Spacecraft formation pose and orbit coupling pre-time control method based on dual quaternion

Abstract

This invention belongs to the field of spacecraft control technology, specifically relating to a spacecraft formation attitude-orbit coupling predetermined time control method based on dual quaternions. First, a spacecraft relative motion attitude-orbit coupling control system is established. Then, a predetermined time attitude-orbit coupling controller for the spacecraft formation is designed. Finally, based on the coupled dynamics model, the attitude-orbit dual quaternion and dual velocity of each spacecraft are output. These are fed back to the input of the coupling control system, and the differences between these errors and the given desired attitude-orbit dual quaternion and desired velocity are calculated to obtain the dual quaternion error and dual velocity error. Based on these two error states, the predetermined time controller for the spacecraft formation attitude-orbit coupling is calculated, and the predetermined time result of the spacecraft formation attitude-orbit coupling is output. This invention considers model uncertainties and external disturbances by constructing an extended state observer and a predetermined time attitude-orbit coupling controller to achieve predetermined time stability of the spacecraft formation system.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft control technology, specifically relating to a spacecraft formation attitude and orbit coupling predetermined time control method based on dual quaternions. Background Technology

[0002] Spacecraft formations are becoming increasingly common in modern space science. The coordinated operation of multiple spacecraft enables high-precision observations and distributed measurements that are difficult for a single spacecraft to achieve. A prime example is the gravitational wave detection formation mission—a task accomplished through international cooperation involving three spacecraft carrying a space laser interferometer. By combining spacecraft formation observation data with ground-based observatories, variations in the solar polar magnetic field can be studied. Spacecraft formations can achieve microarcsecond-level precision in astronomical measurements, thus enabling exoplanet detection. To construct and maintain the formation configurations required for these space missions, research into advanced attitude and orbit control methods for multi-spacecraft formations is urgently needed.

[0003] Because many space science missions are carried out within specific time windows, the attitude adjustments and orbital maneuvers of spacecraft formations must be completed within specified time limits. This requirement for ensuring convergence time has driven significant progress in fixed-time and predetermined-time control theories. Predetermined-time control technology can pre-set the upper bound of the system's convergence time, thus becoming a relatively advanced control method that has been developed in the field of aerospace control in recent years. However, the design of predetermined-time controllers for the attitude-orbit coupled control of spacecraft formations faces the challenge of eliminating attitude-orbit coupling terms. In particular, for spacecraft formation attitude-orbit coupled control systems described by dual quaternions, how to design controllers to achieve predetermined-time stability of the closed-loop system remains unsolved.

[0004] To this end, the present invention provides a spacecraft formation attitude and orbit coupling predetermined time control method based on dual quaternions. Summary of the Invention

[0005] The purpose of this invention is to provide a spacecraft formation attitude-orbit coupling predetermined time control method based on dual quaternions. For a spacecraft formation attitude-orbit coupling control system described by dual quaternions, considering model uncertainties and external disturbances, a predetermined time stability of the spacecraft formation system is achieved by constructing an extended state observer and a predetermined time attitude-orbit coupling controller.

[0006] The specific technical solution adopted by this invention is as follows: A spacecraft formation attitude-orbit coupling predetermined time control method based on dual quaternions includes the following steps: Step 1: Establish a spacecraft relative motion attitude-orbit coupling control system. The spacecraft relative motion attitude-orbit coupling control system designed in this invention comprises three parts: a predetermined time extended state observer, a predetermined time attitude-orbit coupling controller, and a spacecraft attitude-orbit coupling dynamics model described by dual quaternions. First, the error signal is calculated using the desired attitude-orbit information and the actual attitude-orbit information of the spacecraft. Then, the extended state observer is used to estimate the total disturbance term composed of the uncertain parts of the spacecraft formation control system model and external disturbances. The estimated information is provided to the controller module for controller design. Subsequently, the predetermined time controller for spacecraft formation attitude-orbit coupling is driven, and the controller output signal is applied to the spacecraft formation attitude-orbit coupling dynamic system, outputting the attitude and orbit information of the spacecraft formation members. The block diagram of the control system is shown below. Figure 2 As shown; Step 2: Design a timed attitude-orbit coupling controller for spacecraft formation; Step 3: As Figure 2 As shown, the attitude-orbit coupled dynamics model of spacecraft described by dual quaternions outputs the attitude-orbit dual quaternions and dual velocities for each spacecraft, which are respectively and ;Will and The input of the feedback-coupled control system is coupled with the dual quaternions of the given desired attitude trajectory. and expected speed By subtracting, we obtain the dual quaternion error. and dual velocity error Based on the two errors, a mathematical model of the error system is established to obtain the error control model. According to the predetermined time of the spacecraft formation, the attitude and orbit coupling controller is used to achieve convergence of the dual quaternion error within the predetermined time. Uncertainties and external disturbances in a coupled control system are treated as total disturbances and estimated using an extended state observer.

[0007] Preferably, in step 1, the establishment of the spacecraft attitude-orbit coupled dynamics model based on dual quaternions is as follows: This invention focuses on the integrated attitude and position control of spacecraft formations; based on the dual quaternion framework established in existing literature, it employs the first... Dynamic model of a spacecraft in its body coordinate system: (1) (2) in , and They respectively represent the effects on the first Control torque and control force of a spacecraft Indicates interference. The attitude-position dual quaternion is defined as follows: (3) Here Indicates the first The attitude quaternions of a spacecraft, and ,in Indicates the virtual center point and the first The relative position vectors between the spacecraft; in the dynamic models (1) and (2), (4) in Represents angular velocity. Represents the velocity vector. It is the dual inertia matrix, denoted as ; in It is the first The mass of a spacecraft It is the rotational inertia matrix. and These are the definite and indefinite parts of the moment of inertia matrix, respectively.

[0008] Preferably, this invention studies the integrated attitude and position trajectory tracking control of a multi-spacecraft formation system; for this purpose, the dual quaternion error and dual velocity error are defined as follows: (5) (6) in It is the desired pose-position dual quaternion and yes The conjugate of the attitude error quaternion ,in It is the first Quaternion of the desired attitude of a spacecraft conjugate, and These are the error angular velocity and the error linear velocity, respectively. ,in ,and Represents the desired relative position vector, and ; in ; in This is the desired dual velocity; based on the above definition, the mathematical model of the multi-spacecraft formation attitude-orbit integrated error control system is expressed as: (7) (8) In practical engineering, when a spacecraft performs attitude maneuvers or consumes fuel, its moment of inertia changes, introducing model uncertainties. To address this, we consider the dual inertia... Represented as: ; in Indicates the nominally defined portion, while Representing the uncertain part, and being continuously differentiable with respect to time; then the error model (5)-(6) is transformed into the following form (9) (10) in .

[0009] Preferably, the control objective of this invention is: for space missions such as gravitational wave detection, to study the attitude-orbit integrated control problem during the formation of a uniformly distributed configuration of spacecraft formations; to this end, it is assumed that there is a virtual center point in the formation; each spacecraft should start from this virtual center point, be uniformly distributed on a circular position of a certain radius, and maintain the same attitude, such as... Figure 1 As shown; therefore, the core objective of this invention is to design a controller. Make the state of the error control model (9)-(10) converge to (11).

[0010] Preferably, step 2, designing the predetermined time attitude-orbit coupling controller for the spacecraft formation, specifically includes: Define the following error variables (12) in Defined by equation (11); to achieve stabilization of the error model (9)-(10), the following virtual error velocity is constructed. (13) in , , , It is a time constant, and (14) in yes The time derivative of is expressed as: (15) In addition, definition items The residual between the error rate and the virtual error rate, i.e. (16) Using the formula (13) of the virtual control term and the observer, the following preset time control law can be designed for the spacecraft formation attitude-orbit integrated error control model (9)-(10): (17) in For the output of the extended state observer, , , , , It is a constant. It is an adjustable parameter. Given by (16), and Then it is defined according to formula (13).

[0011] The technical effects achieved by this invention are as follows: The advantage of this invention lies in its design of a predetermined-time attitude-orbit coupling control algorithm for spacecraft formations modeled using dual quaternions. Considering model uncertainties and external disturbances present in practical engineering, the algorithm, based on an extended state observer, counteracts the coupling terms generated by attitude-orbit coupling through the design of virtual negative feedback terms, achieving, for the first time, predetermined-time stability of spacecraft formations described by dual quaternions. Simulation experiments demonstrate that the proposed control method can ensure predetermined-time stability of spacecraft formations described by dual quaternions and exhibits good robustness. Attached Figure Description

[0012] Figure 1 This is a schematic diagram of the equilateral triangle spacecraft formation of the present invention; Figure 2 This is a system block diagram of the spacecraft relative motion attitude and orbit coupling control system of the present invention; Figure 3 This is a schematic diagram of an isosceles triangle spacecraft formation in the simulation experiment of this invention; Figure 4 These are the attitude error and orbital error variation curves of the first spacecraft in the formation during the simulation experiment of this invention; Figure 5 These are the attitude error and orbital error variation curves of the second spacecraft in the formation during the simulation experiment of this invention; Figure 6 This is the attitude error and orbital error variation curve of the third spacecraft in the formation during the simulation experiment of this invention. Detailed Implementation

[0013] To make the objectives and advantages of this invention clearer, the invention will be specifically described below with reference to embodiments. It should be understood that the following text is merely used to describe one or more specific embodiments of the invention and does not strictly limit the scope of protection specifically claimed by the invention.

[0014] like Figure 1 As shown, the spacecraft formation attitude-orbit coupling predetermined time control method based on dual quaternions includes the following steps: Step 1: Establish a spacecraft relative motion attitude-orbit coupling control system. The spacecraft relative motion attitude-orbit coupling control system designed in this invention comprises three parts: a predetermined time extended state observer, a predetermined time attitude-orbit coupling controller, and a spacecraft attitude-orbit coupling dynamics model described by dual quaternions. First, the error signal is calculated using the desired attitude-orbit information and the actual attitude-orbit information of the spacecraft. Then, the extended state observer is used to estimate the total disturbance term composed of the uncertain parts of the spacecraft formation control system model and external disturbances. The estimated information is provided to the controller module for controller design. Subsequently, the predetermined time controller for spacecraft formation attitude-orbit coupling is driven, and the controller output signal is applied to the spacecraft formation attitude-orbit coupling dynamic system, outputting the attitude and orbit information of the spacecraft formation members. The block diagram of the control system is shown below. Figure 2 As shown.

[0015] Step 2: Design a timed attitude-orbit coupling controller for spacecraft formation; Step 3: The attitude-orbit coupled dynamics model of the spacecraft, described by dual quaternions, outputs the attitude-orbit dual quaternions and dual velocities for each spacecraft, which are respectively... and ;Will and The input of the feedback-coupled control system is coupled with the dual quaternions of the given desired attitude trajectory. and expected speed By subtracting, we obtain the dual quaternion error. and dual velocity error Based on the two errors, a mathematical model of the error system is established to obtain the error control model. According to the predetermined time of the spacecraft formation, the attitude and orbit coupling controller is used to achieve convergence of the dual quaternion error within the predetermined time. Uncertainties and external disturbances in a coupled control system are treated as total disturbances and estimated using an extended state observer.

[0016] Preferably, in step 1, the establishment of the spacecraft attitude-orbit coupled dynamics model based on dual quaternions is as follows: This invention focuses on the integrated attitude and position control of spacecraft formations; based on the dual quaternion framework established in existing literature, it employs the first... Dynamic model of a spacecraft in its body coordinate system: (1) (2) in , and They respectively represent the effects on the first Control torque and control force of a spacecraft Indicates interference. The attitude-position dual quaternion is defined as follows: (3) Here Indicates the first The attitude quaternions of a spacecraft, and ,in Indicates the virtual center point and the first The relative position vectors between the spacecraft; in the dynamic models (1) and (2), (4) in Represents angular velocity. Represents the velocity vector. It is the dual inertia matrix, denoted as ; in It is the first The mass of a spacecraft It is the rotational inertia matrix. and These are the definite and indefinite parts of the moment of inertia matrix, respectively.

[0017] Preferably, this invention studies the integrated attitude and position trajectory tracking control of a multi-spacecraft formation system; for this purpose, the dual quaternion error and dual velocity error are defined as follows: (5) (6) in It is the desired pose-position dual quaternion and yes The conjugate of the attitude error quaternion ,in It is the first Quaternion of the desired attitude of a spacecraft conjugate, and These are the error angular velocity and the error linear velocity, respectively. ,in ,and Represents the desired relative position vector, and ; in ; in This is the desired dual velocity; based on the above definition, the mathematical model of the multi-spacecraft formation attitude-orbit integrated error control system is expressed as: (7) (8) In practical engineering, when a spacecraft performs attitude maneuvers or consumes fuel, its moment of inertia changes, introducing model uncertainties. To address this, we consider the dual inertia... Represented as: ; in Indicates the nominally defined portion, while Representing the uncertain part, and being continuously differentiable with respect to time; then the error model (5)-(6) is transformed into the following form (9) (10) in .

[0018] Preferably, the control objective of this invention is: for space missions such as gravitational wave detection, to study the attitude-orbit integrated control problem during the formation of a uniformly distributed configuration of spacecraft formations; to this end, it is assumed that there is a virtual center point in the formation; each spacecraft should start from this virtual center point, be uniformly distributed on a circular position of a certain radius, and maintain the same attitude, such as... Figure 1 As shown; therefore, the core objective of this invention is to design a controller. Make the state of the error control model (9)-(10) converge to (11).

[0019] Preferably, in step 2, the design of the predetermined time attitude-orbit coupling controller for the spacecraft formation specifically includes: Define the following error variables (12) in Defined by equation (11); to achieve stabilization of the error model (9)-(10), the following virtual error velocity is constructed. (13) in , , , It is a time constant, and (14) in yes The time derivative of is expressed as: (15) In addition, definition items The residual between the error rate and the virtual error rate, i.e. (16) Using the formula (13) of the virtual control term and the observer, the following preset time control law can be designed for the spacecraft formation attitude-orbit integrated error control model (9)-(10): (17) in For the output of the extended state observer, , , , , It is a constant. It is an adjustable parameter. Given by (16), and Then it is defined according to formula (13).

[0020] During the simulation and verification process of this invention: The effectiveness of the proposed spacecraft formation attitude-orbit integrated predetermined time controller based on dual quaternions was verified through numerical simulation. The three spacecraft in the spacecraft formation of this invention all have the same mass. The inertial matrix components of each spacecraft are configured as follows: (18) Uncertain part of the moment of inertia matrix for ; External interference The real part and dual part are respectively taken as: ; and ; Suppose a spacecraft formation consists of three spacecraft, which are interconnected by an undirected graph topology, such as... Figure 3 As shown. The corresponding adjacency matrix for: ; When simulating the performance of the designed controller, the following initial conditions are used: ; as well as ; Desired attitude information is set as ; in The radius of the formation circle is The initial phase angle is .

[0021] This invention performed 50 Monte Carlo simulations to further verify the controller performance under different random disturbances. To ensure fair comparison, all control parameters were kept consistent throughout the simulations. The simulation results include the first three components of the attitude error quaternion and the three components of the trajectory error, which are plotted below. Figure 4 , Figure 5 as well as Figure 6 middle.

[0022] Simulation results clearly show that in 50 simulations, both attitude and trajectory errors converge within a predetermined time under randomly generated disturbances. These results confirm that the proposed control method exhibits strong robustness while maintaining its excellent performance.

[0023] The above description is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained in this invention are implemented according to conventional methods in the art unless otherwise specified or limited.

Claims

1. A spacecraft formation attitude and orbit coupling predetermined time control method based on dual quaternions, characterized in that: Includes the following steps: Step 1: Establish a spacecraft relative motion attitude-orbit coupling control system; The spacecraft relative motion attitude-orbit coupling control system includes a predetermined time-dilation state observer, a predetermined time attitude-orbit coupling controller, and a spacecraft attitude-orbit coupling dynamics model based on dual quaternions. Step 2: Design a timed attitude-orbit coupling controller for spacecraft formation; Step 3: The attitude-orbit coupled dynamics model of the spacecraft, described by dual quaternions, outputs the attitude-orbit dual quaternions and dual velocities for each spacecraft, which are respectively... and ;Will and The input of the feedback-coupled control system is coupled with the dual quaternions of the given desired attitude trajectory. and expected speed By subtracting, we obtain the dual quaternion error. and dual velocity error A mathematical model of the error system is established based on the two errors to obtain the error control model. The attitude and orbit coupling controller of the spacecraft formation is used to achieve convergence of the dual quaternion error within a predetermined time.

2. The spacecraft formation attitude and orbit coupling predetermined time control method based on dual quaternions according to claim 1, characterized in that: In step 1, the spacecraft attitude-orbit coupled dynamics model based on dual quaternions is established as follows: The established dual quaternion framework adopts the first... Dynamic model of a spacecraft in its body coordinate system: （1） （2） in , and They respectively represent the effects on the first Control torque and control force of a spacecraft Indicates interference. The attitude-position dual quaternion is defined as follows: （3） Here Indicates the first The attitude quaternions of a spacecraft, and ,in Indicates the virtual center point and the first The relative position vectors between the spacecraft; in the dynamic models (1) and (2), （4） in Represents angular velocity. Represents the velocity vector. It is the dual inertia matrix, denoted as ； in It is the first The mass of a spacecraft It is the rotational inertia matrix. and These are the definite and indefinite parts of the moment of inertia matrix, respectively.

3. The spacecraft formation attitude and orbit coupling predetermined time control method based on dual quaternions according to claim 1, characterized in that: The dual quaternion error and dual velocity error are defined as follows: （5） （6） in It is the desired pose-position dual quaternion and yes The conjugate of the attitude error quaternion ,in It is the first Quaternion of the expected attitude of a spacecraft conjugate, and These are the error angular velocity and the error linear velocity, respectively. ,in ,and Represents the desired relative position vector, and ； in ； in This is the desired dual velocity; based on the above definition, the mathematical model of the multi-spacecraft formation attitude-orbit integrated error control system is expressed as: （7） （8） When a spacecraft performs attitude maneuvers or consumes fuel, its moment of inertia changes, introducing uncertainty into the model. To address this, we consider the dual inertia... Represented as: ； in Indicates the nominally defined portion, while Representing the uncertain part, and being continuously differentiable with respect to time; then the error model (5)-(6) is transformed into the following form （9） （10） in 。 4. The spacecraft formation attitude and orbit coupling predetermined time control method based on dual quaternions according to claim 1, characterized in that: Assume there is a virtual center point in the formation; each spacecraft should start from this virtual center point, be evenly distributed on a circle of a certain radius, and maintain the same attitude; design a controller. Make the state of the error control model (9)-(10) converge to （11）。 5. The spacecraft formation attitude and orbit coupling predetermined time control method based on dual quaternions according to claim 1, characterized in that: Step 2, specifically designing the predetermined time attitude-orbit coupling controller for the spacecraft formation: Define the following error variables （12） in Defined by equation (11); to achieve stabilization of the error model (9)-(10), the following virtual error velocity is constructed. （13） in , , , It is a time constant, and （14） in yes The time derivative of is expressed as: （15） In addition, definition items The residual between the error rate and the virtual error rate, i.e. （16） Using the formula (13) of the virtual control term and the observer, the following preset time control law can be designed for the spacecraft formation attitude-orbit integrated error control model (9)-(10): （17） in For the output of the extended state observer, , , , , It is a constant. It is an adjustable parameter. Given by (16), and Then it is defined according to formula (13).

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