from the desired coordinate system F d To the body coordinate system F b The rotation matrix is ​​expressed as:

[0036]

[0037] Applying the properties of rotation matrices Calculate the derivative of the angular velocity error with respect to time:

[0038]

[0039] Therefore, the dynamics of spacecraft attitude tracking error can be expressed as:

[0040]

[0041] Considering the uncertainty of the inertial parameters J = J0 + ΔJ, where J0 and ΔJ correspond to the known nominal part and the unknown perturbation part of the inertial matrix, respectively, the attitude tracking error dynamics can be rewritten as:

[0042]

[0043] Step S2 further includes:

[0044] Define the sliding mode variable as:

[0045] x=ω e +λσ;

[0046] Where σ=sgn(q) e0 (0))q ev q e0 (0) is q e0 The initial value is sgn(·), which represents the sign function; λ>0 is a positive constant.

[0047] Based on the kinematic and dynamic model of the spacecraft attitude tracking error, a nonlinear affine form of the spacecraft dynamic system model is obtained:

[0048]

[0049] In the formula,

[0050]

[0051]

[0052] Step S3 further includes:

[0053] Define an unknown nonlinear function F(x) = -Ax + f(x), where Given the parameter matrix to be designed, the nonlinear affine form of the spacecraft dynamics system model is rewritten as follows:

[0054]

[0055] Design a three-layer neural network to approximate the unknown nonlinear function F(x):

[0056]

[0057] in, It is the ideal weight matrix between the hidden layer and the output layer, n f It is the number of hidden layer nodes; It is an activation function; It is the input to the hidden layer. It is the ideal weight matrix between the input layer and the hidden layer; It is the approximation error.

[0058] Furthermore, a neural network recognizer of the following form is designed:

[0059]

[0060] in, and x and W respectively f The estimate;

[0061] During the identification process, the weight matrix V f Keep it fixed and initialized to a random constant matrix, only for the weight matrix W f To update, the weight matrix W is constructed based on the Lyapunov method. f The renewal law:

[0062]

[0063] In the formula, For sliding mode variable identification error; r f , ρ f >0 represents a positive constant to be designed.

[0064] Step S4 further includes:

[0065] For a spacecraft dynamics system of nonlinear affine form, design an infinite time-domain cost function:

[0066]

[0067] in, It is a symmetric positive definite coefficient matrix.

[0068] The Hamiltonian function corresponding to the system is:

[0069]

[0070] in,

[0071] Define J respectively * and τ * Based on the optimal cost function and optimal control law, and according to the Hamiltonian function, the Hamilton-Jacobi-Bellman (HJB) equations of the system are obtained:

[0072]

[0073] According to boundary conditions The optimal control law is obtained as follows:

[0074]

[0075] Step S5 further includes:

[0076] Construct an evaluation network to approximate the optimal cost function:

[0077]

[0078] in, It is an activation function, n c It is the number of hidden layer nodes; It is an ideal weight vector; This represents the reconstruction error.

[0079] Calculate the partial derivatives of the optimal cost function with respect to the sliding mode variables:

[0080]

[0081] Furthermore, the optimal control law can be expressed as:

[0082]

[0083] Due to the ideal weight vector W c Usually unknown and difficult to obtain, its estimated value is used. To approximate the optimal cost function and optimal control law:

[0084]

[0085]

[0086] in, and J * (x) and τ * The estimated value.

[0087] Substituting the partial derivatives of the optimal cost function with respect to the sliding mode variables into the HJB equation, we get:

[0088]

[0089] Where, G1=g(x)R -1 g T (x); The residual is expressed as:

[0090]

[0091] in, To evaluate the network weight estimation error.

[0092] definition and We can obtain:

[0093]

[0094] Design a first-order filter of the following form:

[0095]

[0096] In the formula, and These are the regression matrix and regression vector, respectively; l>0 represents the parameters to be designed.

[0097] Solving for the first-order filter yields:

[0098]

[0099] Define auxiliary variables Based on this, the evaluation network weight update law is constructed as follows:

[0100]

[0101] Where, γ c >0 represents the learning rate of the network.

[0102] Example 1

[0103] The nominal value of the spacecraft's inertial matrix is ​​chosen as J0 = [20, 0, 0.9; 0, 17, 0; 0.9, 0, 15] kg·m 2 The perturbation component is ΔJ = 0.01J0; the initial attitude and angular velocity are q(0) = [1, 0, 0, 0] respectively.T And ω(0) = [0, 0, 0] T rad / s; desired attitude and angular velocity are respectively set as q d = [-0.6403, -0.5, -0.3, 0.5] T and ω d =[0, 0, 0] T rad / s.

[0104] The parameters of the neural network identifier are set as follows: A = -10I3, n f =10, γ f =2,ρ f =1, weight matrix V f The weight matrix is ​​initialized with fixed random numbers in the range [-0.5, 0.5], and the estimated value is... and sliding mode variable estimates The initial values ​​are respectively and The network activation function is evaluated as follows The parameters of the approximate optimal control law and the evaluation network weight update law are set as follows: λ = 2, R = 0.1I³, A = I³, l = 1, γc ＝ 0.05, the initial value of the evaluation network weight vector is...

[0105] By employing the attitude control method proposed in this invention, the sliding mode variable identification error curve is as follows: Figure 2 As shown in the figure, under the action of the neural network identifier, the sliding mode variable identification error can converge to a small neighborhood near the origin within 5 seconds. Within this system, the state was effectively reconstructed.

[0106] like Figure 3 and Figure 4 As shown, under the attitude control method proposed in this invention, the spacecraft's attitude tracking error and angular velocity error can converge to a small neighborhood |q| near the origin within 5 seconds. ei |≤10⁻⁴ and|ω ei |≤2×10 -5 Within rad / s (i=1,2,3), this indicates that the control method of the present invention has high tracking accuracy and strong robustness for attitude control of spacecraft with inertial uncertainties.

[0107] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and concept of the present invention, should be within the scope of protection of the present invention.

Claims

1. A robust adaptive dynamic programming method for spacecraft attitude control, characterized in that, Includes the following steps: Step S1: Based on attitude quaternions, establish the kinematic and dynamic model of the spacecraft attitude tracking error; Step S2: Introduce sliding mode variables to transform the attitude error dynamics system, and express it as a nonlinear affine system containing unknown dynamic terms; Step S3: For nonlinear affine dynamic systems, design a neural network identifier and construct a corresponding neural network weight adaptive update law to identify and reconstruct unknown dynamic terms in attitude dynamics online. Step S4: Based on the completion of dynamic reconstruction, construct a cost function that includes attitude tracking error and control input according to the principle of optimality, and design the optimal control law for spacecraft attitude tracking accordingly. Step S5: Based on the adaptive dynamic programming method, a first-order filter is introduced to construct the weight update law of the evaluation network, thereby realizing the online estimation of the optimal control law.

2. The robust adaptive dynamic programming method for spacecraft attitude control according to claim 1, characterized in that, In step S1, The specific form of the kinematic and dynamic model of spacecraft attitude error is as follows: in, The unit quaternion representing attitude error, and These are its scalar and vector parts, respectively; In the spacecraft body coordinate system F b The following represents the angular velocity. For the desired angular velocity, For angular velocity error, Indicates from the desired coordinate system F d To the body coordinate system F b The rotation matrix is ​​expressed as follows: Let J0 and ΔJ be the inertia matrix, and J0 and ΔJ be the known nominal part and the unknown perturbation part of the inertia matrix, respectively. To control the input torque; It is a three-dimensional identity matrix; (·) × Represents the antisymmetric matrix of a vector.

3. The robust adaptive dynamic programming method for spacecraft attitude control according to claim 1, characterized in that, In step S2, Define the sliding mode variable as: x=ω e +λσ; Where σ=sgn(q) e0 (0))q ev q e0 (0) is q e0 The initial value is given by sgn(·), which represents the sign function; λ > 0 is a positive constant. The specific form of a nonlinear affine dynamic system containing unknown dynamic terms is as follows: In the formula, 4. The robust adaptive dynamic programming method for spacecraft attitude control according to claim 1, characterized in that, In step S3, The specific form of a neural network identifier is as follows: In the formula, The parameter matrix to be designed; and x and W respectively f The estimate; It is the input to the hidden layer. It is the ideal weight matrix between the input layer and the hidden layer; It is the ideal weight matrix between the hidden layer and the output layer, n f It is the number of hidden layer nodes; It is an activation function; During the identification process, the weight matrix V f Keep it fixed and initialized to a random constant matrix, only for the weight matrix W f To update, the weight matrix W is constructed based on the Lyapunov method. f The adaptive update law is: In the formula, Error in identifying sliding mode variables; γ f , ρ f >0 represents a positive constant to be designed.

5. The robust adaptive dynamic programming method for spacecraft attitude control according to claim 1, characterized in that, In step S4, For a spacecraft dynamics system of nonlinear affine form, design an infinite time-domain cost function: in, It is a symmetric positive definite coefficient matrix; Based on the principle of optimality, the expression for the optimal control law for attitude tracking is obtained as follows: in, 6. The robust adaptive dynamic programming method for spacecraft attitude control according to claim 1, characterized in that, In step S5, Based on the adaptive dynamic programming method, the estimated value of the optimal control law can be expressed as: In the formula, It is the activation function for evaluating the network, n c It is the number of hidden layer nodes; It is an ideal weight vector The estimated value; The specific form of a first-order filter is: In the formula, and These are the regression matrix and regression vector, respectively; l > 0 represents the parameter to be designed. Based on the first-order filter, design the following form of evaluation network weight update law: in, As an auxiliary variable; γ c >0 is used to evaluate the learning rate of the network.

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