Spacecraft anti-unwinding attitude maneuver control method based on full-drive method

Abstract

The application discloses a spacecraft anti-unwinding attitude maneuver control method based on a full drive method, and the method comprises the following steps: step 1, a unit quaternion is used to describe a rigid spacecraft attitude, for a rigid spacecraft with external disturbance, a static-to-static attitude maneuver task is established, and an attitude error kinematics equation and a dynamics equation are established; step 2, a vector part of an attitude quaternion error variable is derived, and a second-order model is established based on a full drive system method; step 3, for the rigid spacecraft with external disturbance, an anti-unwinding sliding mode attitude maneuver control law is designed; and step 4, considering the discontinuous characteristics of a sliding surface, a boundary layer is introduced to realize chattering suppression. The attitude controller designed by the application can make the spacecraft converge along the shortest path in the attitude maneuver process, and effectively avoid the attitude unwinding phenomenon caused by the quaternion double covering characteristics while ensuring the robustness of the system.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft attitude control and relates to a rigid body spacecraft anti-decoupling attitude maneuver control method, specifically a spacecraft anti-decoupling attitude maneuver control method based on the all-drive method. Background Technology

[0002] Spacecraft attitude control methods based on unit quaternions can effectively avoid the geometric singularity problem in Euler angle descriptions, and therefore have been widely used in the field of spacecraft attitude control. However, due to the double-coverage characteristic of unit quaternions, when the control law is not designed properly, the system is prone to attitude decoupling during attitude maneuvers, resulting in unnecessary large-angle attitude maneuvers, increasing control energy consumption and affecting control performance.

[0003] In addition, some existing nonlinear attitude control methods based on quaternions usually design the controller directly for the original nonlinear model, resulting in a relatively complex control structure. The correspondence between the system model and the control law is not intuitive enough, making it difficult to tune the controller parameters. Summary of the Invention

[0004] To address the attitude decoupling problem caused by the quaternion double-coverage characteristic in rigid body spacecraft attitude maneuver control and to simplify the design process of nonlinear attitude controllers, this invention provides a spacecraft anti-decoupling attitude maneuver control method based on the all-drive approach. This method, for static-to-static attitude maneuvering missions, establishes an all-drive system model of attitude error and designs an anti-decoupling sliding mode controller to achieve anti-decoupling attitude maneuver control for the spacecraft.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A spacecraft anti-decoupling attitude maneuver control method based on the all-drive approach includes the following steps:

[0007] Step 1: Using unit quaternions to describe the attitude of rigid body spacecraft, for rigid body spacecraft with external disturbances, the following kinematic and dynamic equations for attitude error are established for static-to-static attitude maneuvering tasks:

[0008]

[0009] in, and They are respectively the body coordinate system Relative to the desired coordinate system Attitude quaternion error and angular velocity error; for The vector part, for The scalar part; It is a 3×3 identity matrix; Here is the rotational inertia matrix of the rigid body spacecraft; This refers to the control torque acting on a rigid spacecraft. External interference;

[0010] Step 2: Differentiate the vector part of the attitude quaternion error variable, and establish the following second-order model based on the all-drive system method:

[0011]

[0012] in, The expression is:

[0013]

[0014] The expression is:

[0015]

[0016] In addition, ,and ;

[0017] Step 3: For rigid body spacecraft with external disturbances, design the following anti-decoupling sliding mode attitude maneuver control law:

[0018]

[0019] in, , and It is a positive number, and satisfy , For the designed sliding mode variables, The expression is:

[0020]

[0021] Step 4: Considering the discontinuities of the sliding surface, a boundary layer is introduced to suppress chattering. Improved to:

[0022]

[0023] in, Given the boundary layer thickness, the system still exhibits resistance to decoupling, and the vector part of the attitude error... and attitude angular velocity error The intervals of convergence are as follows:

[0024]

[0025]

[0026] in, .

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] 1. In view of the strong coupling and nonlinear characteristics of attitude dynamics of rigid body spacecraft, this invention constructs a second-order full-drive model of attitude error based on the full-drive system theory, which transforms the original complex nonlinear dynamic equations into a linear decoupled form, simplifying controller design and parameter tuning.

[0029] 2. In response to the decoupling phenomenon of spacecraft, this invention utilizes the attitude error quaternion vector part to construct a sliding mode surface, ensuring that the system automatically converges along the shortest path, thus realizing anti-decoupling control in static-to-static attitude maneuvering missions. Attached Figure Description

[0030] Figure 1 This is a flowchart of a spacecraft anti-decoupling attitude maneuvering control method based on the all-drive approach;

[0031] Figure 2 In the simulation example, the spacecraft is in case 1 ( The trajectory diagram of the changes in attitude error quaternion, angular velocity error, and control torque;

[0032] Figure 3 In the simulation example, the spacecraft is in case 2 ( The trajectory diagram of the changes in attitude error quaternion, angular velocity error, and control torque. Detailed Implementation

[0033] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0034] This invention provides a spacecraft anti-decoupling attitude maneuvering control method based on the all-drive approach. First, a unit quaternion is used to describe the spacecraft attitude, and the rigid body spacecraft attitude dynamics are transformed into a second-order linear decoupled form based on all-drive system theory. Then, a linear sliding mode surface is constructed using the vector part of the attitude error quaternion, and a saturation function is introduced to design an attitude maneuvering control law with anti-decoupling capability, enabling the spacecraft to perform attitude maneuvers along the shortest path. The attitude controller designed in this invention enables the spacecraft to converge along the shortest path during attitude maneuvers, effectively avoiding attitude decoupling caused by the double-coverage characteristic of quaternions while ensuring system robustness. Figure 1 As shown, the specific steps include the following:

[0035] Step 1: Describe the attitude of the rigid body spacecraft using unit quaternions. For rigid body spacecraft with external disturbances, establish the attitude kinematic equations and dynamic equations:

[0036] (1)

[0037] in, Spacecraft body coordinate system Relative to the inertial coordinate system The posture quaternion, for The scalar part, for The vector part, for The One component; Spacecraft body coordinate system Relative to the inertial coordinate system attitude angular velocity, for The One component; for The identity matrix; For the control input of the attitude tracking and control system of rigid body spacecraft; This refers to the control torque acting on a rigid spacecraft. Here is the rotational inertia matrix of the rigid body spacecraft; furthermore... express:

[0038]

[0039] definition and Desired coordinate system Relative to the inertial coordinate system The desired attitude quaternion and the desired attitude angular velocity, for The One portion, for The scalar part, for The vector part, for The One portion, and They are respectively the body coordinate system Relative to the desired coordinate system The error attitude quaternion and the error attitude angular velocity, for The One portion, for The scalar part, for The vector part, for The If there are multiple components, then the following relationship holds:

[0040] (2)

[0041] in, Represents the body coordinate system To the desired coordinate system The rotation matrix, and satisfy , ,but:

[0042] (3)

[0043] Since we are considering static-to-static attitude maneuvers, then , The kinematic and dynamic equations for attitude error are as follows:

[0044] (4)

[0045] also, It can also be expressed as:

[0046] (5)

[0047] in, Euler angles, It is an Euler axis, and .

[0048] Step 2: Establish a second-order model based on the all-drive system method, and differentiate the vector part of its attitude error variables:

[0049] (6)

[0050] in, The expression is:

[0051]

[0052] The expression is:

[0053]

[0054] In addition, ,and .

[0055] Step 3: For rigid body spacecraft with external disturbances, design the following anti-decoupling sliding mode attitude maneuver control law:

[0056] Based on the second-order all-drive system model of attitude error established in step 2 (6), virtual control variables are introduced. ,make Define the part about the attitude error vector linear sliding surface And set the closed-loop system to satisfy the exponential reaching law. Therefore, we get The expression is By solving the control input in reverse The control law expression can be obtained as follows:

[0057] (7)

[0058] in, , and It is a positive number, and satisfy , , for The One portion, The expression is:

[0059] (8)

[0060] Step 4: Considering the discontinuity of the sliding surface, a boundary layer is introduced to suppress chattering. It can be improved as follows:

[0061] (9)

[0062] in, This represents the boundary layer thickness.

[0063] Analysis of sliding surface Based on the convergence properties of time, the following Lyapunov function is chosen:

[0064] (10)

[0065] Obviously ,Depend on ,but:

[0066] (11)

[0067] Therefore, it can be known that when At that time, only It was only established at that time, then , , ,again ,but .

[0068] Prove that when the sliding surface The system has anti-unwinding properties:

[0069] Depend on Assuming the time it takes to reach the sliding surface is Then we have:

[0070] (12)

[0071] right Differentiating the norm:

[0072] (13)

[0073] so Monotonically decreasing, from (5), according to If initially (Right now ),but Corresponding angle ;initial (Right now ),but Corresponding angle This avoids the phenomenon of unwinding.

[0074] Prove the sliding mode function To make the Lyapunov function tend to 0 in a finite time, choose the following Lyapunov function:

[0075] (14)

[0076] Obviously From (7), then we have:

[0077] (15)

[0078] again ,and Then (15) yields:

[0079] (16)

[0080] because Obviously According to the fast finite-time convergence theorem, It will converge to 0 within a finite amount of time.

[0081] To prove that the system has anti-decoupling performance during the approach phase, the control law (7) is substituted into the all-drive model:

[0082] (17)

[0083] Based on the decoupling characteristics of the all-drive system, the control components of the vector part of the attitude error variable are analyzed using (17). ( =1,2,3):

[0084] (18)

[0085] Initially, since it is a static-to-static attitude maneuver, then: ,have to:

[0086] (19)

[0087] make :

[0088] Scenario 1:

[0089] (20)

[0090] This indicates that the control component is located on the sliding surface at the initial moment, and... Then the state is maintained on the sliding surface, that is:

[0091]

[0092] Scenario 2:

[0093] (twenty one)

[0094] but ,again ,and , ,but:

[0095] (twenty two)

[0096] That is, in =0 + hour:

[0097]

[0098] To prove that the situation is resistant to unwinding during the approach phase, it is necessary to prove... The sign remains unchanged because If a sequence of consecutive terms changes sign, then there must be a certain moment when the sequence changes sign. ,make:

[0099] ,

[0100] at this time, , ,and , ,have to:

[0101] (twenty three)

[0102] This indicates that, The fact that it doesn't cross 0 indicates:

[0103]

[0104] exist The principle of approaching a certain stage will always hold true.

[0105] Therefore, according to

[0106] (twenty four)

[0107] but ,so The monotonically decreasing property, according to (5), indicates that the system also has anti-dewinding properties during the approach phase.

[0108] Prove that the system after introducing a boundary layer ( It still exhibits anti-dewinding properties, and a Lyapunov function with respect to the sliding mode variable is chosen:

[0109] (25)

[0110] but:

[0111] (26)

[0112] again ,but:

[0113] (27)

[0114] Therefore, to make ,but , ,so, The final convergence interval is:

[0115] (28)

[0116] Introducing parameters And satisfy Choose the Lyapunov function: ,but:

[0117] (29)

[0118] To make ,but , ,so, The final convergence interval is:

[0119] (30)

[0120] and ,so Monotonically decreasing, meaning that even after introducing a boundary layer, the system still retains its anti-unwinding performance, according to If the initial (Right now ),but ;initial (Right now ),but .

[0121] consider The interval of convergence, and:

[0122] (31)

[0123] Depend on :

[0124] (32)

[0125] Therefore, we get The interval of convergence is:

[0126] (33)

[0127] The performance of the controller constructed in this invention is demonstrated and verified through a simulation example below:

[0128] Considering the rotational inertia of a rigid body spacecraft for: ;

[0129] External disturbance torque for: ;

[0130] The initial value of the spacecraft attitude error is:

[0131] Situation A: ;

[0132] Situation B: ;

[0133] The initial value of the spacecraft's attitude error angular velocity is: ;

[0134] The parameters of the anti-reverse sliding mode attitude maneuvering control algorithm are: ; ; ; .

[0135] The trajectory of the changes in the attitude error quaternion, angular velocity error, and control torque of the spacecraft obtained by the method of this invention is as follows: Figure 2 and Figure 3 As shown, it can be seen in Eventually, it converges to the equilibrium position. ; Eventually, it converges to the equilibrium position. Meanwhile, the change trajectory of the control torque shows that the chattering is effectively suppressed.

Claims

1. A spacecraft anti-decoupling attitude maneuver control method based on the all-drive approach, characterized in that... The method includes the following steps: Step 1: Using unit quaternions to describe the attitude of rigid body spacecraft, for rigid body spacecraft with external disturbances, the following kinematic and dynamic equations for attitude error are established for static-to-static attitude maneuvering tasks: in, and They are respectively the body coordinate system Relative to the desired coordinate system Attitude quaternion error and angular velocity error; for The vector part, for The scalar part; It is a 3×3 identity matrix; Here is the rotational inertia matrix of the rigid body spacecraft; This refers to the control torque acting on a rigid spacecraft. External interference; Step 2: Differentiate the vector part of the attitude quaternion error variable, and establish the following second-order model based on the all-drive system method: In addition, ,and ; Step 3: For rigid body spacecraft with external disturbances, design the following anti-decoupling sliding mode attitude maneuver control law: in, , and It is a positive number. For the designed sliding mode variables, The expression is: Step 4: Considering the discontinuities of the sliding surface, a boundary layer is introduced to suppress chattering. Improved to: in, At the boundary layer thickness, the system still exhibits resistance to dewinding. and The intervals of convergence are as follows: in, .

2. The spacecraft anti-decoupling attitude maneuver control method based on the all-drive method according to claim 1, characterized in that... The Represented as: in, Euler angles, It is an Euler axis, and .

3. The spacecraft anti-decoupling attitude maneuver control method based on the all-drive method according to claim 1, characterized in that... The The expression is: 。 4. The spacecraft anti-decoupling attitude maneuver control method based on the all-drive method according to claim 1, characterized in that... The The expression is: 。 5. The spacecraft anti-decoupling attitude maneuver control method based on the all-drive method according to claim 1, characterized in that... The satisfy .

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