A low-complexity attitude tracking control method for spacecraft with anti-unwinding preset performance

Abstract

The invention discloses a low-complexity attitude tracking control method for spacecraft with anti-unwinding preset performance. The method is as follows: establishing an attitude tracking model based on a special orthogonal matrix group; using a specified time performance function to design a performance boundary capable of suppressing overshoot, converting the problem of ensuring that the attitude tracking error converges within the performance boundary into the problem of ensuring that the attitude tracking error function converges within the preset performance boundary; designing the conversion error of the attitude tracking error function, converting the original attitude error function constraint problem into the problem of bounded conversion error, designing a virtual input according to the backstepping method to ensure the boundedness of the conversion error; designing a performance boundary for the error between the angular velocity tracking error and the virtual input, converting the constraint problem of the error into the boundedness problem of the conversion error, designing a controller to ensure that the conversion error is bounded, ensuring the boundedness of the angular velocity tracking error, and completing the control target. The invention has the advantages of simple structure and energy saving.

Description

Technical Field

[0001] The present invention belongs to the field of nonlinear system control, and relates to a spacecraft preset performance attitude tracking control method, and specifically to a low-complexity spacecraft anti-unwinding preset performance attitude tracking control method. Background Art

[0002] The spacecraft attitude control system is a highly nonlinear control system with strong time-varying and strong coupling characteristics. It is also prone to attitude unwinding. Therefore, it is a difficult problem to design a high-performance attitude tracking controller with anti-unwinding capability.

[0003] The preset performance control method is an effective method to improve tracking performance. Its main idea is to design a controller so that the tracking error of the closed-loop system converges to a preset allowable range. By adjusting the parameters of the performance boundary, the transient and steady-state performance of the tracking error can be controlled, thereby improving the convergence performance of the control system.

[0004] In recent years, the research on preset performance control of spacecraft tracking systems has achieved fruitful results. However, the controller designed based on the backstepping method will have the problem of "differential blow-up" when the system state is secondarily differentiated. Therefore, auxiliary approximate structures are often required to solve the "differential blow-up" problem, making the controller structure complex. Therefore, it is a very meaningful research to design a spacecraft anti-unwinding preset performance attitude tracking controller without approximate structures. Summary of the invention

[0005] The present invention provides a low-complexity spacecraft anti-unwinding preset performance attitude tracking control method for a spacecraft attitude tracking control system. The method adopts a spacecraft anti-unwinding model based on a special orthogonal matrix group, considers presetting performance boundaries for both spacecraft attitude error and attitude angular velocity error, and designs a preset performance control law that does not require an approximate structure, thereby achieving convergence of the preset performance of the spacecraft attitude and angular velocity.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A low-complexity spacecraft anti-unwinding preset performance attitude tracking control method comprises the following steps:

[0008] Step 1: For a general rigid spacecraft, establish an attitude tracking model based on the special orthogonal matrix group SO(3):

[0009]

[0010] Among them, e R is the posture tracking error, ω e is the attitude angular velocity tracking error, J is the inertia matrix, Re is the rotation matrix of the rigid spacecraft, ω d is the desired attitude angular velocity, u is the control input to be designed, ω × represents an antisymmetric matrix, and E is defined as:

[0011]

[0012] Among them, tr(R e ) represents the trace of the rotation matrix, Represents the mapping from an antisymmetric matrix to a three-dimensional vector, and I3 represents the 3×3 identity matrix;

[0013] Step 2: Use the specified time performance function to design a performance boundary that can suppress overshoot, and introduce the attitude tracking error function ψ. R The relationship between will ensure that the posture tracking error e R The problem of converging into the performance boundary is transformed into the problem of ensuring that the function ψ converges into the preset performance boundary. The specific steps are as follows:

[0014] Step 2-1, introduce the specified time performance function ρ(t):

[0015]

[0016] in, is the initial value of the performance function, is the final value of the performance function, It is the time when the performance function reaches the final value, n≥1 can adjust the decline speed of the performance function;

[0017] Step 2-2: In order to better suppress the overshoot of the attitude tracking error, ρ(t) is used to design the following performance boundary:

[0018]

[0019] Where sgn(·) represents the sign function, ψ(0) represents the initial value of ψ, and 0≤δ 1u ≤1,0≤δ 1l ≤1 is an adjustable parameter, and are the preset upper and lower boundaries respectively;

[0020] Step 2-3, order because Therefore, when When the attitude tracking error is satisfied, R The element e R,i , i=1,2,3 converges to

[0021] Step 3: In order to realize the error constraint problem in step 2, the conversion error of the attitude tracking error function is designed by using the error conversion method, and the original attitude error function constraint problem is converted into a problem of bounded conversion error. Then, according to the backstepping method, the virtual input is designed to ensure the boundedness of the conversion error. The specific steps are as follows:

[0022] Step 3-1: In order to solve the error constraint problem in step 2, define the error conversion function ε1:

[0023]

[0024] Step 3-2, take the derivative of ε1 and get:

[0025]

[0026] Step 3-3: According to the backstepping method, introduce virtual input and remember:

[0027]

[0028] Among them, α1 is the virtual input, e2 is the angular velocity tracking error ω e The difference between the virtual input α1;

[0029] Step 3-4: Consider the Lyapunov function To make Assume the virtual input α1 is:

[0030]

[0031] Among them, k1>0 and k2>0 are adjustable parameters. and The upper and lower performance boundaries are preset for the difference between the virtual error and the angular velocity tracking error. In order to ensure the boundedness of ε1, k1 and k2 satisfy:

[0032]

[0033] Step 4: Set a performance boundary for the error between the angular velocity tracking error and the virtual input. Use the error conversion method to convert the error constraint problem into the boundedness problem of the conversion error. Design a controller to ensure that the conversion error is bounded, thereby ensuring the boundedness of the angular velocity tracking error and achieving the control goal. The specific steps are as follows:

[0034] Step 4-1: The error between the angular velocity tracking error and the virtual input is e2, that is, e2 = ω e -α1, to ensure the angular velocity tracking error ω e The boundedness of e 2,i Set the following performance boundaries:

[0035]

[0036] Among them, e 2,i (0) means e 2,i The initial value of , 0≤δ 2u,i ≤1,0≤δ 1l,i ≤1 is an adjustable parameter, is the specified time performance function, for The final value of

[0037] Step 4-2, e 2,i Respectively limited within the performance boundaries, that is, satisfying:

[0038]

[0039] Then, the angular velocity tracking error satisfies:

[0040]

[0041] That is, the angular velocity tracking error converges within the bounded boundary;

[0042] Step 4-3, in order to solve e 2,i The constraint problem is to use the error conversion method to 2,i To transform, let:

[0043]

[0044] Step 4-4, in order to ensure e 2,i The boundedness of

[0045] Steps 4-5: To ensure Design the following controller:

[0046]

[0047] Among them, k3>0 is the control gain, G2, H and X are the diagonal matrices composed of vectors g2, h and χ respectively, g 2,i 、h i and χ i is defined as follows:

[0048]

[0049] Compared with the prior art, the present invention has the following advantages:

[0050] The present invention designs a simple-structured preset performance attitude controller for a spacecraft attitude tracking control system, and the control object is a spacecraft attitude tracking system that takes attitude unwinding into consideration. The control law is designed by using a preset performance control and conversion error method to ensure that the attitude error converges within a preset performance boundary. The method can preset the expected convergence time and convergence accuracy of the attitude tracking error by changing the preset performance boundary parameters, and can suppress or even eliminate overshoot. The preset performance attitude tracking controller designed by the present invention does not require an additional approximate structure to solve the "differential blow-up" problem, and has the advantages of simple structure and energy saving. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is the time response diagram of the attitude tracking error function ψ and its preset boundary at the preset time T=20s;

[0052] Figure 2 is the posture tracking error e at the preset time T = 20s R and its time response plot for preset boundaries;

[0053] Figure 3 The time response diagram of the intermediate error e2 and its preset boundary at the preset time T=20s;

[0054] Figure 4 is the attitude angular velocity tracking error ω at the preset time T = 20s e Time response diagram of

[0055] Figure 5 It is the response diagram of the control torque time u when the preset time T=20s. DETAILED DESCRIPTION

[0056] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0057] The present invention provides a low-complexity spacecraft anti-unwinding preset performance attitude tracking control method, the method comprising the following steps:

[0058] Step 1: For a general rigid spacecraft, establish an attitude tracking model based on the special orthogonal matrix group SO(3). The specific steps are as follows:

[0059] Remember R e ∈SO(3) is the rotation matrix of the rigid spacecraft, and the attitude tracking error is defined as for:

[0060]

[0061] Among them, tr(R e ) represents the trace of the rotation matrix, Representing the mapping from an antisymmetric matrix to a three-dimensional vector, the rigid spacecraft attitude tracking model based on the special orthogonal matrix group SO(3) can be written as:

[0062]

[0063] in, It is defined as:

[0064]

[0065] in, is the attitude angular velocity tracking error, is the desired attitude angular velocity, is the inertia matrix, is the control input to be designed, I3 represents the 3×3 identity matrix, ω × Represents the following antisymmetric matrix

[0066]

[0067] Step 2: Use the specified time performance function to design a performance boundary that can suppress overshoot, and introduce a function ψ of the attitude tracking error. Use ψ and e R The relationship between will ensure that the posture tracking error e R The problem of converging into the performance boundary is transformed into the problem of ensuring that the function ψ converges into the preset performance boundary. The specific steps are as follows:

[0068] Step 2-1, introduce the specified time performance function ρ(t):

[0069]

[0070] in, is the initial value of the performance function, is the final value of the performance function, It is the time when the performance function reaches the final value. n≥1 can adjust the decline rate of the performance function.

[0071] Step 2-2: In order to better suppress the overshoot of the attitude tracking error, ρ(t) is used to design the following performance boundary:

[0072]

[0073] Where sgn(·) represents the sign function, ψ(0) represents the initial value of ψ, and 0≤δ 1u ≤1,0≤δ 1l≤1 is an adjustable parameter. Compared with the traditional symmetrical performance boundary and asymmetrical performance boundary, the performance boundary used in the present invention has a greater constraint ability on the overshoot and can even eliminate the overshoot.

[0074] Step 2-3, order because Therefore, when When the attitude tracking error is satisfied, R The element e R,i , i=1,2,3 converges to

[0075] Step 3: In order to realize the error constraint problem in step 2, the conversion error of the attitude tracking error function is designed by using the error conversion method, and the original attitude error function constraint problem is converted into a problem of bounded conversion error. Then, according to the backstepping method, the virtual input is designed to ensure the boundedness of the conversion error. The specific steps are as follows:

[0076] Step 3-1: In order to solve the error constraint problem in step 2, define the error conversion function ε1:

[0077]

[0078] From the above formula, it can be seen that when When i →-∞; when ε1→+∞. Therefore, as long as the error ε1 after conversion is bounded, the constraint relationship of the attitude tracking error function ψ can be satisfied, thereby achieving the attitude tracking error e R constraints.

[0079] Step 3-2, take the derivative of ε1, and we get:

[0080]

[0081] Step 3-3: According to the backstepping method, introduce virtual input and remember:

[0082]

[0083] Among them, α1 is the virtual input, e2 is the angular velocity tracking error ω e The difference between the virtual input α1.

[0084] Step 3-4: Consider the Lyapunov function To make Assume the virtual input α1 is:

[0085]

[0086] Among them, k1>0 and k2>0 are adjustable parameters. and The upper and lower performance boundaries are preset for the difference between the virtual error and the angular velocity tracking error. In order to ensure the boundedness of ε1, k1 and k2 must satisfy:

[0087]

[0088] Step 4: Set a performance boundary for the error between the angular velocity tracking error and the virtual input, and use the error conversion method to convert the error constraint problem into the boundedness problem of the conversion error. Design a controller to ensure that the conversion error is bounded, thereby ensuring the boundedness of the angular velocity tracking error and achieving the control goal. The specific steps are as follows:

[0089] Step 4-1: The error between the angular velocity tracking error and the virtual input is e2, that is, e2 = ω e -α1, to ensure the angular velocity tracking error ω e The boundedness of e 2,i Set the following performance boundaries:

[0090]

[0091] Among them, e 2,i (0) means e 2,i The initial value of , 0≤δ 2u,i ≤1,0≤δ 1l,i ≤1, i=1,2,3 are adjustable parameters, is the specified time performance function, for The final value of .

[0092] Step 4-2, e 2,i , i=1,2,3 are respectively limited within the performance boundary, that is, they satisfy:

[0093]

[0094] Then, the angular velocity tracking error satisfies:

[0095]

[0096] That is, the angular velocity tracking error converges within the bounded boundary.

[0097] Step 4-3: Similarly, to solve e 2,i , i=1,2,3, and use the error conversion method to transform e 2,i , i=1,2,3 for transformation, let:

[0098]

[0099] Step 4-4: To ensure ε 2,i , i=1,2,3, and examine the boundedness of the Lyapunov function

[0100] Steps 4-5: To ensure Design the following controller:

[0101]

[0102] Among them, k3>0 is the control gain, G2, H and X are vectors and The diagonal matrix formed by 2,i ,i=1,2,3,h i , i = 1, 2, 3 and χ i , i=1,2,3 are defined as follows:

[0103]

[0104] Example:

[0105] For a general rigid spacecraft, consider the following attitude tracking model based on the special orthogonal matrix group SO(3):

[0106]

[0107] in, is the posture tracking error, which is defined as follows:

[0108]

[0109] It is defined as:

[0110]

[0111] Among them, tr(R e ) represents the trace of the rotation matrix, represents the mapping from an antisymmetric matrix to a three-dimensional vector, R e ∈SO(3) is the attitude error rotation matrix of the rigid spacecraft, is the attitude angular velocity tracking error, is the desired attitude angular velocity, is the inertia matrix, The control torque provided to the actuator.

[0112] Since the mapping between the attitude rotation matrix and the spacecraft attitude is unique, the design of the control law of the spacecraft attitude tracking model based on the special orthogonal matrix group can effectively avoid the attitude unwinding problem. At the same time, in order to solve the "differential blow-up" problem in the backstepping method, the following attitude error function is introduced:

[0113]

[0114] By e R From the definition of and ψ, the following relationship holds:

[0115]

[0116] Then, when ψ is guaranteed to converge within the performance boundary, that is:

[0117]

[0118] in, and are the preset upper and lower boundaries respectively, then the posture tracking error e R,i , i=1,2,3 converges to

[0119]

[0120] The preset performance convergence of the posture tracking error is achieved.

[0121] Next, design the performance boundary and First, introduce the preset performance function for the specified time:

[0122]

[0123] in, is the initial value of the performance function, is the final value of the performance function, is the time when the performance function reaches the final value, and n≥1 can adjust the descent speed of the performance function. In order to better suppress the overshoot of the attitude tracking error, ρ is used to design the following performance boundary:

[0124]

[0125] Where sgn(·) represents the sign function, ψ(0) represents the initial value, and 0≤δ 1u ≤1,0≤δ 1l ≤1. Compared with the traditional symmetrical performance boundary and asymmetrical performance boundary, the performance boundary used in the present invention has a greater constraint ability on the overshoot and can even eliminate the overshoot.

[0126] In order to solve the above error constraint problem (6), the error conversion method is used to convert the problem into a bounded problem for the conversion error. The error conversion function is defined as:

[0127]

[0128] From the above formula, it can be seen that when When i →-∞; when ε1→+∞. Therefore, as long as the error ε1 after conversion is bounded, constraint (6) can be satisfied, thereby ensuring (7) and achieving the control goal of ensuring that the attitude tracking error converges within the preset performance boundary. Taking the derivative of ε1, we can obtain:

[0129]

[0130] According to the backstepping method, virtual input is introduced, and it is recorded:

[0131]

[0132] Among them, α1 is the virtual input, e2=ω e -α1 is the difference between the angular velocity tracking error and the virtual input. In order to ensure the boundedness of ε1, the Lyapunov function is considered Taking the derivative of V1, we get:

[0133]

[0134] To make Assume the virtual input α1 is:

[0135]

[0136] Substituting the above formula into formula (13), we get:

[0137]

[0138] in,

[0139]

[0140] By e R The relationship between and ψ (5) shows that:

[0141]

[0142] in,

[0143]

[0144] When the control gains k1 and k2 satisfy , b1>0,b2>0.

[0145] Let M = -k1ε1(exp(ε1)-1)-k2ε1(1-exp(-ε1))-ε1b1+ε1b2. For M, we have the following analysis:

[0146] (1) When When , -k1ε1(exp(ε1)-1)-k2ε1(1-exp(-ε1))≤0, -b1+b2 is bounded. At this time, ε1 will converge to the following convergence domain:

[0147] Ω1={ε1||ε1|≤δ1} (17)

[0148] Among them, δ1 satisfies k1δ1(exp(δ1)-1)+k2δ1(1-exp(-δ1))=|b2-b1|.

[0149] (2) When When ε1→-∞, b2→∞, b1 is bounded. At this time, -k1ε1(exp(ε1)-1)-k2ε1(1-exp(-ε1))-ε1b1<0, b2ε1<0. So W<0, ε1 will increase and eventually enter Ω1.

[0150] (3) When When ε1→+∞, b1→∞, b2 is bounded. At this time, -k1ε1(exp(ε1)-1)-k2ε1(1-exp(-ε1))+ε1b1<0, -b1ε1<0. So W<0, ε1 will decrease and finally enter Ω1.

[0151] Therefore, the designed virtual input α1 can ensure that M≤0. Next, in order to ensure the boundedness of the angular velocity tracking error, e 2,i , i=1,2,3 are limited to the performance boundary respectively, that is, to achieve:

[0152]

[0153] Then the angular velocity tracking error ω e,i , i=1,2,3 satisfies:

[0154]

[0155] That is, the angular velocity tracking error converges within the bounded boundary and the control target is achieved. Similarly, in order to realize the error constraint problem in equation (18), e is introduced 2,i , the conversion error function of i=1,2,3 is as follows:

[0156]

[0157] As long as ε 2,i, i = 1, 2, 3 is bounded, then equation (18) holds, thus ensuring that the angular velocity tracking error converges under bounded boundaries. Taking the derivative of ε2, we get:

[0158]

[0159] From the definition of e2, we can see that:

[0160]

[0161] in,

[0162]

[0163] Examining the Lyapunov function Taking the derivative of V2, we get:

[0164]

[0165] Among them, k3>0 is the control gain, G2, H and X are vectors and The diagonal matrix formed by 2,i ,i=1,2,3,h i , i = 1, 2, 3 and χ i , i=1,2,3 are defined as follows:

[0166]

[0167] To ensure Design the following controller:

[0168]

[0169] Where k3>0 is the control gain. Substituting the controller into equation (23), we get:

[0170]

[0171] Combined with the above analysis of M, we can see that the designed virtual input α1 and controller u can make It is established. From the Lyapunov stability theorem, it can be concluded that under the action of the virtual input α1 and the controller u, ε1 and ε2 are bounded. According to the corresponding relationship between the conversion error and the attitude tracking error, it can be seen that the constraint (7) set on the attitude tracking error is established at this time, and the control target is achieved.

[0172] It is worth noting that, unlike the conventional preset performance controller based on the conversion error of the posture tracking error, the virtual input α1 designed in the present invention does not include or Therefore, when the controller takes the derivative of the virtual input, the "differential blow-up" problem will not occur, which greatly simplifies the amount of calculation required to construct the controller. In addition, in order to deal with the "differential blow-up" problem, the traditional preset performance controller often needs to be equipped with an approximate structure such as a filter or a neural network to approximate the derivative term of the virtual input, while the controller designed by the present invention can solve the "differential blow-up" problem without any approximate structure. Compared with the traditional preset performance controller based on the backstepping method, the controller designed by the present invention has a simpler structure and can also save energy.

[0173] In order to verify the effectiveness of the proposed controller, a numerical simulation is carried out on the rigid spacecraft attitude tracking control model based on the special orthogonal matrix group SO(3) as shown in equation (1).

[0174] Set the spacecraft's moment of inertia to: The initial attitude value is set to: The initial value of angular velocity is set to ω(0)=

[000] T rad / s; the desired attitude is set to R d =I3, In this simulation, the specified time performance functions selected for the attitude tracking error and the intermediate error are:

[0175]

[0176] The other parameters in the performance boundaries (9) and (18) are chosen as δ 1u =δ 1l =0.8,δ 2u,i =δ 2l,i =0.8, i = 1, 2, 3. The controller gains are selected as k1 = 0.5, k2 = 0.05, k3 = 0.1.

[0177] The simulation results are as follows Figure 1-5 As shown. Figure 1 It can be seen that the designed controller can ensure that the attitude tracking error function ψ changes monotonically from the initial state to the steady state, indicating that the trace of the rotation matrix reaches the stable point after a small rotation angle, and there is no attitude unwinding phenomenon; Figure 1 It can also be seen that the designed controller can ensure that ψ converges within the preset performance boundary. Figure 2 It can be seen that by constraining ψ, the attitude tracking error e can be guaranteed R It can converge within the preset performance boundary, and there is almost no overshoot due to the effect of the performance boundary. Figure 3 and 4 It can be seen that by constraining e2, ω can be guaranteed e is bounded. So far, the control goal is achieved. Figure 5The time response diagram of the proposed controller is given by Figure 5 It can be seen that the control torque provided by the designed controller is smooth and continuous, and the amplitude does not exceed 6N·m, which has the characteristics of low energy consumption.

Claims

1. A low-complexity spacecraft anti-unwinding preset performance attitude tracking control method, characterized in that The method comprises the following steps: Step 1: For a general rigid spacecraft, establish an attitude tracking model based on the special orthogonal matrix group SO(3): Among them, e R is the posture tracking error, ω e is the attitude angular velocity tracking error, J is the inertia matrix, R e is the rotation matrix of the rigid spacecraft, ω d is the desired attitude angular velocity, u is the control input to be designed, ω × represents an antisymmetric matrix, and E is defined as: Among them, tr(R e ) represents the trace of the rotation matrix, Represents the mapping from an antisymmetric matrix to a three-dimensional vector, and I3 represents the 3×3 identity matrix; Step 2: Use the specified time performance function to design a performance boundary that can suppress overshoot, and introduce the attitude tracking error function ψ. R The relationship between will ensure that the attitude tracking error e R The problem of converging into the performance boundary is transformed into the problem of ensuring that the function ψ converges into the preset performance boundary. The specific steps are as follows: Step 2-1, introduce the specified time performance function ρ(t): in, is the initial value of the performance function, is the final value of the performance function, It is the time when the performance function reaches the final value, n≥1 can adjust the decline speed of the performance function; Step 2-2: In order to better suppress the overshoot of the attitude tracking error, ρ(t) is used to design the following performance boundary: Where sgn(·) represents the sign function, ψ(0) represents the initial value of ψ, and 0≤δ 1u ≤1,0≤δ 1l ≤1 is an adjustable parameter, and are the preset upper and lower boundaries respectively; Step 2-3, order because Therefore, when When the attitude tracking error is satisfied, R The element e R,i , i=1,2,3 converges to Step 3: In order to realize the error constraint problem in step 2, the conversion error of the attitude tracking error function is designed by using the error conversion method, and the original attitude error function constraint problem is converted into a problem of bounded conversion error. Then, according to the backstepping method, the virtual input is designed to ensure the boundedness of the conversion error. The specific steps are as follows: Step 3-1: In order to solve the error constraint problem in step 2, define the error conversion function ε1: Step 3-2, take the derivative of ε1 and get: Step 3-3: According to the backstepping method, introduce virtual input and remember: Among them, α1 is the virtual input, e2 is the angular velocity tracking error ω e The difference between the virtual input α1; Step 3-4: Consider the Lyapunov function To make Assume the virtual input α1 is: Among them, k1>0 and k2>0 are adjustable parameters. and The upper and lower performance boundaries are preset for the difference between the virtual error and the angular velocity tracking error, respectively; Step 4: Set a performance boundary for the error between the angular velocity tracking error and the virtual input. Use the error conversion method to convert the error constraint problem into the boundedness problem of the conversion error. Design a controller to ensure that the conversion error is bounded, thereby ensuring the boundedness of the angular velocity tracking error and achieving the control goal. The specific steps are as follows: Step 4-1: The error between the angular velocity tracking error and the virtual input is e2, that is, e2 = ω e -α1, to ensure the angular velocity tracking error ω e The boundedness of e 2,i Set the following performance boundaries: Among them, e 2,i (0) means e 2,i The initial value of , 0≤δ 2u,i ≤1,0≤δ 1l,i ≤1 is an adjustable parameter, is the specified time performance function, for The terminal value of Step 4-2, e 2,i Respectively limited within the performance boundaries, that is, satisfying: Then, the angular velocity tracking error satisfies: That is, the angular velocity tracking error converges within the bounded boundary; Step 4-3, in order to solve e 2,i The constraint problem is to use the error conversion method to 2,i To transform, let: Step 4-4, in order to ensure e 2,i The boundedness of Steps 4-5: To ensure Design the following controller: Among them, k3>0 is the control gain, G2, H and X are the diagonal matrices composed of vectors g2, h and χ respectively, g 2,i 、h i and χ i is defined as follows:

2. The low-complexity spacecraft anti-unwinding preset performance attitude tracking control method according to claim 1 is characterized in that In step 1, the posture tracking error e R for:

3. The low-complexity spacecraft anti-unwinding preset performance attitude tracking control method according to claim 1 is characterized in that In step 1, ω × It is expressed as follows:

4. The low-complexity spacecraft anti-unwinding preset performance attitude tracking control method according to claim 1 is characterized in that In the steps 3-4, in order to ensure the boundedness of ε1, k1 and k2 satisfy:

Images