An adaptive event-triggered spacecraft attitude and orbit coupling control method and system

Abstract

The application belongs to the technical field of spacecraft attitude and orbit control, and relates to a spacecraft attitude and orbit coupling control method and system based on adaptive event triggering, which comprises the following steps: constructing a line-of-sight coordinate system based on modified Rodrigues parameters and the relative position of a controlled spacecraft and a target spacecraft, and a six-degree-of-freedom spacecraft tracking relative attitude and orbit coupling dynamic model satisfying field-of-view pointing constraints; designing a preset performance function capable of controlling convergence speed; performing differential homeomorphism mapping of attitude and orbit state constraints in an unconstrained space through an error conversion mechanism; designing a virtual control law by using a backstepping method and introducing a linear operator to linearize unknown parameters; designing an adaptive controller based on the virtual control law and the linearization term; designing an event triggering mechanism for the adaptive controller to obtain an event-triggered controller, so as to control the controlled spacecraft.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude and orbit control technology, and in particular to an adaptive event-triggered spacecraft attitude and orbit coupling control method and system. Background Technology

[0002] Spacecraft, as the core carrier of space exploration, are an important symbol of technological strength and strategic competitiveness, playing an irreplaceable role in many fields. With the increasing complexity of on-orbit servicing, rendezvous and docking, and formation flying missions, spacecraft control technology has undergone a profound transformation from discrete control to attitude-orbit coupled integrated control. Early discrete control strategies treated orbit (translation) and attitude (rotation) as independent subsystems, neglecting the strong dynamic coupling between the two in close-range operations (e.g., the torque generated by control force eccentricity, and the line-of-sight angular velocity change caused by attitude changes), leading to degraded system performance and even instability. To address this issue, integrated control methods based on a unified six-degree-of-freedom dynamic model have emerged. Adaptive control, sliding mode control, and other nonlinear techniques are widely used to solve model parameter uncertainties and external disturbances, significantly improving control accuracy.

[0003] The existing field of integrated attitude and orbit control for spacecraft has achieved a paradigm shift from discrete control to coupled control. However, significant limitations remain in state-constrained control and communication resource optimization. Patent CN121541492A proposes a method for generating a full-drive convergence time controller. This method first establishes a coupled dynamic model of the spacecraft's attitude and orbit to eliminate the separation between attitude and orbit subsystems, providing a model foundation for integrated attitude and orbit control. Then, through sliding mode control, the coupled dynamic model is equivalently converted into a standard structure that allows direct design of sliding surfaces and low-order error dynamics, solving the complexity surge problem caused by repeated differentiation of virtual control laws in traditional backstepping design. Finally, by designing a predetermined time control method, the convergence time is pre-set, ensuring that the system convergence time can be set and guaranteeing system stability. However, this method sacrifices computational and communication efficiency by introducing a large number of nonlinear operations and high-frequency full-state interactions, leading to increased computational and communication resource consumption. The excessive resource consumption makes it unsuitable for mission scenarios with limited spacecraft computing and communication resources. Patent CN116812170A proposes a spacecraft cluster attitude and orbit cooperative control method under communication resource constraints. This method first establishes a coupled attitude and orbit model of the following spacecraft, including thruster installation errors. It then uses algebraic graph theory to describe the variable dynamic communication topology within the cluster, introduces an event triggering mechanism to conserve communication resources, and designs an adaptive law to handle parameter uncertainties. This method can achieve spacecraft attitude control while conserving communication resources and solving the problem of resource waste. However, this method ignores the spacecraft's attitude constraints, and the control process is prone to risks of excessive overshoot and uncontrollable convergence speed, significantly affecting the spacecraft's transient performance. It cannot be applied to mission scenarios sensitive to overshoot and convergence speed. Furthermore, the threshold coefficient of its event triggering mechanism is a fixed value, failing to achieve dynamic adaptation and precise, efficient on-demand triggering.

[0004] In summary, existing integrated attitude and orbit control schemes for spacecraft cannot balance control accuracy and communication overhead. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the existing spacecraft attitude and orbit integrated control scheme cannot balance the control accuracy and communication overhead of the spacecraft.

[0006] To address the aforementioned technical problems, this invention provides an adaptive event-triggered spacecraft attitude and orbit coupling control method, comprising: Based on the modified Rodriguez parameters and the line-of-sight coordinate system of the relative positions of the controlled spacecraft and the target spacecraft, a coupled dynamic model for six-degree-of-freedom spacecraft tracking relative attitude and orbit is constructed to satisfy the field-of-sight pointing constraint. Based on the error convergence rate, initial state error upper limit, and steady state error upper limit of the controlled spacecraft, a preset performance function is constructed to control the convergence rate of the controlled spacecraft. The attitude and orbit state error constraints of the controlled spacecraft are constructed based on a preset performance function. The attitude and orbit state error constraints are then mapped to an unconstrained space using an error transformation mechanism to obtain the transformed attitude and orbit state errors. The virtual control law of the controlled spacecraft is designed based on the transformed attitude and orbit state errors using the backstepping method. The mass and moment of inertia of the spacecraft are defined as the parameter vector to be estimated, and linear operators are used to convert the nonlinear terms related to the parameter vector to be estimated in the coupled dynamics model into linear terms, thereby updating the coupled dynamics model; A first Lyapunov function is constructed, which includes the transformed attitude and orbit state error, the virtual control error variable, and the estimation error of the parameter vector to be estimated. The error dynamic stability equation is obtained by taking the derivative of the first Lyapunov function. The updated coupled dynamic model is substituted into the error dynamic stability equation, thereby designing an adaptive controller. An event-triggered mechanism is designed for the adaptive controller to obtain the event-triggered controller, which is then used to control the controlled spacecraft.

[0007] Preferably, based on the corrected Rodriguez parameters and the line-of-sight coordinate system of the relative positions of the controlled spacecraft and the target spacecraft, a six-degree-of-freedom coupled dynamic model for spacecraft tracking relative attitude and orbit that satisfies the field-of-sight pointing constraint is constructed, including: Using modified Rodriguez parameters, relative attitude dynamics equations are constructed based on the attitude, angular velocity, moment of inertia, control torque, and disturbance torque of the controlled spacecraft. Based on the distance between the controlled spacecraft and the target spacecraft, the gravitational difference, the line-of-sight tilt angle and the line-of-sight deflection angle, the position and velocity of the controlled spacecraft, the mass of the spacecraft, the control force and the interference force, the relative orbital dynamic equations in the line-of-sight coordinates of the spacecraft are constructed. Based on the relative attitude dynamics equations and the relative orbit dynamics equations, a coupled dynamics model for a six-degree-of-freedom spacecraft tracking relative attitude and orbit is constructed.

[0008] Preferably, the relative attitude dynamics equations are expressed as: , , in, , Indicates the attitude of the controlled spacecraft. Represents the identity matrix. Indicates transpose; express The derivative; This represents the cross product operation; Indicates the angular velocity of the controlled spacecraft; express The derivative; This represents the moment of inertia of a controlled spacecraft. Indicates control torque; Indicates the disturbance torque; The relative orbital dynamics equations are expressed as follows: , , in, , , Indicates the distance between the controlled spacecraft and the target spacecraft. and These represent the tilt angle and deflection angle of the line of sight, respectively. Indicates the position of the controlled spacecraft. Indicates the speed of the controlled spacecraft. , , This represents the gravitational difference between the controlled spacecraft and the target spacecraft in the x, y, and z directions; express The derivative; express The derivative; express The derivative; express The derivative; express The derivative; Indicates the mass of the spacecraft; Indicates control; Indicates interference force; The coupled dynamics model is expressed as: , in, All are attitude and orbital state variables; , , Represents a zero matrix; express The derivative; express The derivative of .

[0009] Preferably, a preset performance function is used. Represented as: , in, This indicates the upper limit of the initial state error of the controlled spacecraft; This represents the upper limit of the steady-state error of a controlled spacecraft; This indicates the error convergence rate of the controlled spacecraft; Indicates time; , , All are normal numbers.

[0010] Preferably, the attitude and orbital state error constraint of the controlled spacecraft is expressed as: , in, ; This represents the attitude and orbital state error of the controlled spacecraft at time t; Indicates the preset performance function; express The i-th element in; express The i-th element in; This represents the initial attitude and orbital state error of the controlled spacecraft. The i-th element in; The differential homeomorphism of an unconstrained space is represented as: , , , , in, Represents a smooth, increasing, and reversible error transformation function; express The derivative; express The derivative; Indicates the error in the converted attitude and orbit state. The i-th element in; express The derivative; Indicates the instantaneous gain of the error transformation; This indicates the preset performance error transformation compensation item.

[0011] Preferably, the virtual control law of the controlled spacecraft is designed based on the transformed attitude and orbit state error using the backstepping method, including: Based on the difference between the attitude and orbital state variables of the controlled spacecraft and the virtual control law to be designed, a virtual control error variable is constructed. ;in, Represents a virtual control law; Construct a second Lyapunov function based on the transformed attitude state error. ; Substituting the virtual control error variable into the second Lyapunov function and differentiating the second Lyapunov function yields the dynamic equation of the virtual control error of the controlled spacecraft. ;in, , This represents the instantaneous gain matrix of the error transformation. This represents the instantaneous gain of the error transformation with respect to the position parameters. This represents the instantaneous gain of the error transformation with respect to the attitude parameters. , This represents the column vector of the preset performance error transformation compensation term. This represents the preset performance error transformation compensation term for the controlled spacecraft regarding its position parameters. This represents the preset performance error transformation compensation term for the controlled spacecraft regarding its attitude parameters; With the negative definiteness of the virtual control error dynamic equation as the objective, the virtual control law is obtained by solving it. ;in, , and and All of these are parameters to be designed. This represents a virtual control law relating to position parameters. This represents a virtual control law relating to attitude parameters.

[0012] Preferably, the updated coupled dynamics model is expressed as: , in, , , , The symbol represents a linear operator. ; Represents the vector of parameters to be estimated. , Represents the first inertia in the moment of inertia matrix. Line number The elements of the column.

[0013] Preferably, the first Lyapunov function Represented as: , in, , This represents the estimation error of the parameter vector to be estimated. This represents the estimated value of the parameter vector to be estimated; Indicates the parameters to be designed; Error dynamic stability equation Represented as: , Adaptive controller Represented as: , , in, and and All are parameters to be designed; Represents the projection operator; express The derivative of .

[0014] Preferably, the event triggering mechanism is as follows: , , , in, This represents the measurement error of the controlled spacecraft at time t; Indicates the dynamic threshold term. , , , , All are normal amounts. express The unknown upper bound; This indicates the input update time; ; Controllers representing continuous time forms, ; This indicates an event-triggered controller.

[0015] The present invention also provides an adaptive event-triggered spacecraft attitude-orbit coupling control system, comprising: The coupled dynamics model construction module is used to construct a six-degree-of-freedom coupled dynamics model for spacecraft tracking relative attitude and orbit that satisfies the field-of-view pointing constraint, based on the line-of-sight coordinate system of the corrected Rodrigues parameters and the relative positions of the controlled spacecraft and the target spacecraft. The preset performance function construction module is used to construct a preset performance function for controlling the convergence speed of the controlled spacecraft based on the error convergence speed, the upper limit of the initial state error, and the upper limit of the steady state error. The virtual control law design module is used to construct the attitude and orbit state error constraints of the controlled spacecraft based on the preset performance function, and to perform a differential homeomorphism mapping of the attitude and orbit state error constraints in an unconstrained space using an error transformation mechanism to obtain the transformed attitude and orbit state errors; and to design the virtual control law of the controlled spacecraft based on the transformed attitude and orbit state errors using the backstepping method. The coupled dynamics model update module is used to define the mass and moment of inertia of the spacecraft as a parameter vector to be estimated, and to use linear operators to convert the nonlinear terms related to the parameter vector to be estimated in the coupled dynamics model into linear terms, thereby updating the coupled dynamics model; The adaptive controller design module is used to construct a first Lyapunov function that includes the transformed attitude and orbit state error, virtual control error variables, and the estimation error of the parameter vector to be estimated. The derivative of the first Lyapunov function is used to obtain the error dynamic stability equation. The updated coupled dynamic model is substituted into the error dynamic stability equation to design the adaptive controller. The event-triggered controller design module is used to design event-triggered mechanisms for adaptive controllers, resulting in event-triggered controllers that are then used to control the managed spacecraft.

[0016] The adaptive event-triggered spacecraft attitude and orbit coupling control method provided in this application has the following advantages: First, a six-DOF spacecraft tracking relative attitude-orbit coupled dynamics model satisfying field-of-view pointing constraints was established by using spacecraft attitude dynamics equations based on modified Rodrigues parameters and relative orbital dynamics equations based on the line-of-sight coordinate system of the relative positions of the controlled and target spacecraft. This model fully considers the coupling effect between spacecraft attitude and orbit, solving the problem of neglecting the mutual coupling effect caused by separate controllers for attitude and orbit in traditional methods. This provides a model foundation for the design of attitude-orbit coupled controllers in spacecraft tracking mission scenarios. Second, by designing a preset performance function, the transient response performance and convergence speed of the spacecraft's attitude-orbit state were pre-controlled, solving the problems of overshoot and uncontrollable convergence speed in traditional unconstrained control methods. Third, by constructing an attitude-orbit error transformation mechanism, the constrained attitude error was mapped to the unconstrained space, transforming the original constrained control problem into an equivalent problem that ensures the boundedness of the transformation error, thus solving the problem of traditional attitude-orbit constrained control methods. This paper addresses the complexity of controller design caused by directly handling constraints in traditional time-triggered controllers. It addresses this by linearizing unknown parameters in the coupled dynamics model using linear operators and introducing projection operators to design an adaptive controller. This avoids control accuracy deviations caused by fuel consumption and mass distribution variations, even when the parameters of the controlled spacecraft (mass and moment of inertia) are uncertain, thus achieving adaptive control and enhancing the controller's robustness. Finally, it solves the problem of wasted spaceborne communication resources caused by traditional time-triggered controllers through an event-triggered controller and a precise adaptive event-triggered mechanism coupled with a preset performance function, achieving communication resource optimization and deep coupling between the event-triggered mechanism and performance constraints. The event-triggered controller designed in this application effectively solves the problem of simultaneously achieving attitude and orbit state constraints and optimized communication resource utilization in tracking scenarios with uncertain parameters, thereby meeting the requirements for high-precision and high-efficiency attitude and orbit coupling control in complex space environments. In addition, this application rigorously proves, based on Lyapunov function theory and Zeno-free phenomenon, that under conditions of parameter uncertainty and limited communication resources, the event-triggered mechanism controller designed in this application can eventually converge the attitude and orbit state error of the spacecraft to a preset region, while not triggering an unlimited number of communications in a finite time, thus meeting the requirements of rapid and high-precision attitude and orbit coupling control for complex missions such as deep space exploration and on-orbit servicing. Attached Figure Description

[0017] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 Flowchart of the adaptive event-triggered spacecraft attitude-orbit coupling control method provided in this application; Figure 2Convergence curves of spacecraft attitude and constraint boundaries under the control of the event-triggered controller provided in this application; Figure 3 The convergence curve of the first orbital parameters and constraint boundaries of the spacecraft under the control of the event-triggered controller provided in this application; Figure 4 Convergence curves of the spacecraft's second orbital parameters and constraint boundaries under the control of the event-triggered controller provided in this application; Figure 5 Convergence curves of the third orbital parameters and constraint boundaries of the spacecraft under the control of the event-triggered controller provided in this application; Figure 6 Curves showing the changes in spacecraft attitude and target attitude over time under the control of the event-triggered controller provided in this application; Figure 7 The curve of the control force of the event-triggered controller provided in this application as a function of time; Figure 8 The curve showing the change of control torque over time for the event-triggered controller provided in this application; Figure 9 A schematic diagram showing the event triggering time and time interval of the event triggering controller provided in this application. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0019] Please see Figure 1 , Figure 1 The diagram shows the flowchart of the adaptive event-triggered spacecraft attitude and orbit coupling control method provided in this application. The method specifically includes steps S10 to S60: S10: Based on the modified Rodriguez parameters and the line-of-sight coordinate system of the relative positions of the controlled spacecraft and the target spacecraft, a coupled dynamic model for six-degree-of-freedom spacecraft tracking relative attitude and orbit is constructed to satisfy the field-of-sight pointing constraint.

[0020] Furthermore, S10 includes S100~S102: S100: Using modified Rodriguez parameters, relative attitude dynamics equations are constructed based on the attitude, angular velocity, moment of inertia, control torque, and disturbance torque of the controlled spacecraft.

[0021] Specifically, the relative attitude dynamics equations are expressed as: , , in, , Indicates the attitude of the controlled spacecraft. Represents the identity matrix. Indicates transpose; express The derivative; This represents the cross product operation; Indicates the angular velocity of the controlled spacecraft; express The derivative; This represents the moment of inertia of a controlled spacecraft. Indicates control torque; This indicates the disturbance torque.

[0022] S101: Based on the distance between the controlled spacecraft and the target spacecraft, the gravitational difference, the line-of-sight tilt angle and the line-of-sight deflection angle, the position and velocity of the controlled spacecraft, the mass of the spacecraft, the control force and the interference force, construct the relative orbital dynamic equations in the line-of-sight coordinates of the spacecraft.

[0023] Specifically, the relative orbital dynamics equations are expressed as: , , in, , , Indicates the distance between the controlled spacecraft and the target spacecraft. and These represent the tilt angle and deflection angle of the line of sight, respectively. Indicates the position of the controlled spacecraft. Indicates the speed of the controlled spacecraft. , , This represents the gravitational difference between the controlled spacecraft and the target spacecraft in the x, y, and z directions; express The derivative; express The derivative; express The derivative; express The derivative; express The derivative; Indicates the mass of the spacecraft; Indicates control; It indicates interference force.

[0024] S102: Based on the relative attitude dynamics equation and the relative orbit dynamics equation, a coupled dynamics model for a six-degree-of-freedom spacecraft tracking relative attitude and orbit is constructed.

[0025] Specifically, the coupled dynamics model is expressed as: , in, All are attitude and orbital state variables; , , Represents a zero matrix; express The derivative; express The derivative of .

[0026] For example, , , , , , , , , , Initial position parameters of the controlled spacecraft The initial velocity of the controlled spacecraft The initial attitude of the controlled spacecraft The initial angular velocity of the controlled spacecraft Target position parameters of the controlled spacecraft The target attitude of the controlled spacecraft The above data describes the following scenario: the target spacecraft is 40 meters away from the controlled spacecraft and the visual sensor of the controlled spacecraft is not aligned with the target spacecraft, while the target spacecraft is in a fixed attitude; the control target is that the controlled spacecraft follows to a distance of 20 meters and the visual sensor is facing the target spacecraft (for easy observation), while its own attitude undergoes small maneuvers.

[0027] S20: Based on the error convergence rate, initial state error upper limit, and steady-state error upper limit of the controlled spacecraft, construct a preset performance function to control the convergence rate of the controlled spacecraft.

[0028] Specifically, preset performance functions Represented as: , in, This indicates the upper limit of the initial state error of the controlled spacecraft; This represents the upper limit of the steady-state error of a controlled spacecraft; This indicates the error convergence rate of the controlled spacecraft; Indicates time; , , All are normal numbers.

[0029] It should be noted that, , , All are pre-defined positive integers. For example, , ; , ,in, This represents the upper limit of the initial state error regarding the position parameters of the controlled spacecraft. This represents the upper limit of the steady-state error regarding the position parameters of the controlled spacecraft. This represents the upper limit of the initial state error regarding the attitude parameters of the controlled spacecraft. This represents the upper limit of the steady-state error of the attitude parameters of the controlled spacecraft. The value was selected as 0.04.

[0030] S30: Construct attitude and orbit state error constraints for the controlled spacecraft based on a preset performance function, and use an error transformation mechanism to perform a differential homeomorphic mapping of the attitude and orbit state error constraints in an unconstrained space to obtain the transformed attitude and orbit state errors; use the backstepping method to design a virtual control law for the controlled spacecraft based on the transformed attitude and orbit state errors.

[0031] Specifically, to ensure that the attitude and orbital state error meets the preset performance, the attitude and orbital state error constraint of the controlled spacecraft is expressed as follows: , in, ; This represents the attitude and orbital state error of the controlled spacecraft at time t; Indicates the preset performance function; express The i-th element in; express The i-th element in; This represents the initial attitude and orbital state error of the controlled spacecraft. The i-th element in the array. For example, One can be chosen.

[0032] Furthermore, the differential homeomorphism of an unconstrained space is expressed as: , , , , in, Represents a smooth, increasing, and reversible error transformation function; express The derivative; express The derivative; Indicates the error in the converted attitude and orbit state. The i-th element in; express The derivative; Indicates the instantaneous gain of the error transformation; This represents a preset performance error transformation compensation term. In a specific example of this application, .

[0033] For example, design an error transformation function. ,but , ,in, .

[0034] Furthermore, the virtual control law for the controlled spacecraft is designed based on the transformed attitude and orbit state error using the backstepping method, including steps 1-1 to 1-4: Step 1-1: Based on the difference between the attitude and orbital state variables of the controlled spacecraft and the virtual control law to be designed, construct the virtual control error variable. ;in, This represents a virtual control law.

[0035] Step 1-2: Construct the second Lyapunov function based on the transformed attitude and orbit state error. .

[0036] Steps 1-3: Substitute the virtual control error variables into the second Lyapunov function and differentiate the second Lyapunov function to obtain the dynamic equation of the virtual control error of the controlled spacecraft. ;in, , This represents the instantaneous gain matrix of the error transformation. This represents the instantaneous gain of the error transformation with respect to the position parameters. This represents the instantaneous gain of the error transformation with respect to the attitude parameters. , This represents the column vector of the preset performance error transformation compensation term. This represents the preset performance error transformation compensation term for the controlled spacecraft regarding its position parameters. This represents the preset performance error transformation compensation term for the controlled spacecraft regarding its attitude parameters.

[0037] Steps 1-4: Using the negative definiteness of the virtual control error dynamic equation as the objective, solve for the virtual control law. ;in, , and and All of these are parameters to be designed. This represents a virtual control law relating to position parameters. This represents a virtual control law relating to the attitude parameters. In one specific embodiment, Designed to be 0.8, It was designed to be 0.6.

[0038] Furthermore, substituting the virtual control law into the dynamic equation of the virtual control error yields the following result. ,at this time For negative definite terms, These are the cross-coupling terms to be processed.

[0039] S40: Define the spacecraft’s mass and moment of inertia as a parameter vector to be estimated, and use linear operators to convert the nonlinear terms related to the parameter vector to be estimated in the coupled dynamics model into linear terms, thereby updating the coupled dynamics model.

[0040] Specifically, considering the influence of factors such as fuel consumption and measurement errors during actual use, the mass and moment of inertia of the spacecraft are uncertain. Therefore, in the design of the controller, it is necessary to construct an adaptive control law to estimate the mass and moment of inertia parameters of the spacecraft. Thus, the mass and moment of inertia are defined as the parameter vector to be estimated. , , Represents the first inertia in the moment of inertia matrix. Line number The elements of the column, while introducing linear operators. The nonlinearity of the parameter vector to be estimated in the coupled dynamics model is transformed into a linear term: , , , , , , , Furthermore, the updated coupled dynamics model is expressed as: .

[0041] S50: Construct a first Lyapunov function that includes the transformed attitude and orbit state error, the virtual control error variable, and the estimation error of the parameter vector to be estimated. Take the derivative of the first Lyapunov function to obtain the error dynamic stability equation. Substitute the updated coupled dynamic model into the error dynamic stability equation to design an adaptive controller.

[0042] Specifically, the first Lyapunov function Represented as: , in, , This represents the estimation error of the parameter vector to be estimated. This represents the estimated value of the parameter vector to be estimated; This represents the parameter to be designed, which is designed as diag{0.01, 0.05, 0.05, 0.05, 0.01, 0.01, 0.01} in one example.

[0043] Error dynamic stability equation Represented as: .

[0044] Adaptive controller Represented as: , , in, and and All are parameters to be designed; Represents the projection operator; express The derivative of . In one specific embodiment, Designed as 3.2, It was designed to be 1.2.

[0045] S60: Design an event-triggered mechanism for the adaptive controller to obtain an event-triggered controller, and use the event-triggered controller to control the controlled spacecraft.

[0046] Specifically, in order to conserve computing and communication resources, the event triggering mechanism designed in this application is as follows: , , , in, This represents the measurement error of the controlled spacecraft at time t; Indicates the dynamic threshold term. , , , , All are normal amounts. express The unknown upper bound; This indicates the input update time; ; Controllers representing continuous time forms, ; This indicates an event-triggered controller.

[0047] Specifically, a time-varying term is introduced into the event triggering mechanism. Time-varying terms This indicates that the event triggering mechanism is deeply coupled with the preset performance function, and that the selected constant triggering threshold coefficient... Subsequently, considering the control of initial errors and preset performance function values Larger Item and The item is relatively small and can be adjusted. Adjusting the time-varying term in this stage This allows for the adjustment of the dynamic threshold; in the later stages of control (approaching and reaching convergence), the error... Through positive parameters prevent The terms diverge; at the same time, they can be adjusted. , To set the error and performance function value The degree of influence within the threshold is used to achieve the adaptive nature of the event triggering mechanism.

[0048] Furthermore, embodiments of this application also construct a Lyapunov function to prove that the attitude and orbital state error of the controlled spacecraft can converge to a preset region: Specifically, first, the same Lyapunov function as that used in continuous-time control is selected and its derivative is taken. It should be noted that the actual input to the event-triggered controller is not... , but Based on this, and taking into account the measurement error of the controlled spacecraft at time t, and assuming... get: , As can be seen from the event triggering mechanism, in any triggering interval All contain Furthermore, it can be proven that under the control of a preset performance function, the attitude and orbital state variables of the controlled spacecraft are... , and attitude and orbital state error and virtual control error variables Both are bounded; at the same time, according to From the expression, it can be seen that the event-triggered controller is a continuous function of these bounded states, therefore It is also bounded, let its upper bound be... ,Right now Then we can further obtain: , Simplifying the above equation, we get: , because There is a lower world and the Upper Realm Therefore There are also lower and upper bounds, denoted as _____. Therefore, the upper bound of the measurement error can be obtained as: , Using Young's inequality (in )right After scaling, we get: , at the same time Then we have: , in, Represents the smallest eigenvalue of a matrix, and selects parameters. Make ,Right now .definition ,in, It is a matrix The largest eigenvalue. Because of We can obtain: , According to the comparison principle, the Lyapunov function satisfy: , Therefore, the system is uniformly and eventually bounded, and all signals... , , , All are bounded and converge to a compact set near the origin, the size of which is equal to the set of all points in the origin. Proportional. By increasing the controller gain , Or reduce the trigger threshold parameter , , , This can narrow the region of convergence.

[0049] Furthermore, the embodiments of this application also demonstrate that the time-triggered controller does not exhibit the Zeno phenomenon (i.e., an infinite number of triggering events within a finite time period): Specifically, it proves that event triggering will not accumulate indefinitely within a finite time, i.e., the minimum triggering interval. During the trigger interval Within this range, the derivative of the measurement error is: , Due to attitude state variables , Bounded, and with a predefined performance function ,matrix , Both are smooth functions of the state. Combined with the expression for the event-triggered controller, it can be seen that the continuous controller... It is a smooth function of the system state. On a bounded closed set, the derivative of a smooth function is bounded, therefore we can assume... ,in It is a constant.

[0050] At the trigger time ,have ， Therefore in Inside: , The event triggering condition is ,because And it has been proven There is a lower bound (under the non-zero expectation trajectory). (It will not always be zero), therefore there exists a positive constant. , making For all Both are valid.

[0051] To satisfy the triggering condition, there must be... Then combine The expression can be obtained as follows: , Therefore, the time interval between any two consecutive triggers is at least 1. This proves that there is a positive lower bound for the minimum trigger interval, ruling out the possibility of the Zeno phenomenon (infinite triggers within a finite time).

[0052] The following MATLAB simulation verifies the effective constraint control of the spacecraft attitude-orbit coupling controller designed in this application on the attitude and orbit state under limited communication resources: Figure 2 The figure shows the convergence curves of the spacecraft attitude and constraint boundaries under the control of the event-triggered controller provided in this application. Figure 3 The figure shows the convergence curve of the first orbital parameters and constraint boundaries of the spacecraft under the control of the event-triggered controller provided in this application. Figure 4 The figure shows the convergence curve of the spacecraft's second orbital parameters and constraint boundaries under the control of the event-triggered controller provided in this application. Figure 5 The figure shows the convergence curve of the third orbital parameters and constraint boundaries of the spacecraft under the control of the event-triggered controller provided in this application. Figure 6The figure shows the time-varying curves of the spacecraft attitude and the target attitude under the control of the event-triggered controller provided in this application. Figure 7 The figure shows the curve of the control force of the event-triggered controller provided in this application changing over time. Figure 8 The figure shows the curve of the control torque of the event-triggered controller provided in this application as a function of time. Figure 9 The diagram shows the event triggering time and time interval of the event triggering controller provided in this application.

[0053] Figure 2 Demonstrates spacecraft attitude In performance function The curves showing the change over time under constraints indicate that the spacecraft attitude remains within the performance constraints and eventually converges to the preset stable region, demonstrating that the method provided in this application can achieve constrained control of the spacecraft attitude.

[0054] Figure 3 , Figure 4 and Figure 5 The spacecraft orbital parameters were displayed respectively. In performance function The curves showing the changes over time under constraints indicate that the spacecraft's attitude and orbital parameters remain within the performance constraints and eventually converge to the preset stable region, demonstrating that the method provided in this application can achieve constrained control of the spacecraft's orbit.

[0055] Figure 6 Demonstrates spacecraft attitude With target attitude The curve showing the change over time indicates that the spacecraft's attitude reaches the target attitude in about 40 seconds and then maneuvers according to the set target.

[0056] Figure 7 and Figure 8 The control force of the event-triggered controller is given respectively. and control torque The graph showing the change over time reveals the control force. and control torque It gradually decreases over a limited time and eventually tends to stabilize (small fluctuations exist because the attitude is maneuvering).

[0057] Figure 9The triggering time and time interval of the event-triggered controller are given. In the initial stage of control (within 25 seconds), the triggering frequency is relatively high, approximately 0.5-30Hz. Thanks to the event-triggered controller, the control signal does not blindly update at a constant frequency. During the convergence and attitude maneuvering phases (after 25 seconds), the triggering frequency is very low, approximately 0.18-0.6Hz, and eventually tends to around 0.37Hz (attitude maneuvering). This fully demonstrates that the event-triggered controller and the event triggering mechanism deeply coupled with preset performance can effectively reduce the communication burden and adaptively adjust the triggering frequency based on the current state variables.

[0058] Based on the adaptive event-triggered spacecraft attitude-orbit coupling control method provided in the above embodiments, this application also provides an adaptive event-triggered spacecraft attitude-orbit coupling control system, which includes: The coupled dynamics model construction module is used to construct a six-degree-of-freedom coupled dynamics model for spacecraft tracking relative attitude and orbit that satisfies the field-of-view pointing constraint, based on the line-of-sight coordinate system of the corrected Rodrigues parameters and the relative positions of the controlled spacecraft and the target spacecraft. The preset performance function construction module is used to construct a preset performance function for controlling the convergence speed of the controlled spacecraft based on the error convergence speed, the upper limit of the initial state error, and the upper limit of the steady state error. The virtual control law design module is used to construct the attitude and orbit state error constraints of the controlled spacecraft based on the preset performance function, and to perform a differential homeomorphism mapping of the attitude and orbit state error constraints in an unconstrained space using an error transformation mechanism to obtain the transformed attitude and orbit state errors; and to design the virtual control law of the controlled spacecraft based on the transformed attitude and orbit state errors using the backstepping method. The coupled dynamics model update module is used to define the mass and moment of inertia of the spacecraft as a parameter vector to be estimated, and to use linear operators to convert the nonlinear terms related to the parameter vector to be estimated in the coupled dynamics model into linear terms, thereby updating the coupled dynamics model; The adaptive controller design module is used to construct a first Lyapunov function that includes the transformed attitude and orbit state error, virtual control error variables, and the estimation error of the parameter vector to be estimated. The derivative of the first Lyapunov function is used to obtain the error dynamic stability equation. The updated coupled dynamic model is substituted into the error dynamic stability equation to design the adaptive controller. The event-triggered controller design module is used to design an event-triggered mechanism for the adaptive controller to obtain the event-triggered controller, and then use the event-triggered controller to control the controlled spacecraft.

[0059] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0060] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0061] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0062] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0063] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. An adaptive event-triggered spacecraft attitude and orbit coupling control method, characterized in that, include: Based on the corrected Rodriguez parameters and the line-of-sight coordinate system of the relative positions of the controlled spacecraft and the target spacecraft, a six-DOF coupled dynamics model for spacecraft tracking relative attitude and orbit is constructed to satisfy the field-of-sight pointing constraint. This model specifically includes: Using modified Rodriguez parameters, relative attitude dynamics equations are constructed based on the attitude, angular velocity, moment of inertia, control torque, and disturbance torque of the controlled spacecraft. Based on the distance between the controlled spacecraft and the target spacecraft, the gravitational difference, the line-of-sight tilt angle and the line-of-sight deflection angle, the position and velocity of the controlled spacecraft, the mass of the spacecraft, the control force and the interference force, the relative orbital dynamic equations in the line-of-sight coordinates of the spacecraft are constructed. Based on the relative attitude dynamics equations and the relative orbit dynamics equations, a coupled dynamics model for a six-degree-of-freedom spacecraft tracking relative attitude and orbit is constructed. Based on the error convergence rate, initial state error upper limit, and steady state error upper limit of the controlled spacecraft, a preset performance function is constructed to control the convergence rate of the controlled spacecraft. The attitude and orbital state error constraints of the controlled spacecraft are constructed based on a preset performance function. An error transformation mechanism is used to perform a differential homeomorphic mapping of the attitude and orbital state error constraints in an unconstrained space to obtain the transformed attitude and orbital state errors. A virtual control law for the controlled spacecraft is designed based on the transformed attitude and orbital state errors using the backstepping method. Specifically, this includes: Based on the difference between the attitude and orbital state variables of the controlled spacecraft and the virtual control law to be designed, a virtual control error variable is constructed. ;in, Represents a virtual control law; Represents attitude and orbit state variables; Construct a second Lyapunov function based on the transformed attitude state error. ; This indicates the attitude and orbital state error. Indicates transpose; Substituting the virtual control error variable into the second Lyapunov function and differentiating the second Lyapunov function yields the dynamic equation of the virtual control error of the controlled spacecraft. ;in, , This represents the instantaneous gain matrix of the error transformation. This represents the instantaneous gain of the error transformation with respect to the position parameters. This represents the instantaneous gain of the error transformation with respect to the attitude parameters. , This represents the column vector of the preset performance error transformation compensation term. This represents the preset performance error transformation compensation term for the controlled spacecraft regarding its position parameters. This represents the preset performance error transformation compensation term for the controlled spacecraft regarding its attitude parameters; With the negative definiteness of the virtual control error dynamic equation as the objective, the virtual control law is obtained by solving it. ;in, , and and All of these are parameters to be designed. This represents a virtual control law relating to position parameters. This represents a virtual control law relating to attitude parameters. , , Indicates the distance between the controlled spacecraft and the target spacecraft. Indicates the angle of view. , Indicates the attitude of the controlled spacecraft. Represents the identity matrix. This represents the cross product operation. Represents a zero matrix; The mass and moment of inertia of the spacecraft are defined as the parameter vector to be estimated, and linear operators are used to convert the nonlinear terms related to the parameter vector to be estimated in the coupled dynamics model into linear terms, thereby updating the coupled dynamics model; A first Lyapunov function is constructed, which includes the transformed attitude and orbit state error, the virtual control error variable, and the estimation error of the parameter vector to be estimated. The error dynamic stability equation is obtained by taking the derivative of the first Lyapunov function. The updated coupled dynamic model is substituted into the error dynamic stability equation, thereby designing an adaptive controller. An event-triggered mechanism is designed for the adaptive controller to obtain the event-triggered controller, which is then used to control the controlled spacecraft.

2. The adaptive event-triggered spacecraft attitude and orbit coupling control method according to claim 1, characterized in that, The relative attitude dynamics equations are expressed as follows: ， ， in, , Indicates the attitude of the controlled spacecraft. Represents the identity matrix. Indicates transpose; express The derivative; This represents the cross product operation; Indicates the angular velocity of the controlled spacecraft; express The derivative; This represents the moment of inertia of a controlled spacecraft. Indicates control torque; Indicates the disturbance torque; The relative orbital dynamics equations are expressed as: ， ， in, , , Indicates the distance between the controlled spacecraft and the target spacecraft. and These represent the tilt angle and deflection angle of the line of sight, respectively. Indicates the position of the controlled spacecraft. Indicates the speed of the controlled spacecraft. , , This represents the gravitational difference between the controlled spacecraft and the target spacecraft in the x, y, and z directions; express The derivative; express The derivative; express The derivative; express The derivative; express The derivative; Indicates the mass of the spacecraft; Indicates control; Indicates interference force; The coupled dynamics model is expressed as: ， in, All are attitude and orbital state variables; , , Represents a zero matrix; express The derivative; express The derivative of .

3. The adaptive event-triggered spacecraft attitude and orbit coupling control method according to claim 2, characterized in that, Preset performance functions Represented as: ， in, This indicates the upper limit of the initial state error of the controlled spacecraft; This represents the upper limit of the steady-state error of a controlled spacecraft; This indicates the error convergence rate of the controlled spacecraft; Indicates time; , , All are normal numbers.

4. The adaptive event-triggered spacecraft attitude and orbit coupling control method according to claim 3, characterized in that, The attitude and orbital state error constraints of a controlled spacecraft are expressed as follows: ， in, ; This represents the attitude and orbital state error of the controlled spacecraft at time t; Indicates the preset performance function; express The i-th element in; express The i-th element in; This represents the initial attitude and orbital state error of the controlled spacecraft. The i-th element in; The differential homeomorphism of an unconstrained space is represented as: ， ， ， ， in, Represents a smooth, increasing, and reversible error transformation function; express The derivative; express The derivative; Indicates the error in the converted attitude and orbit state. The i-th element in; express The derivative; Indicates the instantaneous gain of the error transformation; This indicates the preset performance error transformation compensation item.

5. The adaptive event-triggered spacecraft attitude and orbit coupling control method according to claim 4, characterized in that, The updated coupled dynamics model is expressed as follows: ， in, , , , Represents a linear operator. ; Represents the vector of parameters to be estimated. , Represents the first inertia in the moment of inertia matrix. Line number The elements of the column.

6. The adaptive event-triggered spacecraft attitude and orbit coupling control method according to claim 5, characterized in that, First Lyapunov function Represented as: ， in, , This represents the estimation error of the parameter vector to be estimated. This represents the estimated value of the vector of parameters to be estimated; Indicates the parameters to be designed; Error dynamic stability equation Represented as: ， Adaptive controller Represented as: ， ， in, and and All are parameters to be designed; Represents the projection operator; express The derivative of .

7. The adaptive event-triggered spacecraft attitude and orbit coupling control method according to claim 6, characterized in that, The event triggering mechanism is as follows: ， ， ， in, This represents the measurement error of the controlled spacecraft at time t; Indicates the dynamic threshold term. , , , , All are normal amounts. express The unknown upper bound; This indicates the input update time; ; Controllers representing continuous time forms, ; This indicates an event-triggered controller.

8. An adaptive event-triggered spacecraft attitude-orbit coupling control system, characterized in that, The system is used to implement the adaptive event-triggered spacecraft attitude and orbit coupling control method according to any one of claims 1 to 7, comprising: The coupled dynamics model construction module is used to construct a six-degree-of-freedom coupled dynamics model for spacecraft tracking relative attitude and orbit that satisfies the field-of-view pointing constraint, based on the line-of-sight coordinate system of the corrected Rodrigues parameters and the relative positions of the controlled spacecraft and the target spacecraft. The preset performance function construction module is used to construct a preset performance function for controlling the convergence speed of the controlled spacecraft based on the error convergence speed, the upper limit of the initial state error, and the upper limit of the steady state error. The virtual control law design module is used to construct the attitude and orbit state error constraints of the controlled spacecraft based on the preset performance function, and to perform a differential homeomorphism mapping of the attitude and orbit state error constraints in an unconstrained space using an error transformation mechanism to obtain the transformed attitude and orbit state errors; and to design the virtual control law of the controlled spacecraft based on the transformed attitude and orbit state errors using the backstepping method. The coupled dynamics model update module is used to define the mass and moment of inertia of the spacecraft as a parameter vector to be estimated, and to use linear operators to convert the nonlinear terms related to the parameter vector to be estimated in the coupled dynamics model into linear terms, thereby updating the coupled dynamics model; The adaptive controller design module is used to construct a first Lyapunov function that includes the transformed attitude and orbit state error, virtual control error variables, and the estimation error of the parameter vector to be estimated. The derivative of the first Lyapunov function is used to obtain the error dynamic stability equation. The updated coupled dynamic model is substituted into the error dynamic stability equation to design the adaptive controller. The event-triggered controller design module is used to design an event-triggered mechanism for the adaptive controller to obtain the event-triggered controller, and then use the event-triggered controller to control the controlled spacecraft.

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