A self-triggered attitude cooperative control method for spacecraft formation considering disturbances

Abstract

The present invention discloses a disturbance-considered self-triggered attitude cooperative control method for a spacecraft formation. The method establishes a kinematic model and a dynamic model for the spacecraft's attitude, designs a state error function and a state measurement error function for the spacecraft, and designs a self-triggered attitude cooperative control law and a self-triggering function based on the state error function and the state measurement error function. The self-triggered attitude cooperative control law and the self-triggering function are then calculated based on the self-triggering function. The current triggering moment corresponding to each spacecraft in the spacecraft formation is then transmitted to adjacent spacecraft at the current triggering moment. The self-triggered attitude cooperative control law and the self-triggering function are then updated based on the state of each spacecraft at the current triggering moment and the received states of adjacent spacecraft at the respective current triggering moments. The control input torque and the next triggering moment are then calculated, thereby achieving self-triggered attitude cooperative control of the spacecraft formation. This method avoids continuous communication and calculation and significantly improves cooperative control performance.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft control technology, and in particular to a disturbance-considered self-triggered attitude collaborative control method for a spacecraft formation. Background Art

[0002] With the rapid development of aerospace microelectronics technology, the operational model of spacecraft formation systems composed of a number of small spacecraft has attracted widespread attention from scholars. Compared with a single large spacecraft, spacecraft formations offer greater robustness, greater flexibility, and lower costs. Therefore, spacecraft formations have great application potential in Earth observation, space-based synthetic aperture radar, and other applications.

[0003] However, communication and computing resources on board spacecraft are limited, and the continuous updating of formation controllers consumes significant amounts of these resources. To conserve formation system resources, a common approach is to have the digital controller periodically send control instructions, known as sampling. However, this approach lacks flexibility and scalability, and its resource conservation efficiency is low. Event-triggered control, by designing the response conditions of the control system, offers significant potential for resource conservation. Therefore, research is needed on event-triggered spacecraft formation control algorithms to conserve resources on formation spacecraft.

[0004] It should be noted that event-triggered control algorithms require a continuous computational trigger mechanism to determine whether the triggering conditions are met, which significantly consumes the computing resources of the formation spacecraft. Therefore, to further avoid the introduction of continuous detection devices, it is necessary to design a self-triggering formation control algorithm to conserve the computing resources of the formation spacecraft.

[0005] Currently, most self-triggered formation control algorithms proposed by researchers are designed for linear systems and cannot be directly applied to complex nonlinear spacecraft formation attitude systems. Furthermore, most existing algorithms require logarithmic calculations to calculate the next trigger moment, making the calculation overly conservative and severely impacting the algorithm's resource efficiency. Summary of the Invention

[0006] In view of the technical problem that the communication and computing resources of the above-mentioned spacecraft formation are limited and continuous updating of the controllers of the spacecraft formation consumes a large amount of the communication and computing resources of the spacecraft formation, the present invention aims to provide a disturbance-considered self-triggered attitude cooperative control method for a spacecraft formation, the method comprising:

[0007] S1. Preset a spacecraft formation, which includes several spacecraft and several spacecraft communication connections, and establish attitude kinematic models and dynamic models of the several spacecraft according to the actual operating environment of the spacecraft formation;

[0008] S2. Design state error functions of several spacecraft based on their attitude kinematic models and dynamic models, design state measurement error functions based on the state error functions, and design self-triggering attitude cooperative control laws and self-triggering functions based on the state error functions and the state measurement error functions;

[0009] S3. Calculate the current triggering time corresponding to each spacecraft in the spacecraft formation according to the self-triggering function, and send the state corresponding to each spacecraft to the adjacent spacecraft at the current triggering time. At the current triggering time corresponding to each spacecraft, update the self-triggering attitude cooperative control law and the self-triggering function according to the state of each spacecraft at the corresponding current triggering time and the received states of the adjacent spacecraft at their respective corresponding current triggering times.

[0010] S4. Calculate the control input torque of each spacecraft at the corresponding current trigger moment according to the self-triggering attitude cooperative control law, and calculate the next trigger moment corresponding to each spacecraft according to the self-triggering function, thereby realizing the self-triggering attitude cooperative control of the spacecraft formation.

[0011] Preferably, in S1, attitude kinematic models and dynamic models of several spacecraft are established according to the actual operating environment of the spacecraft formation. The attitude kinematic model is specifically:

[0012]

[0013] in,

[0014] Where, σ i is the real-time attitude of the i-th spacecraft, is the real-time attitude σ of the i-th spacecraft i The first derivative of ω i is the real-time angular velocity of the i-th spacecraft, I3 is the 3×3 dimensional unit matrix, G(σ i ) is the intermediate process variable, ||σ i || represents the real-time attitude σ of the i-th spacecraft i 2-norm, σ i × represents the real-time attitude σ of the i-th spacecraft i The antisymmetric matrix of

[0015] Preferably, in S1, attitude kinematic models and dynamic models of several spacecraft are established according to the actual operating environment of the spacecraft formation. The dynamic model is specifically:

[0016]

[0017] Where, is the inertia matrix of the i-th spacecraft, is the real-time angular velocity ω of the i-th spacecraft i The first derivative of ω i × represents the real-time attitude of the i-th spacecraft ω i The antisymmetric matrix of is the control input torque of the i-th spacecraft, is the generalized perturbation torque of the i-th spacecraft.

[0018] Preferably, in S2, the state error functions of the multiple spacecraft are designed according to the attitude kinematic models and dynamic models of the multiple spacecraft, specifically including the following:

[0019] S21, preset the expected attitude of the spacecraft σ d and the desired angular velocity ω d ;

[0020] S22, based on the real-time attitude of each spacecraft σ i , the attitudes of adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected attitudes of the preset spacecraft σ d Design the attitude error of each spacecraft relative to the spacecraft formation;

[0021] S23, based on the real-time angular velocity ω of each spacecraft i , the angular velocity of the adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected angular velocity ω of the preset spacecraft d Design the angular velocity error of each spacecraft relative to the spacecraft formation;

[0022] S24. Design a state error function for each spacecraft relative to the spacecraft formation based on the attitude error and angular velocity error.

[0023] Preferably, the attitude error of each spacecraft relative to the spacecraft formation in S22 can be expressed as:

[0024]

[0025] Where, χ 1i is the attitude error of the i-th spacecraft relative to the spacecraft formation, is the current triggering moment corresponding to the j-th spacecraft, is the attitude of the jth spacecraft at the current triggering moment, σ d is the desired attitude of the spacecraft, a ij represents the communication correlation coefficient between the i-th spacecraft and the j-th spacecraft, b i represents the expected information acquisition coefficient of the i-th spacecraft, and n is the total number of spacecraft in the spacecraft formation.

[0026] Preferably, the angular velocity error of each spacecraft relative to the spacecraft formation in S23 can be expressed as:

[0027]

[0028] Where, χ 2i is the angular velocity error of the i-th spacecraft relative to the spacecraft formation, ω d is the desired angular velocity of the spacecraft, is the angular velocity of the jth spacecraft at the current triggering moment.

[0029] Preferably, the state error function of each spacecraft relative to the spacecraft formation in S24 can be expressed as:

[0030] s i =rχ 1i +χ 2i

[0031] Where s i is the state error of the i-th spacecraft relative to the spacecraft formation, and r is a positive constant.

[0032] Preferably, in S2, a state measurement error function is designed according to the state error function, and the state measurement error function can be expressed by the formula:

[0033]

[0034] Where, is the state measurement error of the i-th spacecraft, is the current triggering moment corresponding to the i-th spacecraft, is the state error of the i-th spacecraft at the current triggering moment.

[0035] Preferably, in S2, a self-triggering attitude cooperative control law and a self-triggering function are designed according to the state error function and the state measurement error function. The self-triggering attitude cooperative control law can be expressed as follows:

[0036]

[0037] in,

[0038] Where u i is the control input torque of the i-th spacecraft, υ i is the intermediate process variable, m is the feedback coefficient, m>1, is the attitude error χ of the i-th spacecraft relative to the spacecraft formation at the current triggering moment 1i The first derivative of is the angular velocity of the i-th spacecraft at the current triggering moment, is the expected angular velocity ω of the i-th spacecraft at the current triggering moment d The first derivative of .

[0039] Preferably, in S2, a self-triggering attitude cooperative control law and a self-triggering function are designed according to the state error function and the state measurement error function. The self-triggering function can be expressed as follows:

[0040]

[0041] in,

[0042] δ≥||f i ||

[0043]

[0044] Where, is the next triggering moment of the i-th spacecraft, f i is the nonlinear term of the i-th spacecraft, δ is the nonlinear term ||f i The upper bound of ||, η i is the intermediate process variable, η i (0) is the intermediate process variable η i The initial value of is the intermediate process variable η i The first derivative of , α and All are normal numbers.

[0045] The above-mentioned disturbance-considered self-triggered attitude cooperative control method for a spacecraft formation first establishes an attitude kinematic model and a dynamic model of each spacecraft according to the actual operating environment of the spacecraft formation, then designs a state error function of each spacecraft based on the attitude kinematic model and the dynamic model, and designs a state measurement error function according to the state error function of each spacecraft, and designs a self-triggered attitude cooperative control law and a self-triggered function according to the state error function and the state measurement error function; then, the current triggering moment corresponding to each spacecraft in the spacecraft formation is calculated according to the self-triggered function, and the state corresponding to each spacecraft is sent to the adjacent spacecraft at the current triggering moment, and at the current triggering moment corresponding to each spacecraft, the self-triggered attitude cooperative control law and the self-triggered function are updated according to the state of each spacecraft at the corresponding current triggering moment and the state of the adjacent spacecraft at the corresponding current triggering moment that has been received; finally, the control input torque of each spacecraft at the corresponding current triggering moment is calculated according to the self-triggered attitude cooperative control law, and the next triggering moment corresponding to each spacecraft is calculated according to the self-triggered function, thereby realizing self-triggered attitude cooperative control of the spacecraft formation. This method uses the current trigger moment state to estimate the next trigger moment, which can avoid continuous calculation. The operation of the trigger mechanism does not require the continuous state of adjacent spacecraft. Compared with traditional event-triggered control, this method can avoid continuous calculation and significantly improve the control system performance while appropriately increasing the trigger frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a flow chart of a method for self-triggered attitude cooperative control of a spacecraft formation considering disturbances in one embodiment of the present invention;

[0047] Figure 2 is a communication topology diagram of a spacecraft formation in one embodiment of the present invention;

[0048] Figure 3 is the attitude error of each spacecraft in the spacecraft formation in one embodiment of the present invention;

[0049] Figure 4 is the angular velocity error of each spacecraft in the spacecraft formation in one embodiment of the present invention;

[0050] Figure 5 is the control input torque of each spacecraft in the spacecraft formation in one embodiment of the present invention;

[0051] Figure 6 It is the triggering moment of each spacecraft in the spacecraft formation in one embodiment of the present invention. DETAILED DESCRIPTION

[0052] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below with reference to the accompanying drawings.

[0053] A disturbance-considered self-triggered attitude cooperative control method for a spacecraft formation is proposed, which specifically includes:

[0054] S1. Preset a spacecraft formation, which includes several spacecraft and several spacecraft communication connections, and establish attitude kinematic models and dynamic models of the several spacecraft according to the actual operating environment of the spacecraft formation;

[0055] S2. Design state error functions of several spacecraft based on their attitude kinematic models and dynamic models, design state measurement error functions based on the state error functions, and design self-triggering attitude cooperative control laws and self-triggering functions based on the state error functions and the state measurement error functions;

[0056] S3. Calculate the current triggering time corresponding to each spacecraft in the spacecraft formation according to the self-triggering function, and send the state corresponding to each spacecraft to the adjacent spacecraft at the current triggering time. At the current triggering time corresponding to each spacecraft, update the self-triggering attitude cooperative control law and the self-triggering function according to the state of each spacecraft at the corresponding current triggering time and the received states of the adjacent spacecraft at their respective corresponding current triggering times.

[0057] S4. Calculate the control input torque of each spacecraft at the corresponding current trigger moment according to the self-triggering attitude cooperative control law, and calculate the next trigger moment corresponding to each spacecraft according to the self-triggering function, thereby realizing the self-triggering attitude cooperative control of the spacecraft formation.

[0058] Specifically, see Figure 1 , Figure 1 The present invention is a flowchart of a method for self-triggered attitude collaborative control of a spacecraft formation taking disturbance into consideration in one embodiment of the present invention.

[0059] A method for self-triggered attitude cooperative control of a spacecraft formation considering disturbances is provided. First, a spacecraft formation is preset, and the spacecraft formation includes several spacecraft. The communication connections of the several spacecraft enable each spacecraft to directly or indirectly obtain desired information (including desired attitude and desired angular velocity). An attitude kinematic model and a dynamic model of each spacecraft are established according to the actual operating environment of the spacecraft formation. Then, a state error function of each spacecraft is designed based on the attitude kinematic model and the dynamic model, and a state measurement error function is designed according to the state error function. A self-triggered attitude cooperative control law and a self-triggering function are designed according to the state error function and the state measurement error function. Then, a current triggering moment corresponding to each spacecraft in the spacecraft formation (the current triggering moment corresponding to each spacecraft) is calculated according to the self-triggering function. The triggering moments may be the same or different), and the state (including attitude and angular velocity) corresponding to each spacecraft is sent to the adjacent spacecraft at the current triggering moment (the adjacent spacecraft here refers to each other spacecraft in the spacecraft formation that can communicate with the current spacecraft). At the current triggering moment corresponding to each spacecraft, the self-triggered attitude cooperative control law and the self-triggering function are updated according to the state of each spacecraft at the corresponding current triggering moment and the received states of the adjacent spacecraft at their respective corresponding current triggering moments. Finally, the control input torque of each spacecraft at the corresponding current triggering moment is calculated according to the self-triggering attitude cooperative control law, and the next triggering moment corresponding to each spacecraft is calculated according to the self-triggering function, thereby realizing the self-triggered attitude cooperative control of the spacecraft formation.

[0060] In one embodiment, in S1, attitude kinematic models and dynamic models of several spacecraft are established according to the actual operating environment of the spacecraft formation. The attitude kinematic model is specifically:

[0061]

[0062] in,

[0063] Where, σ i is the real-time attitude of the i-th spacecraft, is the real-time attitude σ of the i-th spacecraft i The first derivative of ω i is the real-time angular velocity of the i-th spacecraft, I3 is the 3×3 dimensional unit matrix, G(σ i ) is the intermediate process variable, ||σ i || represents the real-time attitude σ of the i-th spacecraft i 2-norm, σ i × represents the real-time attitude σ of the i-th spacecraft i The antisymmetric matrix of

[0064] In one embodiment, in S1, attitude kinematic models and dynamic models of several spacecraft are established according to the actual operating environment of the spacecraft formation. The dynamic model is specifically:

[0065]

[0066] Where, is the inertia matrix of the i-th spacecraft, is the real-time angular velocity ω of the i-th spacecraft i The first derivative of ω i × represents the real-time attitude of the i-th spacecraft ω i The antisymmetric matrix of is the control input torque of the i-th spacecraft, is the generalized perturbation torque of the i-th spacecraft.

[0067] Specifically, the attitude kinematic model and dynamic model of each spacecraft are established according to the actual operating environment of the spacecraft formation:

[0068] The attitude kinematic model of the i-th spacecraft is as follows:

[0069]

[0070] in,

[0071] The dynamic model of the i-th spacecraft is as follows:

[0072]

[0073] Where, is the real-time attitude of the i-th spacecraft in the spacecraft formation described by the modified Rodriguez parameters, is the real-time attitude σ of the i-th spacecraft i The first derivative of is the real-time angular velocity of the i-th spacecraft, is the real-time angular velocity ω of the i-th spacecraft i The first derivative of is the inertia matrix of the i-th spacecraft, I3 is the 3×3 dimensional unit matrix, is the control torque of the i-th spacecraft, is the generalized disturbance torque of the i-th spacecraft including external disturbance and model uncertainty, G(σ i ) is an intermediate process variable. In general, for a vector or matrix x, ||x|| represents the 2-norm of x. For a three-dimensional vector The definition is as follows:

[0074]

[0075] In the above-mentioned attitude kinematics model and dynamics model of the i-th spacecraft, x corresponds to the real-time attitude σ of the i-th spacecraft. i and real-time angular velocity ω i .

[0076] In one embodiment, in S2, state error functions of several spacecraft are designed based on their attitude kinematic models and dynamic models, specifically including the following:

[0077] S21, preset the expected attitude of the spacecraft σ d and the desired angular velocity ω d ;

[0078] S22, based on the real-time attitude of each spacecraft σ i , the attitudes of adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected attitudes of the preset spacecraft σ d Design the attitude error of each spacecraft relative to the spacecraft formation;

[0079] S23, based on the real-time angular velocity ω of each spacecraft i , the angular velocity of the adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected angular velocity ω of the preset spacecraft d Design the angular velocity error of each spacecraft relative to the spacecraft formation;

[0080] S24. Design a state error function for each spacecraft relative to the spacecraft formation based on the attitude error and angular velocity error.

[0081] In one embodiment, the attitude error of each spacecraft relative to the spacecraft formation in S22 can be expressed as:

[0082]

[0083] Where, χ 1i is the attitude error of the i-th spacecraft relative to the spacecraft formation, is the current triggering moment corresponding to the j-th spacecraft, is the attitude of the jth spacecraft at the current triggering moment, σ d is the desired attitude of the spacecraft, a ij represents the communication correlation coefficient between the i-th spacecraft and the j-th spacecraft, b i represents the expected information acquisition coefficient of the i-th spacecraft, and n is the total number of spacecraft in the spacecraft formation.

[0084] In one embodiment, the angular velocity error of each spacecraft relative to the spacecraft formation in S23 can be expressed as:

[0085]

[0086] Where, χ 2i is the angular velocity error of the i-th spacecraft relative to the spacecraft formation, ω d is the desired angular velocity of the spacecraft, is the angular velocity of the jth spacecraft at the current triggering moment.

[0087] In one embodiment, the state error function of each spacecraft relative to the spacecraft formation in S24 can be expressed as:

[0088] s i =rχ 1i +χ 2i

[0089] Where s i is the state error of the i-th spacecraft relative to the spacecraft formation, and r is a positive constant.

[0090] Specifically, the state error function of each spacecraft is designed according to its attitude kinematic model and dynamic model. The process is as follows:

[0091] 1) Preset the expected attitude of the spacecraft σ d and the desired angular velocity ω d ;

[0092] 2) According to the real-time attitude σ of the i-th spacecraft i , the attitudes of adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected attitude of the spacecraft σ d Design the attitude error of the i-th spacecraft relative to the spacecraft formation. The specific formula is:

[0093]

[0094] Where, χ 1i is the attitude error of the i-th spacecraft relative to the spacecraft formation, σ i is the real-time attitude of the i-th spacecraft, is the current triggering moment corresponding to the j-th spacecraft, is the attitude of the jth spacecraft at the current triggering moment, σ d is the desired attitude of the spacecraft, a ij represents the communication correlation coefficient between the i-th spacecraft and the j-th spacecraft in the spacecraft formation, b irepresents the coefficient for obtaining the expected information (including expected attitude and expected angular velocity) of the i-th spacecraft, and n is the total number of spacecraft in the spacecraft formation.

[0095] It should be noted that if the i-th spacecraft in the spacecraft formation can receive the information of the j-th spacecraft, then the j-th spacecraft is the adjacent spacecraft of the i-th spacecraft, and a ij > 0, otherwise, a ij = 0, in addition, the spacecraft has no self-loop communication, i.e. a ii = 0. If the i-th spacecraft can obtain the expected information, then b i =1, otherwise b i =0.

[0096] 3) According to the real-time angular velocity ω of the i-th spacecraft i , the angular velocity of the adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected angular velocity ω of the spacecraft d Design the angular velocity error of the i-th spacecraft relative to the spacecraft formation. The specific formula is:

[0097]

[0098] Where, χ 2i is the angular velocity error of the i-th spacecraft relative to the spacecraft formation, ω i is the real-time angular velocity of the i-th spacecraft, ω d is the desired angular velocity of the spacecraft, is the angular velocity of the jth spacecraft at the current triggering moment.

[0099] 4) Design the state error function of the i-th spacecraft relative to the spacecraft formation based on the attitude error and angular velocity error of the i-th spacecraft relative to the spacecraft formation. The specific formula is:

[0100] s i =rχ 1i +χ 2i (6)

[0101] Where s i is the state error of the i-th spacecraft relative to the spacecraft formation, and r is a positive constant.

[0102] In one embodiment, in S2, a state measurement error function is designed based on the state error function. The state measurement error function can be expressed as:

[0103]

[0104] Where, is the state measurement error of the i-th spacecraft, is the current triggering moment corresponding to the i-th spacecraft, is the state error of the i-th spacecraft at the current triggering moment.

[0105] Specifically, a state measurement error function for the i-th spacecraft is designed based on the state error of the i-th spacecraft relative to the spacecraft formation and the state error of the i-th spacecraft at the current triggering moment. This function is used to determine whether the state measurement error of the i-th spacecraft exceeds a preset state measurement error threshold and decide whether the state of the i-th spacecraft needs to be updated. The state measurement error function for the i-th spacecraft is designed as follows:

[0106]

[0107] in,

[0108]

[0109]

[0110] Where, is the current triggering moment corresponding to the i-th spacecraft, is the state measurement error of the i-th spacecraft, is the state error of the i-th spacecraft at the current triggering moment, s i is the state error of the i-th spacecraft relative to the spacecraft formation.

[0111] In one embodiment, in S2, a self-triggering attitude cooperative control law and a self-triggering function are designed based on the state error function and the state measurement error function. The self-triggering attitude cooperative control law can be expressed as follows:

[0112]

[0113] in,

[0114] Where u i is the control input torque of the i-th spacecraft, υ i is the intermediate process variable, m is the feedback coefficient, m>1, is the attitude error χ of the i-th spacecraft relative to the spacecraft formation at the current triggering moment 1i The first derivative of is the angular velocity of the i-th spacecraft at the current triggering moment, is the expected angular velocity ω of the i-th spacecraft at the current triggering moment d The first derivative of .

[0115] In one embodiment, in S2, a self-triggering attitude cooperative control law and a self-triggering function are designed based on the state error function and the state measurement error function. The self-triggering function can be expressed as follows:

[0116]

[0117] in,

[0118] δ≥||f i ||

[0119]

[0120] Where, is the next triggering moment of the i-th spacecraft, f i is the nonlinear term of the i-th spacecraft, δ is the nonlinear term ||f i The upper bound of ||, η i is the intermediate process variable, η i (0) is the intermediate process variable η i The initial value of is the intermediate process variable η i The first derivative of , α and All are normal numbers.

[0121] Specifically, the design process of the self-triggering attitude cooperative control law and the self-triggering function is as follows:

[0122] According to formulas (1) to (7), the state error s of the i-th spacecraft relative to the spacecraft formation can be calculated as i The first derivative of :

[0123]

[0124] Where, is the state error s of the i-th spacecraft relative to the spacecraft formation i The first derivative of .

[0125] According to formula (8), the design idea of ​​the self-triggered attitude cooperative control law of the i-th spacecraft is: To reduce ω i × J i ω i Impact on spacecraft formations, The term is used to control the coefficient is the feedback item, Used to reduce The impact on the spacecraft formation. Based on this, in order to save system resources, a self-triggered attitude cooperative control law is designed. The control input torque of the i-th spacecraft can be calculated through the self-triggered attitude cooperative control law. The self-triggered attitude cooperative control law is designed as follows:

[0126]

[0127] in,

[0128] Where u i is the control input torque of the i-th spacecraft, is the current triggering moment corresponding to the i-th spacecraft, υ i is the intermediate process variable, m is the feedback coefficient, m>1, is the attitude error χ of the i-th spacecraft relative to the spacecraft formation at the current triggering moment 1i The first derivative of is the angular velocity of the i-th spacecraft at the current triggering moment, is the expected angular velocity ω of the i-th spacecraft at the current triggering moment d The first derivative of .

[0129] Substituting formula (9) and (9)-1 into formula (8), we can obtain:

[0130]

[0131] Where, f i is the nonlinear term of the i-th spacecraft.

[0132] By solving formula (10), the nonlinear term f of the i-th spacecraft can be obtained: i Specifically:

[0133]

[0134] Based on formula (7), the dynamic event trigger function is designed as follows:

[0135]

[0136] in,

[0137] Where, The next triggering moment of the i-th spacecraft, represents the current triggering moment corresponding to the i-th spacecraft, inf represents the lower limit function, η i is the intermediate process variable, η i (0) is the initial value of the intermediate process variable, η i (0)>0, is the intermediate process variable η i The first derivative of , m is the feedback coefficient, m>1, α and are all control parameters, and α>0,

[0138] Since the above dynamic event trigger function (12) needs to be calculated continuously to determine whether the triggering conditions are met, this brings a heavy computational burden to the spacecraft formation.

[0139] Taking into account Increase from 0 to right Taking the derivative we get:

[0140]

[0141] Where δ is the nonlinear term ||f i The upper bound of ||, that is, δ≥||f i ||.

[0142] according to The definition of and dynamic event trigger function (12) show that Thus we can get η i ≥η i (0)e -(α+m / 2)t , and η i is a monotonically decreasing function.

[0143] Based on this, a self-triggering function is designed to calculate the next triggering moment of the i-th spacecraft through the self-triggering function, where the self-triggering function is designed as:

[0144]

[0145] Where, is the next triggering moment corresponding to the i-th spacecraft, η i is the intermediate process variable, which can be obtained from formula (12)-1, f i is the nonlinear term of the i-th spacecraft, which can be obtained from formula (11), and δ is the nonlinear term ||f i The upper bound of ||, δ≥||f i ‖,η i (0) is the intermediate process variable η i The initial values ​​of α and are all control parameters, and η i (0)>0,α>0,

[0146] Through the above-mentioned self-triggered attitude cooperative control law and self-triggering function, each spacecraft in the spacecraft formation updates the self-triggered attitude cooperative control law at its corresponding current triggering moment, and calculates the control input torque and the next triggering moment accordingly. The spacecraft executes the control input torque and sends the corresponding state of the spacecraft to the adjacent spacecraft at the current triggering moment, thereby controlling the attitude and angular velocity of each spacecraft in the spacecraft formation and realizing self-triggered attitude cooperative control of the spacecraft formation.

[0147] Furthermore, the control effect of the above-mentioned spacecraft formation self-triggered attitude cooperative control method considering disturbances was verified through numerical simulation.

[0148] See also Figure 2 , Figure 2 is a communication topology diagram of a spacecraft formation in one embodiment of the present invention, Figure 2 There are 4 spacecraft in the spacecraft formation shown. In the experiment, the relevant parameters of these 4 spacecraft are set as follows:

[0149] The inertia matrix is ​​set as:

[0150] J1=[10.2,0.1,0.1;0.1,10.3,0.2;0.1,0.2,9.8]kg·m 2

[0151] J2=[8.9,0.2,0.1;0.2,9.4,0.2;0.1,0.2,10]kg·m 2

[0152] J3=[9.9,0.2,0.2;0.2,9.8,0.1;0.2,0.1,10.5]kg·m 2

[0153] J4=[8.8,0.1,0.2;0.1,9.6,0.1;0.2,0.1,10.1]kg·m 2

[0154] The generalized perturbation torque is set as:

[0155] ρ1=[2sin(0.1t),2sin(0.2t),cos(0.2t)] T ×10 -3 N·m

[0156] ρ2=[3sin(0.2t),2cos(0.3t),2sin(0.1t)] T ×10 -3 N·m

[0157] ρ3=[cos(0.2t),2cos(0.1t),sin(0.1t)] T ×10 -3 N·m

[0158] ρ4=[2cos(0.1t),sin(0.2t),sin(0.2t)] T ×10 -3 N·m

[0159] The initial posture selection is:

[0160] σ1(0)=[0.3,-0.1,0.2] T

[0161] σ2(0)=[0.1,0.2,0.3] T

[0162] σ3(0)=[0.3,-0.2,-0.1] T

[0163] σ4(0)=[0.1,0.4,-0.3] T

[0164] The initial angular velocity is chosen as:

[0165] ω1(0)=[0.05,0.1,0.05] T rad / s

[0166] ω2(0)=[-0.03,0.04,0.04] T rad / s

[0167] ω3(0)=[-0.05,0.03,0.02] T rad / s

[0168] ω4(0)=[0.03,-0.04,-0.04] T rad / s

[0169] The desired pose is set as:

[0170] σ d =[3sin(0.05t),2sin(0.03t),-cos(0.03t)] T ×10 -3

[0171] The maximum control torque is set as:

[0172] |u il |≤0.2Nm, where l=x,y,z

[0173] The relevant control parameters are set as:

[0174] k=1.6, r=0.5, α=2, δ=0.05, η i (0)=1, i=1,2,3,4.

[0175] Under the above simulation conditions, the simulation results are as follows Figures 3 to 6 shown. Figure 3 is the attitude error of each spacecraft in the spacecraft formation in one embodiment of the present invention, Figure 4 is the angular velocity error of each spacecraft in the spacecraft formation in one embodiment of the present invention, Figure 5 is the control input torque of each spacecraft in the spacecraft formation in one embodiment of the present invention, Figure 6 It is the triggering moment of each spacecraft in the spacecraft formation in one embodiment of the present invention.

[0176] See Table 1, which shows the control performance of the above-mentioned spacecraft formation under the self-triggered attitude cooperative control algorithm.

[0177] Table 1

[0178] Attitude error Angular velocity error Convergence time (s) X-axis <![CDATA[1.1×10 -3 ]]> <![CDATA[5.6×10 -4 ]]> 40 Y-axis <![CDATA[6.3×10 -4 ]]> <![CDATA[4.4×10 -4 ]]> 40 Z-axis <![CDATA[6.9×10 -4 ]]> <![CDATA[3.0×10 -4 ]]> 40

[0179] As can be seen in Table 1, the proposed algorithm achieves excellent control performance, with high convergence accuracy and rapid convergence. Furthermore, compared to a cooperative control algorithm with a 10Hz update frequency, the proposed algorithm reduces the number of triggers by over 85%. This means that communication between spacecraft in the formation and the computational effort required to update the cooperative control algorithm can be reduced by over 85%.

[0180] The above-mentioned disturbance-considered self-triggered attitude cooperative control method for a spacecraft formation first establishes an attitude kinematic model and a dynamic model of each spacecraft according to the actual operating environment of the spacecraft formation, then designs a state error function of each spacecraft based on the attitude kinematic model and the dynamic model, and designs a state measurement error function according to the state error function, and designs a self-triggered attitude cooperative control law and a self-triggered function according to the state error function and the state measurement error function; then, the current triggering moment corresponding to each spacecraft in the spacecraft formation is calculated according to the self-triggered function, and the state corresponding to each spacecraft is sent to the adjacent spacecraft at the current triggering moment, and at the current triggering moment corresponding to each spacecraft, the self-triggered attitude cooperative control law and the self-triggered function are updated according to the state of each spacecraft at the corresponding current triggering moment and the state of the adjacent spacecraft at the corresponding current triggering moment that has been received; finally, the control input torque of each spacecraft at the corresponding current triggering moment is calculated according to the self-triggered attitude cooperative control law, and the next triggering moment corresponding to each spacecraft is calculated according to the self-triggered function, thereby realizing self-triggered attitude cooperative control of the spacecraft formation. This method uses the current trigger moment state to estimate the next trigger moment, which can avoid continuous calculation. The operation of the trigger mechanism does not require the continuous state of adjacent spacecraft. Compared with traditional event-triggered control, this method can avoid continuous calculation and significantly improve the control system performance while appropriately increasing the trigger frequency.

[0181] The above is a detailed introduction to the disturbance-taking self-triggered attitude collaborative control method for a spacecraft formation provided by the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the core idea of ​​the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for self-triggered attitude cooperative control of a spacecraft formation considering disturbances, characterized in that: The method comprises: S1. Preset a spacecraft formation, the spacecraft formation including a plurality of spacecraft, the plurality of spacecraft being communicatively connected, and establish attitude kinematic models and dynamic models of the plurality of spacecraft according to an actual operating environment of the spacecraft formation; S2. Designing state error functions of the spacecraft based on their attitude kinematic models and dynamic models, designing state measurement error functions based on the state error functions, and designing self-triggering attitude cooperative control laws and self-triggering functions based on the state error functions and the state measurement error functions; S3. Calculate the current triggering moment corresponding to each spacecraft in the spacecraft formation according to the self-triggering function, and send the state corresponding to each spacecraft to the adjacent spacecraft at the current triggering moment. At the current triggering moment corresponding to each spacecraft, update the self-triggering attitude cooperative control law and the self-triggering function according to the state of each spacecraft at the corresponding current triggering moment and the received states of the adjacent spacecraft at their respective corresponding current triggering moments. S4. Calculate the control input torque of each spacecraft at the corresponding current trigger moment according to the self-triggering attitude collaborative control law, and calculate the next trigger moment corresponding to each spacecraft according to the self-triggering function, thereby realizing the self-triggering attitude collaborative control of the spacecraft formation.

2. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 1, characterized in that: In S1, several attitude kinematic models and dynamic models of the spacecraft are established according to the actual operating environment of the spacecraft formation. The attitude kinematic model is specifically: in, Where, σ i is the real-time attitude of the i-th spacecraft, is the real-time attitude σ of the i-th spacecraft i The first derivative of ω i is the real-time angular velocity of the i-th spacecraft, I3 is the 3×3 dimensional unit matrix, G(σ i ) is the intermediate process variable, ||σ i || represents the real-time attitude σ of the i-th spacecraft i 2-norm, σ i × represents the real-time attitude σ of the i-th spacecraft i The antisymmetric matrix of 3. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 2, characterized in that: In S1, several attitude kinematic models and dynamic models of the spacecraft are established according to the actual operating environment of the spacecraft formation. The dynamic models are specifically: Where, is the inertia matrix of the i-th spacecraft, is the real-time angular velocity ω of the i-th spacecraft i The first derivative of ω i × represents the real-time attitude of the i-th spacecraft ω i The antisymmetric matrix of is the control input torque of the i-th spacecraft, is the generalized perturbation torque of the i-th spacecraft.

4. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 3, characterized in that: In S2, the state error functions of the spacecraft are designed according to the attitude kinematic models and dynamic models of the spacecraft, specifically including the following: S21, preset the expected attitude of the spacecraft σ d and the desired angular velocity ω d ; S22, based on the real-time attitude of each spacecraft σ i , the attitudes of adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected attitudes of the preset spacecraft σ d designing an attitude error of each spacecraft relative to the spacecraft formation; S23, based on the real-time angular velocity ω of each spacecraft i , the angular velocity of the adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected angular velocity ω of the preset spacecraft d designing the angular velocity error of each spacecraft relative to the spacecraft formation; S24. Design a state error function of each spacecraft relative to the spacecraft formation based on the attitude error and angular velocity error.

5. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 4, characterized in that: The attitude error of each spacecraft relative to the spacecraft formation in S22 can be expressed as: Where, χ 1i is the attitude error of the i-th spacecraft relative to the spacecraft formation, is the current triggering moment corresponding to the j-th spacecraft, is the attitude of the jth spacecraft at the current triggering moment, σ d is the desired attitude of the spacecraft, a ij represents the communication correlation coefficient between the i-th spacecraft and the j-th spacecraft, b i represents the expected information acquisition coefficient of the i-th spacecraft, and n is the total number of spacecraft in the spacecraft formation.

6. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 5, characterized in that: The angular velocity error of each spacecraft relative to the spacecraft formation in S23 can be expressed as follows: Where, χ 2i is the angular velocity error of the i-th spacecraft relative to the spacecraft formation, ω d is the desired angular velocity of the spacecraft, is the angular velocity of the jth spacecraft at the current triggering moment.

7. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 6, characterized in that: The state error function of each spacecraft relative to the spacecraft formation in S24 can be expressed as: s i =rx 1i +x 2i Where s i is the state error of the i-th spacecraft relative to the spacecraft formation, and r is a positive constant.

8. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 7, characterized in that: In S2, a state measurement error function is designed according to the state error function. The state measurement error function can be expressed as follows: Where, is the state measurement error of the i-th spacecraft, is the current triggering moment corresponding to the i-th spacecraft, is the state error of the i-th spacecraft at the current triggering moment.

9. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 8, characterized in that: In S2, a self-triggering attitude cooperative control law and a self-triggering function are designed according to the state error function and the state measurement error function. The self-triggering attitude cooperative control law can be expressed as follows: in, Where u i is the control input torque of the i-th spacecraft, υ i is the intermediate process variable, m is the feedback coefficient, m>1, is the attitude error χ of the i-th spacecraft relative to the spacecraft formation at the current triggering moment 1i The first derivative of is the angular velocity of the i-th spacecraft at the current triggering moment, is the expected angular velocity ω of the i-th spacecraft at the current triggering moment d The first derivative of .

10. The method for self-triggered attitude coordinated control of a spacecraft formation considering disturbances according to claim 9, characterized in that: In S2, a self-triggering attitude cooperative control law and a self-triggering function are designed according to the state error function and the state measurement error function. The self-triggering function can be expressed as follows: in, δ≥||f i || Where, is the next triggering moment of the i-th spacecraft, f i is the nonlinear term of the i-th spacecraft, δ is the nonlinear term ||f i The upper bound of ||, η i is the intermediate process variable, η i (0) is the intermediate process variable η i The initial value of is the intermediate process variable η i The first derivative of , α and All are normal numbers.

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