Spacecraft formation self-triggering attitude cooperative control method considering disturbance

Abstract

The invention discloses a spacecraft formation self-triggering attitude cooperative control method considering disturbance, and the method comprises the steps: building an attitude kinematics model and a dynamics model of a spacecraft, and designing a state error function and a state measurement error function of the spacecraft; designing a self-triggering attitude cooperative control law and a self-triggering function according to the state error function and the state measurement error function, calculating a current triggering moment corresponding to each spacecraft in the spacecraft formation according to the self-triggering function, and sending a state corresponding to each spacecraft at the current triggering moment to an adjacent spacecraft, updating a self-triggering attitude cooperative control law and a self-triggering function according to the state of each spacecraft at the corresponding current triggering moment and the received state of the adjacent spacecraft at the corresponding current triggering moment, and calculating a control input torque and the next triggering moment; therefore, the self-triggering attitude cooperative control of the spacecraft formation is realized. According to the method, continuous communication and calculation can be avoided, and the cooperative control performance is remarkably improved.

Description

Technical Field

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

[0002] With the rapid development of aerospace microelectronics technology, the working mode of a spacecraft formation system composed of a number of small spacecraft has attracted widespread attention from scholars. Compared with a single large spacecraft, a spacecraft formation has stronger robustness, better flexibility and lower cost. Therefore, spacecraft formation has great application potential in earth observation, space-based synthetic aperture radar, etc.

[0003] However, the communication and computing resources on the spacecraft are limited, and the continuous update of the formation controller will consume a large amount of communication and computing resources of the formation spacecraft. In order to save the resources of the formation system, a common method is to let the digital controller send control instructions regularly, that is, sampling. However, this method lacks flexibility and scalability, and the resource saving efficiency is not high. Event-triggered control saves system resources by designing the response conditions of the control system, and has great potential in resource saving. Therefore, it is necessary to study the spacecraft formation control algorithm based on event triggering to save the resources of the formation spacecraft.

[0004] It should be noted that the event-triggered control algorithm needs to introduce a continuous calculation trigger mechanism to determine whether the trigger condition is met, which greatly consumes the computing resources of the formation spacecraft. Therefore, in order to further avoid the introduction of continuous detection devices, it is necessary to design a self-triggered formation control algorithm to save the computing resources of the formation spacecraft.

[0005] At present, most of the self-triggered formation control algorithms proposed by researchers are designed for linear systems and cannot be directly applied to spacecraft formation attitude systems with complex nonlinearities. In addition, in the calculation of the next trigger moment, most existing algorithms require logarithmic calculations, which makes the calculation of the next trigger moment too conservative, seriously affecting the resource saving efficiency of the algorithm. Summary of the invention

[0006] In view of the technical problem that the communication and computing resources on the above-mentioned spacecraft formation are limited and the continuous updating of the controller on the spacecraft formation will consume a large amount of communication and computing resources of the spacecraft formation, the object of the present invention is to provide a spacecraft formation self-triggered attitude cooperative control method considering disturbances, the method comprising:

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

[0008] S2. designing state error functions of several spacecraft according to attitude kinematic models and dynamic models of several spacecraft, designing state measurement error functions according to the state error functions, and designing self-triggering attitude cooperative control laws and self-triggering functions according to 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 states of the adjacent spacecraft at the corresponding current triggering time that have been received.

[0010] S4. Calculate the control input torque of each spacecraft at the corresponding current triggering moment according to the self-triggering attitude collaborative control law, and calculate the next triggering moment corresponding to each spacecraft according to the self-triggering function, thereby realizing the self-triggering attitude collaborative 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] In the formula, 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 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 The 2-norm of 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, and the dynamic model is specifically:

[0016]

[0017] In the formula, 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 i × represents the real-time attitude of the i-th spacecraft ω i The antisymmetric matrix of is the control input torque of the ith spacecraft, is the generalized perturbation torque of the ith spacecraft.

[0018] Preferably, in S2, the state error functions of the several spacecraft are designed according to the attitude kinematics models and dynamics models of the several spacecraft, which specifically include 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 the adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected attitude 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 of each spacecraft relative to the spacecraft formation based on the attitude error and the angular velocity error.

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

[0024]

[0025] In the formula, χ 1i is the attitude error of the ith spacecraft relative to the spacecraft formation, is the current triggering time 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 by the formula:

[0027]

[0028] In the formula, 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 by the formula:

[0030] s i = rx 1i +χ 2i

[0031] In the formula, s i is the state error of the ith 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] In the formula, is the state measurement error of the i-th spacecraft, is the current triggering time 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 by the formula:

[0036]

[0037] in,

[0038] In the formula, u i is the control input torque of the ith 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 by the formula:

[0040]

[0041] in,

[0042] δ≥||f i ||

[0043]

[0044] In the formula, is the next triggering time 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 method for self-triggered attitude cooperative control of spacecraft formation considering disturbance first establishes the attitude kinematic model and dynamic model of each spacecraft according to the actual operating environment of the spacecraft formation, then designs the state error function of each spacecraft based on the attitude kinematic model and the dynamic model, and designs the state measurement error function according to the state error function of each spacecraft, and designs the self-triggered attitude cooperative control law and the self-triggered function according to the state error function and the state measurement error function; then calculates the current triggering moment corresponding to each spacecraft in the spacecraft formation according to the self-triggered function, and sends the state corresponding to each spacecraft to the adjacent spacecraft at the current triggering moment, and updates the self-triggered attitude cooperative control law and the self-triggered function 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, calculates the control input torque of each spacecraft at the corresponding current triggering moment according to the self-triggered attitude cooperative control law, and calculates the next triggering moment corresponding to each spacecraft according to the self-triggered function, thereby realizing the self-triggered attitude cooperative control of the spacecraft formation. This method uses the current trigger state to estimate the next trigger time, which can avoid continuous calculation, and 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 under the premise of appropriately increasing the trigger frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flow chart of a method for self-triggered attitude cooperative control of a spacecraft formation taking disturbance into consideration 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 in conjunction with the accompanying drawings.

[0053] A method for self-triggered attitude cooperative control of spacecraft formation considering disturbances, specifically comprising:

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

[0055] S2. designing state error functions of several spacecraft according to attitude kinematic models and dynamic models of several spacecraft, designing state measurement error functions according to the state error functions, and designing self-triggering attitude cooperative control laws and self-triggering functions according to 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 states of the adjacent spacecraft at the corresponding current triggering time that have been received.

[0057] S4. Calculate the control input torque of each spacecraft at the corresponding current triggering moment according to the self-triggering attitude collaborative control law, and calculate the next triggering moment corresponding to each spacecraft according to the self-triggering function, thereby realizing the self-triggering attitude collaborative 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 cooperative 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, firstly, a spacecraft formation is preset, the spacecraft formation includes a plurality of spacecrafts, the plurality of spacecrafts are connected in communication so that each spacecraft can 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, and 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 (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, 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, the self-triggered attitude collaborative control law and the self-triggering function are updated, and finally, the control input torque of each spacecraft at the corresponding current triggering moment is calculated according to the self-triggered attitude collaborative 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 collaborative 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] In the formula, 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 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 The 2-norm of 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] In the formula, 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 i × represents the real-time attitude of the i-th spacecraft ω i The antisymmetric matrix of is the control input torque of the ith spacecraft, is the generalized perturbation torque of the ith spacecraft.

[0067] Specifically, the attitude kinematics model and dynamics 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] In the formula, 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 ith spacecraft, is the generalized disturbance torque of the ith 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 the real-time angular velocity ω i .

[0076] In one embodiment, in S2, state error functions of several spacecraft are designed according to attitude kinematic models and dynamic models of the several spacecraft, which specifically include 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 the adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected attitude 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 of each spacecraft relative to the spacecraft formation based on the attitude error and the angular velocity error.

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

[0082]

[0083] In the formula, χ 1i is the attitude error of the ith spacecraft relative to the spacecraft formation, is the current triggering time 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 by the formula:

[0085]

[0086] In the formula, 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 by the formula:

[0088] s i = rx 1i +χ 2i

[0089] In the formula, s i is the state error of the ith 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 the attitude kinematics model and dynamics model of each spacecraft. 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] In the formula, 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 time 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 expected information (including expected attitude and expected angular velocity) acquisition coefficient of the ith 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, that is, 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] In the formula, 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 ith spacecraft relative to the spacecraft formation according to the attitude error and angular velocity error of the ith spacecraft relative to the spacecraft formation. The specific formula is:

[0100] s i = rx 1i +χ 2i (6)

[0101] In the formula, s i is the state error of the ith 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 according to the state error function. The state measurement error function can be expressed by the formula:

[0103]

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

[0105] Specifically, the state measurement error function of the i-th spacecraft is designed according to 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, which is used to determine whether the state measurement error of the i-th spacecraft exceeds the preset state measurement error threshold and decide whether the state of the i-th spacecraft needs to be updated. The state measurement error function of the i-th spacecraft is designed as follows:

[0106]

[0107] in,

[0108]

[0109]

[0110] In the formula, is the current triggering time 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 ith 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 according to the state error function and the state measurement error function. The self-triggering attitude cooperative control law can be expressed by the formula:

[0112]

[0113] in,

[0114] In the formula, u i is the control input torque of the ith 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 according to the state error function and the state measurement error function. The self-triggering function can be expressed by the formula:

[0116]

[0117] in,

[0118] δ≥||f i ||

[0119]

[0120] In the formula, is the next triggering time 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: i The first derivative of :

[0123]

[0124] In the formula, 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 Based on this, in order to save system resources, a self-triggered attitude cooperative control law is designed, through which the control input torque of the i-th spacecraft can be calculated, and the self-triggered attitude cooperative control law is designed as follows:

[0126]

[0127] in,

[0128] In the formula, u i is the control input torque of the ith spacecraft, is the current triggering time 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] In the formula, f i is the nonlinear term of the ith spacecraft.

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

[0133]

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

[0135]

[0136] in,

[0137] In the formula, The next triggering time of the i-th spacecraft is, represents the current triggering time 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-order derivative of , m is the feedback coefficient, m>1, α and are control parameters, and α>0,

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

[0139] Taking into account Increase from 0 to right The derivative is:

[0140]

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

[0142] according to From the definition of and the dynamic event trigger function (12), we can see 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, where the self-triggering function is designed as:

[0144]

[0145] In the formula, is the next triggering time 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 ith 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 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 to:

[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 posture is set to:

[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] It can be seen from Table 1 that under the action of the proposed algorithm, the control system has good control performance, high convergence accuracy and fast convergence speed. In addition, compared with the cooperative control algorithm with an update frequency of 10Hz, the proposed algorithm can reduce the number of triggers by more than 85%, which means that the communication between spacecraft in the spacecraft formation and the update calculation of the cooperative control algorithm can be reduced by more than 85%.

[0180] The above-mentioned method for self-triggered attitude cooperative control of spacecraft formation considering disturbance first establishes the attitude kinematic model and dynamic model of each spacecraft according to the actual operating environment of the spacecraft formation, then designs the state error function of each spacecraft based on the attitude kinematic model and the dynamic model, and designs the state measurement error function according to the state error function, and designs the self-triggered attitude cooperative control law and the self-triggered function according to the state error function and the state measurement error function; then calculates the current triggering moment corresponding to each spacecraft in the spacecraft formation according to the self-triggered function, and sends the state corresponding to each spacecraft to the adjacent spacecraft at the current triggering moment, and updates the self-triggered attitude cooperative control law and the self-triggered function 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, calculates the control input torque of each spacecraft at the corresponding current triggering moment according to the self-triggered attitude cooperative control law, and calculates the next triggering moment corresponding to each spacecraft according to the self-triggered function, thereby realizing the self-triggered attitude cooperative control of the spacecraft formation. This method uses the current trigger state to estimate the next trigger time, which can avoid continuous calculation, and 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 under the premise of appropriately increasing the trigger frequency.

[0181] The above is a detailed introduction to a method for self-triggered attitude cooperative control of a spacecraft formation taking disturbances into consideration provided by the present invention. This article uses specific examples 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, wherein the spacecraft formation includes a plurality of spacecrafts, the plurality of spacecrafts are in communication connection, and establish attitude kinematic models and dynamic models of the plurality of spacecrafts according to an actual operating environment of the spacecraft formation; S2. designing state error functions of several spacecraft according to attitude kinematic models and dynamic models of the several spacecraft, designing state measurement error functions according to the state error functions, and designing self-triggering attitude cooperative control laws and self-triggering functions according to the state error functions and the state measurement error functions; S3, calculating the current triggering moment corresponding to each spacecraft in the spacecraft formation according to the self-triggering function, and sending the state corresponding to each spacecraft to the adjacent spacecraft at the current triggering moment, and updating 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 the respective corresponding current triggering moments at the current triggering moment corresponding to each spacecraft at the current triggering moment; S4. Calculate the control input torque of each spacecraft at the corresponding current triggering moment according to the self-triggering attitude collaborative control law, and calculate the next triggering 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 cooperative control of a spacecraft formation considering disturbances as claimed in 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, In the formula, 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 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 The 2-norm of i × represents the real-time attitude σ of the i-th spacecraft i The antisymmetric matrix of 3. The method for self-triggered attitude cooperative control of a spacecraft formation considering disturbances as claimed in claim 2, characterized in that: In S1, a plurality of attitude kinematic models and dynamic models of the spacecraft are established according to the actual operating environment of the spacecraft formation. The dynamic model is specifically: In the formula, 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 i × represents the real-time attitude of the i-th spacecraft ω i The antisymmetric matrix of is the control input torque of the ith spacecraft, is the generalized perturbation torque of the ith spacecraft.

4. The method for self-triggered attitude cooperative control of a spacecraft formation considering disturbances as claimed in claim 3, characterized in that: In S2, the state error functions of the spacecraft are designed according to the attitude kinematics models and dynamics models of the spacecraft, which specifically include 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 the adjacent spacecraft in the spacecraft formation at their respective current triggering moments and the expected attitude of the preset spacecraft σ d designing the 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 according to the attitude error and angular velocity error.

5. The method for self-triggered attitude cooperative control of a spacecraft formation considering disturbances as claimed in claim 4, characterized in that: The attitude error of each spacecraft relative to the spacecraft formation in S22 can be expressed by the formula: In the formula, χ 1i is the attitude error of the ith spacecraft relative to the spacecraft formation, is the current triggering time 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 cooperative control of a spacecraft formation considering disturbances as claimed in claim 5, characterized in that: The angular velocity error of each spacecraft relative to the spacecraft formation in S23 can be expressed by the formula: In the formula, 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 cooperative control of a spacecraft formation considering disturbances as claimed in claim 6, characterized in that: The state error function of each spacecraft relative to the spacecraft formation in S24 can be expressed by the formula: s i =rx 1i +x 2i In the formula, s i is the state error of the ith spacecraft relative to the spacecraft formation, and r is a positive constant.

8. The method for self-triggered attitude cooperative control of a spacecraft formation considering disturbances as claimed in 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 by the formula: In the formula, is the state measurement error of the i-th spacecraft, is the current triggering time 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 cooperative control of a spacecraft formation considering disturbances as claimed in 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 by the formula: in, In the formula, u i is the control input torque of the ith 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 cooperative control of a spacecraft formation considering disturbances as claimed in 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 by the formula: in, δ≥||f i || In the formula, is the next triggering time 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.

Images