Attitude and orbit integrated fault-tolerant control method, system, medium and equipment

Abstract

The invention discloses an attitude and orbit integrated fault-tolerant control method, system, medium and equipment for a flexible spacecraft, and the method comprises the steps: building a geocentric inertial coordinate system and a spacecraft body coordinate system, and carrying out the modeling of a rigid body and a flexible solar panel of the flexible spacecraft through a finite element theorem, obtaining a dynamic formula and a kinematics formula of the single-satellite spacecraft; establishing a relative kinematics equation between the tracking spacecraft and the target spacecraft; performing mathematical modeling on the fault type of the actuator, wherein the mathematical modeling comprises a gain fault, a deviation fault and a clamping stagnation fault; constructing a nonsingular terminal sliding mode surface, wherein the sliding mode surface comprises a relative dual quaternion error item and an auxiliary sliding mode surface item; and deriving a spacecraft system error kinematical equation based on the sliding mode surface, deriving a control moment calculation formula in combination with an actuator output moment expression, generating a control instruction according to the control moment formula, and driving the tracking spacecraft to realize integrated fault-tolerant control of attitude and orbit.

Description

Technical Field

[0001] The present invention belongs to the field of spacecraft attitude and orbit coordinated control, and in particular to an attitude and orbit integrated fault-tolerant control method, system, medium and equipment for flexible spacecraft. Background Art

[0002] With the continuous advancement of aerospace technology, the complexity of spacecraft on-orbit missions is increasing. This is especially true for close-range operations such as rendezvous and docking, formation flying, and on-orbit servicing, which require spacecraft to possess higher control precision and autonomy. At the same time, the widespread use of large-scale flexible structures, such as flexible solar panels and antennas, has effectively enhanced spacecraft mission capabilities and energy acquisition efficiency. However, it has also significantly exacerbated the system's nonlinear coupling characteristics and dynamic complexity, posing significant challenges to the design of attitude and orbit control systems.

[0003] Traditional spacecraft control methods generally adopt a design approach that separates attitude control from orbit control, making it difficult to accurately describe the attitude-orbit coupling characteristics. This is especially true when flexible structures are subject to significant disturbances, the interference environment is complex, or actuator failures occur. System stability and control accuracy are often difficult to guarantee. Furthermore, the difficulty of maintaining a relatively stable state between spacecraft and the short acquisition time place high demands on control accuracy and efficiency. Therefore, it is urgent to propose an integrated attitude-orbit control method that balances system robustness and fault tolerance, targeting the attitude-orbit coupling characteristics of flexible spacecraft. This method can achieve precise and stable control of the system state under multi-source fault conditions and enhance the spacecraft's autonomous operation capabilities in complex space environments.

[0004] The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art. Summary of the Invention

[0005] In response to the problems existing in the prior art, the present invention proposes a fault-tolerant control method, system, medium and equipment for attitude and orbit integration of flexible spacecraft, which can achieve high-precision robust control of attitude and orbit integration of flexible spacecraft under complex environments and actuator failure conditions.

[0006] In one aspect of the present invention, a method for attitude and orbit integrated fault-tolerant control of a flexible spacecraft comprises the following steps:

[0007] In the first step, the geocentric inertial coordinate system and the spacecraft body coordinate system are established. The rigid body and flexible solar panels of the flexible spacecraft are modeled using the finite element theorem to obtain the dynamic and kinematic formulas of the single-satellite spacecraft.

[0008] In the second step, the relative kinematic equations between the tracking spacecraft and the target spacecraft are established, the relative dual quaternion and the relative dual velocity spinor are defined, and the dynamic relationship between the modal coordinates and the dual velocity spinor error is established;

[0009] In the third step, mathematical modeling is performed on the actuator fault types, including gain fault, bias fault, and stuck fault, and the influence of gravity gradient torque and external disturbance torque is considered; a non-singular terminal sliding surface is constructed, which includes a relative dual quaternion error term and an auxiliary sliding surface term;

[0010] In the fourth step, the spacecraft system error kinematic equation is derived based on the sliding surface, and the control torque calculation formula is derived in combination with the actuator output torque expression. Control instructions are generated according to the control torque formula to drive the tracking spacecraft to achieve integrated fault-tolerant control of attitude and orbit.

[0011] In the method described, in the first step, a geocentric inertial coordinate system and a spacecraft body coordinate system are established to describe the spacecraft's on-orbit spatial position and attitude direction, respectively. Based on the finite element method, the rigid body and flexible components of the flexible spacecraft are modeled, and the single-satellite spacecraft dynamic formula is obtained as follows: in is the dual force acting on the tracking spacecraft B, where F B is the force, T B is the acting torque, is the dual mass, where M B and J B are the mass and moment of inertia of tracking spacecraft B, is the dual velocity spinor, where and are the angular velocity and linear velocity of the tracking spacecraft B in its body coordinate system, is the dual rotation matrix, where B tran and B rot are the translation coupling matrix and the rotation coupling matrix respectively, and η is the modal coordinate; the single star kinematic formula is: in is the dual quaternion for tracking spacecraft B.

[0012] In the method described above, in the second step, the relative kinematic formula between the tracking spacecraft B and the target spacecraft A is established. is the relative dual quaternion, let the relative angular velocity and relative linear velocity between the tracking spacecraft B and the target spacecraft A in the coordinate system B be and Then the relative dual velocity spinor Specifically:

[0013]

[0014] in is the representation of the dual velocity spinor of target spacecraft A in the coordinate system of tracking spacecraft B, and The angular velocity and linear velocity of the target spacecraft A in the coordinate system B are respectively. The relationship between the modal coordinates and the dual velocity spinor error can be expressed as: Where ζ is the modal damping coefficient and Λ is the modal stiffness coefficient.

[0015] In the method described above, in the third step, the actuator outputs a dual torque To restrict: represents the theoretically required dual torque, Indicates a gain fault, Indicates a deviation fault, Indicates a stuck fault and can be specifically expressed as represents the maximum dual torque that the actuator can output under normal working conditions, then the dual torque acting on the tracking spacecraft B can be specifically expressed as is the dual gravity gradient force (changed to the previous one), where μ is the gravitational constant of the central celestial body, r B To track the position vector between spacecraft B and the center of the celestial body, To counteract the interference force, in order to increase the robustness and control efficiency of the spacecraft system, the relative dual quaternion is rewritten as And design the non-singular terminal sliding surface: in is the gain parameter, is the auxiliary sliding surface and l1=(2-λ)δ λ-1 , l2=(λ-1)δ λ-2 , 0<λ<1.

[0016] In the method described, in the fourth step, the sliding mode surface is differentiated with time to obtain the spacecraft system error kinematic equation:

[0017]

[0018] in Substituting the dual torque expression into the above formula, the specific expression of the control torque is obtained after calculation:

[0019]

[0020] Among them, 0<γ1<1<γ2, is the control parameter.

[0021] In the method described above, the maximum convergence time of the system state variable T m satisfy

[0022]

[0023] In the method, the flexible spacecraft includes a satellite or a space module.

[0024] A system for implementing the method includes:

[0025] The finite element module establishes the geocentric inertial coordinate system and the spacecraft body coordinate system, uses the finite element theorem to model the rigid body and flexible solar panels of the flexible spacecraft, and obtains the dynamic and kinematic formulas of the single-satellite spacecraft;

[0026] The relative kinematics module establishes the relative kinematic equations between the tracking spacecraft and the target spacecraft, defines the relative dual quaternion and the relative dual velocity spinor, and establishes the dynamic relationship between the modal coordinates and the dual velocity spinor error;

[0027] a modeling module that mathematically models actuator fault types, including gain fault, bias fault, and stuck fault, and considers the effects of gravity gradient torque and external disturbance torque; constructs a non-singular terminal sliding surface, which includes a relative dual quaternion error term and an auxiliary sliding surface term;

[0028] The control module derives the spacecraft system error kinematic equation based on the sliding surface, and derives the control torque calculation formula based on the actuator output torque expression. The control command is generated according to the control torque formula to drive the tracking spacecraft to achieve integrated fault-tolerant control of attitude and orbit.

[0029] A computer storage medium includes computer instructions, which, when executed on a computer, cause the computer to execute the method described above.

[0030] An electronic device, comprising:

[0031] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein:

[0032] When the processor executes the program, the method described is implemented.

[0033] Compared with the existing technology, the advantages of the present invention are: the present invention uniformly considers factors such as flexible solar panel vibration, attitude-orbit coupling, environmental disturbances and actuator failures, establishes a rigid-flexible coupling attitude-orbit dynamics model, and proposes a timed fault-tolerant sliding mode control method, which can achieve system stability within a preset time and has good robustness against uncertainty and failures. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are intended only to illustrate preferred embodiments and are not to be construed as limiting the present invention. It should be understood that the drawings described below are merely examples of the present invention, and that those skilled in the art will be able to derive other drawings from these drawings without inventive effort. Throughout the drawings, identical reference numerals are used to denote identical components.

[0035] In the attached figure:

[0036] Figure 1 It is a schematic diagram of the process of the present invention;

[0037] Figure 2 A schematic diagram showing the effect of establishing the coordinate system of the present invention;

[0038] Figure 3 Schematic diagram of the relative angular velocity error control effect of the present invention;

[0039] Figure 4 This is a schematic diagram of the relative linear velocity error control effect of the present invention;

[0040] Figure 5 Schematic diagram of the relative attitude quaternion error control effect of the present invention;

[0041] Figure 6 Schematic diagram of the relative position error control effect of the present invention;

[0042] Figure 7 This is a schematic diagram of the actual output force control effect of the actuator of the present invention;

[0043] Figure 8 This is a schematic diagram of the actual output torque control effect of the actuator of the present invention;

[0044] Figure 9 Schematic diagram of the modal coordinate control effect of the present invention.

[0045] The present invention will be further explained below with reference to the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0046] Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0047] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the invention. The scope of protection of the present invention shall be as defined in the attached claims.

[0048] To facilitate understanding of the embodiments of the present invention, further explanation will be given below using specific embodiments as examples in conjunction with the accompanying drawings, and the accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0049] like Figures 1 to 9 As shown, the invented flexible spacecraft attitude and orbit integrated fault-tolerant control method includes the following steps:

[0050] In the first step S1, the geocentric inertial coordinate system and the spacecraft coordinate system are first established. The rigid body and the flexible solar panels are modeled using the finite element theorem, and the single-satellite spacecraft dynamics formula is obtained as follows: in is the dual force acting on the tracking spacecraft B, where F B is the force, T B is the acting torque, is the dual mass, where M B and J B are the mass and moment of inertia of tracking spacecraft B, is the dual velocity spinor, where and are the angular velocity and linear velocity of the tracking spacecraft B in its body coordinate system, is the dual rotation matrix, where B tran and B rot are the translation coupling matrix and the rotation coupling matrix respectively, and η is the modal coordinate; the single star kinematic formula is: in is the dual quaternion for tracking spacecraft B.

[0051] In the second step S2, the relative kinematic formula between the tracking spacecraft B and the target spacecraft A is established. is the relative dual quaternion, let the relative angular velocity and relative linear velocity between the tracking spacecraft B and the target spacecraft A in the coordinate system B be and Then the relative dual velocity spinor Specifically:

[0052]

[0053] in is the representation of the dual velocity spinor of target spacecraft A in the coordinate system of tracking spacecraft B, and The angular velocity and linear velocity of the target spacecraft A in the coordinate system B are respectively. The relationship between the modal coordinates and the dual velocity spinor error can be expressed as: Where ζ is the modal damping coefficient and Λ is the modal stiffness coefficient.

[0054] In the third step S3, in order to cope with the complex space environment interference and actuator failure, mathematical modeling is first performed to output the dual torque of the actuator. To restrict: represents the theoretically required dual torque, Indicates a gain fault, Indicates a deviation fault, Indicates a stuck fault and can be specifically expressed as represents the maximum dual torque that the actuator can output under normal working conditions. Then the dual torque acting on the tracking spacecraft B can be specifically expressed as is the dual gravity gradient force (changed to the previous one), where μ is the gravitational constant of the central celestial body, r B To track the position vector between spacecraft B and the center of the celestial body, is the dual disturbance force. Based on the above foundation, in order to increase the robustness and control efficiency of the spacecraft system, the relative dual quaternion is rewritten as And design the non-singular terminal sliding surface: in is the gain parameter, is the auxiliary sliding surface and l1=(2-λ)δ λ-1 , l2=(λ-1)δ λ-2 , 0<λ<1.

[0055] In the fourth step S4, the sliding mode surface designed in step S3 is differentiated with respect to time to obtain the spacecraft system error kinematic equation:

[0056]

[0057] in Substituting the dual torque expression in step S3 into the above formula, the specific expression of the control torque can be obtained through calculation:

[0058]

[0059] Among them, 0<γ1<1<γ2, is the control parameter.

[0060] To further illustrate the method of the present invention, Figure 1 This diagram illustrates the process structure of the present invention's integrated attitude and orbit fault-tolerant control method, including modeling, controller design, and fault handling modules. This diagram can be used to understand the overall technical solution and logical relationships of the present invention. Figure 2 The coordinate system established by the present invention for tracking spacecraft and target spacecraft is shown. Figure 3 This represents the relative angular velocity error between the spacecraft and the target, and can be used to evaluate the response performance of the attitude control module. This graph provides the trend of the angular velocity error signal, reflecting the attitude dynamic response characteristics of the control system. Figure 4 This chart shows the relative linear velocity error, which indicates the spacecraft's tracking capability in orbital control. This chart can be used to extract the linear velocity error and assist in analyzing the convergence of orbital states. Figure 5 This is the relative attitude quaternion error map, which describes the relative attitude difference between the tracking spacecraft and the target spacecraft. This map can be used to obtain quaternion error information, which can be used to determine the effectiveness of attitude alignment. Figure 6 This plot represents the relative position error between spacecraft and reflects the spatial accuracy of orbital control. This plot provides the evolution of the position error signal, assisting in the performance evaluation of attitude-orbit coupled control. Figure 7 It reflects the actual force output of the actuator during the control process, can characterize the fault-tolerant adjustment capability of the actuator in the presence of faults or disturbances, and is used to verify the actual execution of force control instructions. Figure 8 It represents the actual output torque of the actuator under different working conditions and is used to analyze the adjustment ability of the torque control strategy on the actuator output, as well as the effectiveness of the fault modeling and compensation mechanism. Figure 9 This graph shows the changes in the flexible modal coordinates, reflecting the vibration response of the flexible structure under control. This graph provides modal displacement information, which is used to evaluate the flexible vibration suppression effect and the dynamic response of the structure.

[0061] In the first step S1 of the preferred embodiment of the flexible spacecraft attitude and orbit integrated fault-tolerant control method of the present invention: the tracking spacecraft B parameter is set to: M B =100kg, J B =[140,-5,-8.5;-5,357,30;-8.5,30,353]kg·m 2 .

[0062] In the second step S2 of the preferred embodiment of the flexible spacecraft attitude and orbit integrated fault-tolerant control method of the present invention: the initial values ​​of the parameters related to the target spacecraft A and the modal coordinates are set as: qA =[0.8,0.4,-0.4,0.2] T ,

[0063] ζ=0.005,Λ=1.727,B tran =[0.155,-0.155,0.225] T , B rot =[0.2,0.05,0.15] T ,

[0064] In the third step S3 of the preferred embodiment of the flexible spacecraft attitude and orbit integrated fault-tolerant control method of the present invention: the initial error of the state variables and the non-singular timing sliding mode surface parameters between the tracking spacecraft B and the target spacecraft A are set as: q e =[0.8,0.4,-0.4,0.2] T , r e =[-150,200,100] T m,ω e =[0.001,0.002,0.001] T rad / s,v e =[0.3,0.1,0.25] T m / s, λ=0.9,δ=0.01,

[0065] In the fourth step S4 of the preferred embodiment of the flexible spacecraft attitude and orbit integrated fault-tolerant control method of the present invention: the relevant parameters of the non-singular timing sliding mode controller are set as: u fmax =10N,u tmax =1N·m, γ1=0.5, γ2=1.1, The simulated actuator fault parameters and external environmental interference force are set as:

[0066]

[0067] In one embodiment, Figure 3 The convergence of the relative angular velocity error over time under the control strategy of the present invention is demonstrated. It can be observed that the error approaches zero within a fixed time, verifying the rapid convergence of the controller to the angular motion state. Figure 4 This is the dynamic variation curve of the relative linear velocity error. The curve drops rapidly and then tends to be stable, indicating that the track velocity error is precisely controlled within the set time and meets the attitude and track integration requirements. Figure 5The graph below shows the relative attitude quaternion error variation, which reflects the controller's ability to adjust the relative attitude direction. In this graph, the quaternion error decreases rapidly under control, and the system achieves attitude synchronization. Figure 6 This reflects the evolution of the relative position error between the spacecraft. The rapid convergence of the position error indicates that the controller effectively coordinates the orbital attitude coupling factors and achieves precise space position control. Figure 7 and Figure 8 The two graphs represent the dual force and torque responses of the actuator's actual output, respectively. In the presence of gain, deviation, and stuck faults, the controller can effectively identify and compensate for the faults, ensuring that the actual output still meets the control target, demonstrating excellent fault tolerance. Figure 9 The flexible modal coordinate response curve is shown. Under the action of the controller, the flexible vibration can be quickly suppressed and the modal response is stable, verifying the dynamic suppression effect of this method on flexible structures.

[0068] In one embodiment, a method for attitude and orbit integrated fault-tolerant control of a flexible spacecraft includes the following steps:

[0069] In the first step, the geocentric inertial coordinate system and the spacecraft coordinate system are established. The rigid body and the flexible solar panels are modeled using the finite element theorem, and the single-satellite spacecraft dynamics formula is obtained as follows: in is the dual force acting on the tracking spacecraft B, where F B is the force, T B is the acting torque, is the dual mass, where M B and J B are the mass and moment of inertia of tracking spacecraft B, is the dual velocity spinor, where and are the angular velocity and linear velocity of the tracking spacecraft B in its body coordinate system, is the dual rotation matrix, where B tran and B rot are the translation coupling matrix and the rotation coupling matrix respectively, and η is the modal coordinate; the single star kinematic formula is: in is the dual quaternion for tracking spacecraft B.

[0070] In the second step, the relative kinematic formula between the tracking spacecraft B and the target spacecraft A is established. is the relative dual quaternion, let the relative angular velocity and relative linear velocity between the tracking spacecraft B and the target spacecraft A in the coordinate system B be and Then the relative dual velocity spinor Specifically:

[0071]

[0072] in is the representation of the dual velocity spinor of target spacecraft A in the coordinate system of tracking spacecraft B, and The angular velocity and linear velocity of the target spacecraft A in the coordinate system B are respectively. The relationship between the modal coordinates and the dual velocity spinor error can be expressed as: Where ζ is the modal damping coefficient and Λ is the modal stiffness coefficient.

[0073] In the third step, in order to cope with the interference of complex space environment and actuator failure, mathematical modeling is first performed to output the dual torque of the actuator. To restrict:

[0074] represents the theoretically required dual torque, Indicates a gain fault, Indicates a deviation fault, Indicates a stuck fault and can be specifically expressed as

[0075] represents the maximum dual torque that the actuator can output under normal working conditions. Then the dual torque acting on the tracking spacecraft B can be specifically expressed as

[0076] is the dual gravity gradient force (changed to the previous one), where μ is the gravitational constant of the central celestial body, r B To track the position vector between spacecraft B and the center of the celestial body, is the dual disturbance force. Based on the above foundation, in order to increase the robustness and control efficiency of the spacecraft system, the relative dual quaternion is rewritten as

[0077] And design the non-singular terminal sliding surface: in

[0078] is the gain parameter,

[0079] is the auxiliary sliding surface and

[0080] l1=(2-λ)δ λ-1 , l2=(λ-1)δ λ-2 , 0<λ<1.

[0081] In the fourth step, the sliding mode designed in step three is differentiated with respect to time to obtain the spacecraft system error kinematic equation:

[0082]

[0083] in

[0084] Substituting the dual torque expression in step 3 into the above formula, the specific expression of the control torque can be obtained after calculation:

[0085]

[0086] Among them, 0<γ1<1<γ2, is the control parameter.

[0087] Preferably, establish the geocentric inertial coordinate system and the spacecraft body coordinate system, respectively used to describe the spacecraft's on-orbit spatial position and attitude direction; based on the finite element method, model the spacecraft's rigid body and its flexible components to obtain the structural dynamic characteristics of the flexible spacecraft; construct a single-satellite spacecraft attitude-orbit coupled dynamics model, and use dual quaternions and dual mechanics theory to describe the overall motion state of the spacecraft; establish the single-satellite kinematic and dynamic equations, which are specifically in the form of

[0088] Preferably, a relative kinematic model is established between the tracking spacecraft and the target spacecraft, and the relative attitude and orbit states are expressed using dual quaternions, where the relative dual quaternions are used to describe the relative attitude and relative orbital position relationship between the two spacecraft, and the relative dual velocity spinor is used to describe the difference between the dual velocity spinors of the two spacecraft. The dynamic relationship between the modal coordinates and the dual velocity spinor error is further established, which is specifically in the form of

[0089] Preferably, the dual torque output by the actuator is modeled and constrained, and the gravity gradient disturbance and external interference are comprehensively considered. The actual dual torque acting on the tracking spacecraft is expressed as In order to improve the system robustness and control accuracy, the dual quaternion is redefined and designed in the form of The non-singular terminal sliding surface of .

[0090] Preferably, for nonlinear systems If there exists a continuously differentiable, positive definite and radially unbounded function V(x) that satisfies And a1>0, a2>0, 0<γ<1<α, then the maximum convergence time of the system is T m satisfy Based on this theorem, the controller designed in step 4 is proved to have a fixed time convergence: define the operation And consider the Lyapunov function Substituting the specific kinetic formula derived in step S4 into the equation, we obtain:

[0091]

[0092] Substitute the specific expression of the control torque derived in step 4 into the above formula and let

[0093]

[0094] It can be deduced that

[0095] According to the above theorem, we can know that the maximum convergence time T of the system state variable is m satisfy

[0096]

[0097] The dual quaternion modeling (Dual Quaternion Modeling) of the present invention uses dual quaternions to uniformly describe the attitude and position state of the spacecraft, unifying the attitude and orbit description: avoiding the coupling problem caused by the separate modeling of attitude and orbit in traditional methods; reducing computational complexity: dual quaternions can simultaneously express rotation and translation information; being suitable for nonlinear system control: naturally suitable for rigid-flexible coupling dynamics modeling of spacecraft; improving convergence efficiency: facilitating the construction of nonlinear controllers such as sliding surfaces. Figure 5 The model demonstrates that the relative attitude quaternion error rapidly approaches zero, verifying its excellent attitude synchronization capability. Rigid-Flexible Coupled Dynamics (RFD) models the spacecraft's rigid body and flexible solar panels based on the finite element theorem; introduces modal coordinates, modal damping coefficients, and modal stiffness coefficients to describe the dynamics of the flexible structure; truly reflects the spacecraft's physical characteristics by accounting for vibration and energy dissipation caused by the flexible structure; improves control accuracy by effectively suppressing flexible oscillations through the introduction of modal coordinate feedback; enhances model applicability for spacecraft mission scenarios with large flexible attachments; and supports subsequent controller design by providing a precise dynamic foundation for robust controllers. Figure 9The response curve of the flexible modal coordinates is shown, and vibration is quickly suppressed under the action of the controller, indicating good coordination between the modeling and control strategies. The Nonsingular Terminal Sliding Mode Surface (NTS) design constructs a sliding surface to avoid singularities: compared to traditional terminal sliding modes, this structure does not encounter singularities during convergence; achieves fixed-time convergence, ensuring that the system state stabilizes to an equilibrium point within a finite time; improves system robustness, providing strong immunity to external interference and internal uncertainties; and adapts to complex spatial environments, enabling the system to cope with uncertainties such as actuator failures and gravitational disturbances. Figure 3 and Figure 4 The rapid convergence of angular velocity error and linear velocity error was demonstrated, verifying the effectiveness of sliding mode control. The Actuator Fault Modeling and Compensation mechanism models three typical actuator faults, enhancing system reliability: even if some actuator performance degrades, control functionality can still be maintained; reducing the risk of mission failure: common faults during on-orbit operation, such as gain faults and bias faults, are mitigated; and improving mission adaptability: suitable for high-reliability missions such as long-term deep space exploration and satellite formations. Figure 7 and Figure 8 The curves of the actuator's output force and torque are displayed. The control system can still maintain stable output in the presence of faults, proving the effectiveness of the fault-tolerant mechanism. Suppressing flexible structure vibration: Preventing attitude instability caused by flexible sailboard vibration; Improving control accuracy: Reducing tracking errors caused by flexible deformation; Accelerating system response: Shortening the time required for attitude adjustment. The multivariable integrated control strategy (Integrated Attitude-Orbit Control Strategy) simultaneously controls the attitude and orbit state of the spacecraft; Using relative dual quaternion error and relative velocity spinor error to construct control input; Solving the attitude-orbit coupling problem: Avoiding the limitations of attitude and orbit separation control in traditional control methods; Improving control efficiency: Reducing mutual interference between control channels; Enhancing mission flexibility: Suitable for various mission requirements such as rendezvous and docking, formation flying, etc.; Simplifying system architecture: Reducing the number of controllers and reducing hardware resource usage. Figure 6 Rapid convergence of relative position error was demonstrated, indicating excellent track control performance; Figure 5 and Figure 3Further verifying the accuracy and response speed of attitude control. This invention achieves high-precision attitude and orbit control: attitude and orbit errors converge rapidly within a finite time; strong robustness and stability: control performance can be maintained in the face of external interference and actuator failures; dynamic suppression of flexible structures: effectively suppressing vibrations caused by flexible components, improving overall control quality; good engineering practicality: suitable for missions such as satellite rendezvous and docking, on-orbit servicing, and formation flying; and high integration and intelligence: supporting embedded deployment to meet the needs of onboard autonomous control.

[0098] Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments and application fields. The above-mentioned specific embodiments are merely illustrative and instructive, and are not restrictive. A person skilled in the art, guided by this specification and without departing from the scope of protection of the claims of the present invention, may also devise various forms, all of which fall within the scope of protection of the present invention.

Claims

1. A method for attitude and orbit integrated fault-tolerant control of a flexible spacecraft, characterized in that: The method comprises the following steps: In the first step (S1), the geocentric inertial coordinate system and the spacecraft body coordinate system are established, and the rigid body and flexible solar panels of the flexible spacecraft are modeled using the finite element theorem to obtain the dynamic and kinematic formulas of the single-star spacecraft; In the second step (S2), the relative kinematic equations between the tracking spacecraft and the target spacecraft are established, the relative dual quaternion and the relative dual velocity spinor are defined, and the dynamic relationship between the modal coordinates and the dual velocity spinor error is established; In the third step (S3), a mathematical model is performed on the actuator fault types, including gain fault, bias fault and stuck fault, and the influence of gravity gradient torque and external disturbance torque is considered; a non-singular terminal sliding surface is constructed, and the sliding surface includes a relative dual quaternion error term and an auxiliary sliding surface term; In the fourth step (S4), the spacecraft system error kinematic equation is derived based on the sliding surface, and the control torque calculation formula is derived in combination with the actuator output torque expression. According to the control torque formula, a control instruction is generated to drive the tracking spacecraft to achieve integrated fault-tolerant control of attitude and orbit.

2. The method according to claim 1, characterized in that Preferably, in the first step (S1), a geocentric inertial coordinate system and a spacecraft body coordinate system are established to describe the spacecraft's on-orbit spatial position and attitude direction, respectively; the rigid body and flexible components of the flexible spacecraft are modeled based on the finite element method, and the single-satellite spacecraft dynamics formula is obtained as follows: in is the dual force acting on the tracking spacecraft B, where F B is the force, T B is the acting torque, is the dual mass, where M B and J B are the mass and moment of inertia of tracking spacecraft B, is the dual velocity spinor, where and are the angular velocity and linear velocity of the tracking spacecraft B in its body coordinate system, is the dual rotation matrix, where B tran and B rot are the translation coupling matrix and rotation coupling matrix respectively, η is the modal coordinate; The kinematic formula for a single star is: in is the dual quaternion for tracking spacecraft B.

3. The method according to claim 1, characterized in that In the second step (S2), the relative kinematic formula between the tracking spacecraft B and the target spacecraft A is established is the relative dual quaternion, let the relative angular velocity and relative linear velocity between the tracking spacecraft B and the target spacecraft A in the coordinate system B be and Then the relative dual velocity spinor Specifically: in is the representation of the dual velocity spinor of target spacecraft A in the coordinate system of tracking spacecraft B, and The angular velocity and linear velocity of the target spacecraft A in the coordinate system B are respectively. The relationship between the modal coordinates and the dual velocity spinor error can be expressed as: Where ζ is the modal damping coefficient and Λ is the modal stiffness coefficient.

4. The method according to claim 1, wherein In the third step (S3), the dual torque is output to the actuator To restrict: represents the theoretically required dual torque, Indicates a gain fault, Indicates a deviation fault, Indicates a stuck fault and can be specifically expressed as represents the maximum dual torque that the actuator can output under normal working conditions, then the dual torque acting on the tracking spacecraft B can be specifically expressed as is the dual gravity gradient force (changed to the previous one), where μ is the gravitational constant of the central celestial body, r B To track the position vector between spacecraft B and the center of the celestial body, To counteract the interference force, in order to increase the robustness and control efficiency of the spacecraft system, the relative dual quaternion is rewritten as And design the non-singular terminal sliding surface: in is the gain parameter, is the auxiliary sliding surface and l1=(2-λ)δ λ-1 , l2=(λ-1)δ λ-2 , 0<λ<1.

5. The method according to claim 4, characterized in that In the fourth step (S4), the sliding mode plane is differentiated with respect to time to obtain the spacecraft system error kinematic equation: in Substituting the dual torque expression into the above formula, the specific expression of the control torque is obtained after calculation: Among them, 0<γ1<1<γ2, is the control parameter.

6. The method according to claim 5, characterized in that The maximum convergence time T of the system state variables m satisfy 7. The method according to claim 1, characterized in that Flexible spacecraft include satellites or space capsules.

8. A system for implementing the method according to any one of claims 1 to 7, characterized in that: It includes: The finite element module establishes the geocentric inertial coordinate system and the spacecraft body coordinate system, uses the finite element theorem to model the rigid body and flexible solar panels of the flexible spacecraft, and obtains the dynamic and kinematic formulas of the single-satellite spacecraft; The relative kinematics module establishes the relative kinematic equations between the tracking spacecraft and the target spacecraft, defines the relative dual quaternion and the relative dual velocity spinor, and establishes the dynamic relationship between the modal coordinates and the dual velocity spinor error; a modeling module that mathematically models actuator fault types, including gain fault, bias fault, and stuck fault, and considers the effects of gravity gradient torque and external disturbance torque; constructs a non-singular terminal sliding surface, which includes a relative dual quaternion error term and an auxiliary sliding surface term; The control module derives the spacecraft system error kinematic equation based on the sliding surface, and derives the control torque calculation formula based on the actuator output torque expression. The control command is generated according to the control torque formula to drive the tracking spacecraft to achieve integrated fault-tolerant control of attitude and orbit.

9. A computer storage medium, characterized in that The storage medium includes computer instructions, which, when executed on a computer, enable the computer to perform the method according to any one of claims 1 to 7.

10. An electronic device, characterized in that: The electronic device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

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