Adaptive Nonsingular Sliding Mode Attitude Control Method for Spacecraft Unwinding Problem

Abstract

The present invention relates to the technical field of spacecraft attitude control, and in particular provides an adaptive non-singular sliding mode attitude control method for spacecraft unwinding problems. The method includes establishing a spacecraft attitude kinematics and dynamics model; constructing an attitude tracking motion model of the spacecraft based on the spacecraft attitude kinematics and dynamics model; establishing a non-singular sliding mode surface with anti-unwinding fixed-time convergence characteristics according to the attitude error model; designing an attitude tracking adaptive controller based on the spacecraft attitude tracking motion model and the non-singular sliding mode surface. In the case of external disturbances and uncertain moments of inertia, this method combines sliding mode control and adaptive algorithms to achieve the attitude tracking control task and improve the accuracy of attitude control.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft attitude control, and particularly to an adaptive non-singular sliding mode attitude control method for spacecraft under the problem of unwinding. Background Art

[0002] Spacecraft attitude control technology has important application values in multiple fields, such as information communication, resource exploration, meteorological monitoring, safety rescue, and national defense construction, and is also one of the core technologies for completing various space missions. However, in an actual space system, it is often inevitably affected by various uncertain factors, such as non-ideal factors like external disturbances and system uncertainties, which reduces the accuracy of attitude control. Summary of the Invention

[0003] In view of this, the present invention provides an adaptive non-singular sliding mode attitude control method for spacecraft under the problem of unwinding to improve the accuracy of attitude control.

[0004] In a first aspect, the present invention provides an adaptive non-singular sliding mode attitude control method for spacecraft under the problem of unwinding, and the method includes:

[0005] Step 1, establish a spacecraft attitude kinematics and dynamics model;

[0006] Step 2, construct an attitude tracking motion model of the spacecraft based on the spacecraft attitude kinematics and dynamics model;

[0007] Step 3, establish a non-singular sliding mode surface with anti-unwinding fixed-time convergence characteristics according to the attitude error model;

[0008] Step 4, design an attitude tracking adaptive controller based on the spacecraft attitude tracking motion model and the non-singular sliding mode surface.

[0009] Optionally, the spacecraft attitude kinematics and dynamics model is:

[0010] ;

[0011] ;

[0012] ;

[0013] Wherein, 、 are respectively the vector and scalar parts of the quaternion , is the cross product matrix of ; is the identity matrix; is the angular velocity vector of the spacecraft body system relative to the inertial system, is the cross product matrix of; is the spacecraft control torque vector; is the external disturbance torque vector acting on the spacecraft.

[0014] Optionally, the , and its cross product matrix is:

[0015] .

[0016] Optionally, the process of constructing the attitude tracking motion model of the spacecraft in step 2 includes:

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] wherein, , are respectively the vector and scalar parts of the quaternion error ; , are respectively the vector and scalar parts of the quaternion error ; is the desired angular velocity of the spacecraft, is the vector transformation matrix from the inertial frame to the body frame of the spacecraft;

[0022] Then the attitude tracking motion model of the spacecraft is:

[0023] ;

[0024] ;

[0025] ;

[0026] wherein, ; is the angular velocity of the desired attitude; is the moment of inertia of the spacecraft; is the spacecraft control torque vector; d is the external disturbance torque vector acting on the spacecraft;

[0027] Since is the moment of inertia of the spacecraft, then we get:

[0028] ;

[0029] Among them, ;

[0030] ;

[0031] ;

[0032] Obtained: , among which,

[0033] ; It includes two parts: the first part is the nonlinearity of the system; the second part is the external disturbance; according to and , obtained , where .

[0034] Optionally, the non-singular sliding mode surface is:

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] Among them, , is the angular velocity of the desired attitude; represents the scalar part of the attitude error quaternion; is the vector part of the attitude error quaternion; , , all represent the sliding mode surface parameters, and the relationship between the sliding mode surface parameters is , , ; for the vector , , among which, ; represents the sign function, represents taking the absolute value.

[0041] Optionally, the designed attitude tracking adaptive controller is:

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] wherein, 0 is a positive constant gain; is a time - related adaptive term, i.e., the adaptive gain; is the estimated value of the adaptive gain, i.e., the adaptive law; is a small positive value; and , is a constant.

[0047] In a second aspect, an embodiment of the present invention provides a computer - readable storage medium, the computer - readable storage medium includes a stored program, wherein, when the program runs, it controls the device where the computer - readable storage medium is located to execute the adaptive non - singular sliding - mode attitude control method for the spacecraft unwinding problem in the first aspect or any possible implementation manner of the first aspect.

[0048] In a third aspect, an embodiment of the present invention provides an electronic device, including: one or more processors; a memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, and the one or more computer programs include instructions, when the instructions are executed by the device, the device is caused to execute the adaptive non - singular sliding - mode attitude control method for the spacecraft unwinding problem in the first aspect or any possible implementation manner of the first aspect.

[0049] In the technical solution provided by the present invention, the method includes establishing a spacecraft attitude kinematics and dynamics model;

[0050] Based on the spacecraft attitude kinematics and dynamics model, constructing a spacecraft attitude tracking motion model; establishing a non - singular sliding - mode surface with anti - unwinding fixed - time convergence characteristics according to the attitude error model; based on the spacecraft attitude tracking motion model and the non - singular sliding - mode surface, designing an attitude tracking adaptive controller. In the case of external disturbances and uncertain moments of inertia, this method combines sliding - mode control and adaptive algorithms, realizes the attitude tracking control task, and improves the accuracy of attitude control. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained according to these drawings.

[0052] Figure 1 Flowchart of the adaptive non - singular sliding - mode attitude control method for spacecraft unwinding problems provided by the embodiments of the present invention;

[0053] Figure 2 Simulation diagram of the change of quaternion error of the adaptive controller provided by the embodiments of the present invention;

[0054] Figure 3 Simulation diagram of the change of angular velocity error of the adaptive controller provided by the embodiments of the present invention;

[0055] Figure 4 Simulation diagram of the change of control torque of the adaptive controller provided by the embodiments of the present invention;

[0056] Figure 5 Simulation diagram of the response of the sliding - mode surface of the adaptive controller provided by the embodiments of the present invention;

[0057] Figure 6 Simulation diagram of the response of the adaptive parameter of the adaptive controller provided by the embodiments of the present invention;

[0058] Figure 7 Schematic diagram of an electronic device provided by the embodiments of the present invention. Detailed implementation manners

[0059] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0060] It should be clear that the described embodiments are only some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0061] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments, and are not intended to limit the present invention. The singular forms "a", "said" and "the" used in the embodiments of the present invention are also intended to include the plural forms unless the context clearly indicates otherwise.

[0062] It should be understood that the term "and / or" used herein is merely a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. Additionally, the character " / " in this text generally represents an "or" relationship between the preceding and following associated objects.

[0063] Depending on the context, as used herein, the word "if" can be interpreted as "when" or "while" or "in response to determining" or "in response to detecting". Similarly, depending on the context, the phrase "if determined" or "if detected (stated condition or event)" can be interpreted as "when determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)".

[0064] Figure 1 The flowchart of the adaptive non-singular sliding mode attitude control method for the spacecraft unwinding problem provided by the embodiments of the present invention is as Figure 1 shown, and the method includes:

[0065] Step 1: Establish the spacecraft attitude kinematics and dynamics models.

[0066] In the embodiments of the present invention, the spacecraft attitude kinematics and dynamics models are:

[0067] ;

[0068] ;

[0069] ;

[0070] Wherein, and are respectively the vector and scalar parts of the quaternion , is the cross product matrix of ; is the identity matrix; is the angular velocity vector of the spacecraft's body coordinate system relative to the inertial coordinate system, is 's cross product matrix; is the spacecraft control torque vector; is the external disturbance torque vector acting on the spacecraft.

[0071] In the embodiments of the present invention, , and its cross product matrix is:

[0072] .

[0073] Step 2: Based on the spacecraft attitude kinematics and dynamics model, construct the attitude tracking motion model of the spacecraft.

[0074] In the embodiment of the present invention, the process of constructing the attitude tracking motion model of the spacecraft in Step 2 includes:

[0075] ;

[0076] ;

[0077] ;

[0078] ;

[0079] wherein, , are the vector and scalar parts of the quaternion error respectively; , are the vector and scalar parts of the quaternion error respectively; is the desired angular velocity of the spacecraft, is the vector transformation matrix from the inertial frame to the spacecraft body frame;

[0080] Then the attitude tracking motion model of the spacecraft is:

[0081] ;

[0082] ;

[0083] ;

[0084] wherein, ; is the angular velocity of the desired attitude; is the moment of inertia of the spacecraft; is the spacecraft control torque vector; d is the external disturbance torque vector acting on the spacecraft;

[0085] Since is the moment of inertia of the spacecraft, then we get:

[0086] ;

[0087] wherein, ;

[0088] ;

[0089] ;

[0090] We get: , where

[0091] ; It includes two parts: the first part is the nonlinearity of the system; the second part is the external disturbance; according to and , we get , where .

[0092] Step 3: Establish a nonsingular sliding surface with anti-unwinding fixed-time convergence characteristics according to the attitude error model.

[0093] In the embodiments of the present invention, before designing the nonsingular sliding surface and the adaptive controller, the following definitions and lemmas are first given:

[0094] Definition 1: Consider the following nonlinear system

[0095] ;

[0096] where is continuous on the non-empty set , is the state vector of the system; if the equilibrium of the system at the origin has finite-time stability, then there exists a convergence time function such that when , the system state converges;

[0097] Definition 2: If the equilibrium point of the nonlinear system in has fixed-time stability, it means that the system is stable in finite time, and the convergence time has a user-defined upper bound , that is, , where can be selected according to specific requirements; in addition, this upper bound is independent of the initial state of the system;

[0098] Lemma 1: Consider the system in and a Lyapunov function that satisfies , where and is a parameter chosen by oneself, then the system is fixed-time stable at the preset time and afterwards, and this stability does not depend on the initial conditions of the system;

[0099] Lemma 2: For any , and , the following inequality always holds: ;

[0100] Lemma 3: For and , the function is monotonically increasing;

[0101] Theorem: When the sliding surface satisfies s , the system will converge to within a fixed time , and there is no unwinding phenomenon;

[0102] Further design a nonsingular sliding surface with the characteristics of anti-unwinding fixed-time convergence, and the proof is as follows:

[0103] Since the sliding surface satisfies s , we get ; Define a positive Lyapunov function as: , and discuss it in the following two cases:

[0104] Case 1: For , we can get , which indicates that ; Therefore, the derivative of the Lyapunov function with respect to time is:

[0105] ;

[0106] According to Lemma 2 and Lemma 3, and , we get:

[0107] ;

[0108] Case 2: For , then , which indicates that ; Similar to Case 1, we get:

[0109] ;

[0110] Based on the analysis of Case 1 and Case 2, we get: ;

[0111] where ;

[0112] According to Lemma 1, the system will converge to within a fixed time , and , regardless of the initial state, and the upper bound of the convergence time can be adjusted by choosing appropriate parameters;

[0113] In the embodiment of the present invention, based on the above analysis, a non-singular sliding mode surface with the characteristic of anti-unwinding fixed-time convergence is established, which is:

[0114] ;

[0115] ;

[0116] ;

[0117] ;

[0118] ;

[0119] Wherein, , is the angular velocity of the desired attitude; represents the scalar part of the attitude error quaternion; is the vector part of the attitude error quaternion; , , all represent sliding mode surface parameters, and the relationship of each sliding mode surface parameter is , , ; For the vector , , wherein, ; represents the sign function, represents taking the absolute value.

[0120] Step 4: Design an attitude tracking adaptive controller based on the attitude tracking motion model and the non-singular sliding mode surface of the spacecraft.

[0121] In the embodiment of the present invention, the designed attitude tracking adaptive controller is:

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] Wherein, 0 is a positive constant gain; is a time-dependent adaptive term, that is, an adaptive gain; is an estimated value of the adaptive gain, that is, an adaptive law; is a small positive value; and , is a constant.

[0127] The present invention also includes the stability analysis of the closed-loop system, and defines the Lyapunov function:

[0128] ;

[0129] Derive the function V and substitute the formula and the adaptation law to obtain:

[0130] ;

[0131] Considering that and , Arrange it as:

[0132] ;

[0133] In the context of adaptive control and stability analysis, the update rule of the parameter and the discussion of the Lyapunov function :

[0134] ,

[0135] and

[0136] ;

[0137] Obtain according to the adaptive controller:

[0138] ;

[0139] Among them, the analysis shows that , that is, the Lyapunov function is bounded; thus, it is concluded that:

[0140] , , , Ensure that , and maintain a time interval of ; Further explanation, these conclusions apply to any finite , that is, no matter how large is taken, the solution will exist and be bounded throughout the time period; In addition, from the equations and it can be seen that when is outside certain specific sets, will be less than zero, which means that the state of the system will tend to be stable and remain within these sets;

[0141] ,

[0142] or

[0143] ,

[0144] Since , the set contains . Therefore, although the system state can move between these two sets, once it enters , they will be attracted back to , thus ensuring that the system state always remains within the constraint state; the norm of the angular velocity error is restricted within , ensuring that the angular velocity of the system always remains within a bounded range and does not increase infinitely;

[0145] ;

[0146] This indicates the stability of the attitude control system, ensuring that all state variables are bounded and continuous.

[0147] In the embodiments of the present invention, from Figure 2 it can be seen that under the influence of sliding mode control, the attitude quaternion error quickly converges to 0. This indicates that the spacecraft has successfully tracked the desired attitude, and the initial large error gradually decreases over time and converges to 0 in less than 2 seconds. Since the scalar part of the attitude quaternion was initially selected as , which is within the interval (0, 1), the scalar part of the attitude quaternion converges to 1 instead of -1, further ensuring the anti-windup performance of the system.

[0148] In the embodiments of the present invention, as Figure 3 shown, the angular velocity tracking error exhibits some initial fluctuations caused by external disturbances. However, with the adjustment of the adaptive control gain, the error gradually decreases and converges to 0 in 2 seconds, ensuring accurate velocity tracking.

[0149] In the embodiments of the present invention, as Figure 4 shown, the control torque response is highlighted, which is dynamically adjusted based on the attitude quaternion and the angular velocity error. The adaptive parameter update mechanism enables the control system to effectively manage external disturbances and uncertainties, converges the control torque to 0 within 3 seconds, and ensures effective attitude control.

[0150] In the embodiments of the present invention, as Figure 5The behavior of the sliding mode surface shown emphasizes the effectiveness of the proposed control method. The sliding mode surface s quickly converges to 0, ensuring that the system reaches the desired attitude within a fixed time. This behavior highlights the stability of the system throughout the control process, as the sliding mode surface always pushes the error towards 0.

[0151] In the embodiments of the present invention, as Figure 6 shows the adaptive parameter , which is adjusted in real time according to the error of the system and external disturbances. Over time, the parameter converges smoothly and finally tends to a stable value. This shows that the adaptive parameter can effectively cope with the uncertainties of the system and external disturbances, ensuring the robustness and stability of the control system. The stability of the adaptive parameter further proves the effectiveness of the control strategy.

[0152] In summary, the present invention effectively solves the problems of system uncertainties and external disturbances. By designing the sliding mode surface and combining the adaptive parameter update law, the proposed control method ensures global stability under different disturbances and uncertainties, making it more suitable for applications where fast response and precise tracking are crucial. In addition, the simulation results verify the effectiveness and robustness of the control method. Compared with traditional control methods, its tracking performance has been significantly improved, especially in maintaining stability and anti-unwinding characteristics under uncertain conditions. At the same time, the computational burden of the spacecraft onboard system is reduced by optimizing the calculation, and it does not involve time-consuming design processes.

[0153] In the technical solution provided by the present invention, the method includes establishing a spacecraft attitude kinematics and dynamics model; based on the spacecraft attitude kinematics and dynamics model, constructing an attitude tracking motion model of the spacecraft; establishing a non-singular sliding mode surface with anti-unwinding fixed-time convergence characteristics according to the attitude error model; based on the attitude tracking motion model and non-singular sliding mode surface of the spacecraft, designing an attitude tracking adaptive controller. Under the conditions of external disturbances and uncertain moments of inertia, the method combines sliding mode control and adaptive algorithms to achieve the attitude tracking control task and improve the accuracy of attitude control.

[0154] Each step of the embodiments of the present invention can be executed by an electronic device. Among them, the electronic device includes but is not limited to mobile phones, tablet computers, portable PCs, desktop computers, etc.

[0155] The embodiments of the present invention provide a computer-readable storage medium. The computer-readable storage medium includes a stored program, wherein when the program runs, it controls the electronic device where the computer-readable storage medium is located to execute the embodiments of the above-mentioned adaptive non-singular sliding mode attitude control method for spacecraft unwinding problems.

[0156] Figure 7Schematic diagram of an electronic device provided by an embodiment of the present invention, as Figure 7 shown, the electronic device 21 includes: a processor 211, a memory 212, and a computer program 213 stored in the memory 212 and executable on the processor 211. When the computer program 213 is executed by the processor 211, it implements the adaptive non-singular sliding mode attitude control method under the problem of spacecraft unwinding in the embodiment. To avoid repetition, it will not be elaborated here one by one.

[0157] The electronic device 21 includes, but is not limited to, a processor 211 and a memory 212. Those skilled in the art can understand that Figure 7 merely examples of the electronic device 21, do not constitute a limitation on the electronic device 21, and may include more or fewer components than shown, or combine certain components, or different components. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0158] The so-called processor 211 may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0159] The memory 212 may be an internal storage unit of the electronic device 21, such as the hard disk or memory of the electronic device 21. The memory 212 may also be an external storage device of the electronic device 21, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the electronic device 21. Further, the memory 212 may also include both the internal storage unit and the external storage device of the electronic device 21. The memory 212 is used to store the computer program and other programs and data required by the network device. The memory 212 may also be used to temporarily store the data that has been output or will be output.

[0160] Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working processes of the above-described systems, devices, and units can refer to the corresponding processes in the foregoing method embodiments, and will not be elaborated here again.

[0161] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention shall be included within the scope of protection of the present invention.

Claims

1. An adaptive non-singular sliding mode attitude control method for a spacecraft unwinding problem, characterized in that: The method comprises: Step 1: Establish the spacecraft attitude kinematics and dynamics model; Step 2: constructing a spacecraft attitude tracking motion model based on the spacecraft attitude kinematics and dynamics model; Step 3: Establish a non-singular sliding surface with anti-unwinding fixed time convergence characteristics according to the attitude error model; Step 4: Based on the attitude tracking motion model of the spacecraft and the non-singular sliding surface, an attitude tracking adaptive controller is designed; The process of constructing the attitude tracking motion model of the spacecraft in step 2 includes: ； ； ； ； in, , The quaternion errors are The vector and scalar parts of , The quaternion errors are The vector and scalar parts of is the desired angular velocity of the spacecraft, is the vector transformation matrix from the inertial system to the spacecraft system; , Quaternions The vector and scalar parts of for The cross product matrix of is the angular velocity vector of the spacecraft system relative to the inertial system; is the identity matrix; Then the attitude tracking motion model of the spacecraft is: ； ； ； in, ; is the angular velocity of the desired attitude; is the moment of inertia of the spacecraft; is the spacecraft control torque vector; d is the external disturbance torque vector of the spacecraft; because is the moment of inertia of the spacecraft, then we get: ； in, ; ； ； get: ,in, ; It consists of two parts: the first part is the nonlinearity of the system; the second part is the external interference; and ,get ,in ; The non-singular sliding surface is: ； ； ； ； ； in, , is the angular velocity of the desired attitude; Represents the scalar part of the attitude error quaternion; is the vector part of the attitude error quaternion; , , All represent sliding surface parameters. The relationship between the sliding surface parameters is as follows: , , ; For vector , ,in, ; represents the symbolic function, Represents absolute value.

2. The method according to claim 1, characterized in that The spacecraft attitude kinematics and dynamics model is: ； ； ； in, , Quaternions The vector and scalar parts of for The cross product matrix of is the identity matrix; is the angular velocity vector of the spacecraft system relative to the inertial system, for The cross product matrix of is the spacecraft control torque vector; is the external disturbance torque vector acting on the spacecraft.

3. The method according to claim 2, characterized in that Said , whose cross product matrix for: 。 4. The method according to claim 1, characterized in that: The designed attitude tracking adaptive controller is: ； ； ； ； in, 0 is a positive constant gain; is a time-dependent adaptive term, i.e., adaptive gain; is the estimated value of the adaptive gain, i.e., the adaptive law; is a small positive value; and , is a constant.

5. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored program, wherein when the program is running, the device where the computer-readable storage medium is located is controlled to execute the adaptive non-singular sliding mode attitude control method for the spacecraft unwinding problem described in any one of claims 1 to 4.

6. An electronic device, characterized in that: include: one or more processors; Memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, and the one or more computer programs include instructions, which, when executed by the device, enable the device to perform the adaptive non-singular sliding mode attitude control method for the spacecraft unwinding problem according to any one of claims 1 to 4.

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