Methods, devices, equipment and media for coordinated control of multiple spacecraft formation flight

Abstract

This application relates to a method, apparatus, device, and medium for the coordinated control of multiple spacecraft formation flight. It includes: establishing a control pulse calculation model driven by control expectations; based on the control pulse calculation model, establishing a hierarchical control topology, and determining the overall position control strategy and formation configuration control strategy for the multiple spacecraft formation flight according to the hierarchical control topology; establishing a coordinated control topology, optimizing the formation configuration control strategy based on the coordinated control topology, and coordinating the flight of multiple spacecraft formations based on the overall position control strategy and the optimized formation configuration control strategy. Thus, by using the control pulse calculation model to perform hierarchical optimization design of the overall position and formation configuration of the formation, low-frequency coordinated control of spacecraft formations is achieved, solving the problems of complex variables and excessive computation time required for designing control strategies in existing technologies, and improving the detection accuracy of space gravitational waves.

Description

Technical Field

[0001] This application relates to the field of spacecraft trajectory optimization technology, and in particular to a method, device, equipment and medium for the coordinated control of multiple spacecraft flying in formation. Background Technology

[0002] With the advancement of space technology, the observation of astronomical phenomena has expanded from visible light to electromagnetic waves. Gravitational waves may become a new method of astronomical observation, thereby deepening our understanding of the universe. Due to the inconsistent orbital distribution of multiple spacecraft, the configuration of space-based gravitational wave detectors inevitably changes with their orbital positions. Analyzing the impact of configuration changes on the accuracy of gravitational wave detection and designing the detector's orbit from the perspectives of initial configuration deployment and configuration maintenance control is crucial to ensuring high-precision gravitational wave detection over long operating periods. Optimizing the design of gravitational wave detectors with different configurations helps deepen the understanding of gravitational wave detection theory, provides data support for selecting the optimal deployment scheme, achieves better detection performance, and promotes the development of gravitational wave astronomy.

[0003] Among related technologies, there are several methods for optimizing the initial configuration of detectors, including the formation plane tilt correction method, particle swarm optimization method, hybrid reaction tabu search method, and cascade optimization method.

[0004] However, existing methods require complex variables to be determined when designing control strategies, and the calculations are too time-consuming, so they urgently need to be improved. Summary of the Invention

[0005] This application provides a method, apparatus, equipment, and medium for the coordinated control of multiple spacecraft in formation flight, in order to solve the problems of complex variables and excessive calculation time required to design control strategies in existing technologies, and to improve the detection accuracy of space gravitational waves.

[0006] To achieve the above objectives, the first aspect of this application proposes a cooperative control method for multiple spacecraft flying in formation, comprising the following steps:

[0007] Establish a calculation model for control impulses driven by control expectations;

[0008] Based on the control pulse calculation model, a hierarchical control topology is established, and the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flights are determined according to the hierarchical control topology.

[0009] A cooperative control topology is established, and the control strategy of the formation configuration is optimized based on the cooperative control topology. The formation flight of the multiple spacecraft is then coordinated based on the overall position control strategy of the multiple spacecraft formation flight and the optimized formation configuration control strategy.

[0010] According to one embodiment of this application, after establishing the cooperative control topology and optimizing the control strategy of the formation configuration based on the cooperative control topology, the method further includes:

[0011] Based on the preset dynamic model extension algorithm, an optimization model for the maintenance control strategy of the formation configuration is established;

[0012] Based on the optimization model of the formation control strategy, the formation flight of the multiple spacecraft is coordinated.

[0013] According to one embodiment of this application, establishing the control pulse calculation model for the desired control drive includes:

[0014] Based on the circular restricted three-body model, the equations of formation motion are established;

[0015] Based on the desired position and the formation motion equation, the first control pulse is determined;

[0016] Based on the preset target-hitting strategy and the first control pulse, the second control pulse is determined.

[0017] According to one embodiment of this application, the overall position control strategy for the formation flight of the multiple spacecraft is as follows:

[0018]

[0019] st||δR c || max ≤δR c0

[0020] δθ c0 ≤δθ c ≤δθ c1

[0021] t ci ≤t c(i+1) (i = 1, 2, ..., N-1);

[0022] Wherein, δR c For virtual spacecraft SC c The change in distance to the Sun, δθ c For virtual spacecraft SC c The amount of change in the Earth's angle that lags behind; ΔV ci For loading in the virtual spacecraft SC c The i-th pulse on the signal, N represents the total number of pulses, w c1 w c2 w c3 For the corresponding weighting coefficient, t ci To load the i-th pulse into the virtual spacecraft SCc The moment above.

[0023] According to one embodiment of this application, the control strategy for the optimized formation configuration is as follows:

[0024]

[0025] st|△V djk ||≤ΔV dmax

[0026] t d(k+1) -t dk ≥Δt dmin (k = 1, 2, ..., M) i -1);

[0027] Among them, M i ΔV represents the number of bottom-level control pulses in the i-th segment. djk For the i-th segment loaded on the real spacecraft SC j The kth pulse on, δL arm δθ is the change in arm length. breath V is the change in respiratory angle. arm w is the rate of change of arm length. d1 w d2 w d3 w d4 For the corresponding weighting coefficient, t dk To load the k-th pulse from the i-th segment into the real spacecraft SC j The moment above.

[0028] The collaborative control method for multiple spacecraft formation flight proposed in this application establishes a control pulse calculation model driven by control expectations. Based on this model, a hierarchical control topology can be established, and the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flight can be determined according to the hierarchical control topology. By establishing a collaborative control topology, the control strategy for the formation configuration can be optimized, and the overall position control strategy and optimized formation configuration control strategy of multiple spacecraft formation flight can be used to collaboratively control the flight of multiple spacecraft formations. Therefore, by using the control pulse calculation model to perform hierarchical optimization design of the overall position and formation configuration of the formation, low-frequency collaborative control of spacecraft formations can be achieved. This solves the problems of complex variables and excessive computation time required for designing control strategies in existing technologies, and improves the detection accuracy of space gravitational waves.

[0029] To achieve the above objectives, a second aspect of this application provides a cooperative control device for multiple spacecraft flying in formation, comprising:

[0030] Establish a module to build a calculation model for the control pulses driven by the desired control.

[0031] The determination module is used to establish a hierarchical control topology based on the control pulse calculation model, and to determine the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flights according to the hierarchical control topology.

[0032] The control module is used to establish a cooperative control topology, optimize the control strategy of the formation configuration based on the cooperative control topology, and coordinate the formation flight of the multiple spacecraft based on the overall position control strategy of the multiple spacecraft formation flight and the optimized formation configuration control strategy.

[0033] According to one embodiment of this application, after establishing the cooperative control topology and optimizing the control strategy of the formation configuration based on the cooperative control topology, the control module is further configured to:

[0034] Based on the preset dynamic model extension algorithm, an optimization model for the maintenance control strategy of the formation configuration is established;

[0035] Based on the optimization model of the formation control strategy, the formation flight of the multiple spacecraft is coordinated.

[0036] According to one embodiment of this application, the establishment module is specifically used for:

[0037] Based on the circular restricted three-body model, the equations of formation motion are established;

[0038] Based on the desired position and the formation motion equation, the first control pulse is determined;

[0039] Based on the preset target-hitting strategy and the first control pulse, the second control pulse is determined.

[0040] According to one embodiment of this application, the overall position control strategy for the formation flight of the multiple spacecraft is as follows:

[0041]

[0042] st||δR c || max ≤δR c0

[0043] δθ c0 ≤δθ c ≤δθ c1

[0044] t ci ≤t c(i+1) (i = 1, 2, ..., N-1);

[0045] Wherein, δR c For virtual spacecraft SC c The change in distance to the Sun, δθ c For virtual spacecraft SC c The amount of change in the Earth's angle that lags behind; ΔV ci For loading in the virtual spacecraft SC c The i-th pulse on the signal, N represents the total number of pulses, w c1 w c2 w c3 For the corresponding weighting coefficient, t ci To load the i-th pulse into the virtual spacecraft SC c The moment above.

[0046] According to one embodiment of this application, the control strategy for the optimized formation configuration is as follows:

[0047]

[0048] st|ΔV djk ||≤ΔV dmax

[0049] t d(k+1) -t dk ≥Δt dmin (k = 1, 2, ..., M) i -1);

[0050] Among them, M i ΔV represents the number of bottom-level control pulses in the i-th segment. djk For the i-th segment loaded on the real spacecraft SC j The kth pulse on, δL arm δθ is the change in arm length. breath V is the change in respiratory angle. arm w is the rate of change of arm length. d1 w d2 w d3 w d4 For the corresponding weighting coefficient, t dk To load the k-th pulse from the i-th segment into the real spacecraft SC j The moment above.

[0051] According to the cooperative control device for multiple spacecraft formation flight proposed in the embodiments of this application, by establishing a control pulse calculation model driven by control expectations, a hierarchical control topology can be established based on the control pulse calculation model. Based on the hierarchical control topology, the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flight can be determined respectively. By establishing a cooperative control topology, the control strategy for the formation configuration can be optimized based on the cooperative control topology. Furthermore, based on the overall position control strategy and the optimized formation configuration control strategy, the multiple spacecraft formation flight can be cooperatively controlled. Therefore, by using the control pulse calculation model to perform hierarchical optimization design of the overall position and formation configuration of the formation, low-frequency cooperative control of spacecraft formations can be achieved. This solves the problems of complex variables and excessively long calculation time required for designing control strategies in existing technologies, and improves the detection accuracy of space gravitational waves.

[0052] To achieve the above objectives, a third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a cooperative control method for multiple spacecraft formation flight as described in the above embodiments.

[0053] To achieve the above objectives, a fourth aspect of this application provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement a cooperative control method for flight of multiple spacecraft in formation as described in the above embodiments.

[0054] To achieve the above objectives, a fifth aspect of this application provides a computer program product, including a computer program that, when executed by a processor, is used to implement a cooperative control method for the formation flight of multiple spacecraft as described in the above embodiments.

[0055] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through practice of the present application. Attached Figure Description

[0056] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0057] Figure 1 This is a flowchart illustrating a cooperative control method for multiple spacecraft flying in formation according to an embodiment of this application;

[0058] Figure 2 This is a block diagram of a cooperative control device for multiple spacecraft flying in formation according to an embodiment of this application;

[0059] Figure 3 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0060] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0061] The following description, with reference to the accompanying drawings, outlines a method, apparatus, equipment, and medium for coordinated control of multiple spacecraft formation flight according to embodiments of this application.

[0062] Figure 1 This is a flowchart of a method for coordinated control of multiple spacecraft formation flight according to one embodiment of this application.

[0063] Before introducing the cooperative control method for multiple spacecraft formation flight proposed in the embodiments of this application, let's briefly introduce the relevant technical background.

[0064] Among related technologies, the successful detection of gravitational waves generated by the merger of binary black holes by the ground-based detectors LIGO and Virgo in 2016 demonstrated the feasibility of direct gravitational wave detection technology. Ground-based detection is limited by gravity gradient perturbations and deployment scale, but offers a cleaner environment and allows for larger deployment scales. NASA first proposed the LISA project in 1996; JAXA proposed the DECIGO and B-DECIGO projects; and China proposed the Tianqin project in 2014 and the Taiji project in 2016. Space-based gravitational wave detection is mostly based on the principle of laser interferometry. To ensure the stable operation of the detectors, it is necessary to prevent external factors from interfering with the laser link.

[0065] Gravitational wave detectors can be broadly categorized into three configurations based on their satellite deployment locations: heliocentric, geocentric, and Lagrange point configurations. After reaching their operational orbits, they undergo drag-free control, causing the test masses to move in an approximately geodesic motion. As gravitational waves pass, the acceleration of the test masses changes, as does the distance between the laser links between the two test masses. Measuring these two physical quantities allows for the acquisition of gravitational wave signals. Current space-based gravitational wave detection missions primarily focus on the optical path variation of the laser. The arm length of the space gravitational wave detector determines the sensitive frequency band for detection. The rate of change in arm length is limited by the accuracy of time-delay interferometry (TDI) technology and the measurement bandwidth of the phase meter. Changes in the breathing angle affect the alignment accuracy of the onboard optical components. Therefore, the configuration stability of the detector is a prerequisite for ensuring the accuracy of gravitational wave scientific detection. Furthermore, to ensure communication between the detector and Earth, the distance between the satellite and the Earth is also limited. The spatiotemporal scale changes caused by gravitational waves are minute, and the noise generated by the orbital thrusters has a significant impact, making scientific detection impossible during orbital maneuvers. Therefore, in order to ensure the continuity of gravitational wave detection, it is necessary to ensure that the configuration control of the detector formation is kept at a low frequency, that is, the interval between two adjacent active control operations is long enough.

[0066] Space-based gravitational wave detectors need to maintain long-term formation stability in scientific detection mode to achieve high-precision measurements of gravitational waves. However, the noise from the orbital control engines is too high and can easily mask subtle gravitational wave signals, causing significant data processing difficulties. To fit the practical engineering context, it is necessary to study the evolution of detector formation configuration under a high-precision dynamic model and propose a low-frequency configuration-maintaining control strategy to improve the scientific detection accuracy of space-based gravitational waves. However, space-based gravitational wave detectors have long operating lifetimes, require high model accuracy, and their configuration indices depend on numerical integration, resulting in long computation times. Furthermore, the collaborative detection by multiple spacecraft necessitates a large number of variables to be determined when designing control strategies, leading to a vast solution space. The requirement for low-frequency control renders continuous thrust unsuitable and prevents the direct application of existing navigation and guidance strategies.

[0067] Based on the above problems, this application proposes a collaborative control method for multiple spacecraft formations. By using a control pulse calculation model, the overall position and formation configuration of the formation are optimized in a hierarchical manner to achieve low-frequency collaborative control of the spacecraft formation. This solves the problems of complex variables and long calculation time required to design control strategies in existing technologies, and improves the detection accuracy of space gravitational waves.

[0068] The following will describe in detail the cooperative control method for multiple spacecraft formation flight according to the embodiments of this application.

[0069] For example, such as Figure 1 As shown, the cooperative control method for multiple spacecraft formation flight includes the following steps:

[0070] In step S101, a calculation model for the control pulse driven by the desired control is established.

[0071] Here, control expectation refers to the state that the system is expected to reach or maintain in the embodiments of this application. A framework is constructed based on the expected system behavior or state to determine and generate the required control pulse signals, thereby driving the system to reach or approach these expectations.

[0072] To facilitate understanding, the following details how to establish a calculation model for the control pulse driven by the desired control.

[0073] As one possible approach, in some embodiments, a control pulse calculation model driven by control expectations is established, including: establishing formation motion equations based on a circular restricted three-body model; determining a first control pulse based on the desired position and the formation motion equations; and determining a second control pulse based on a preset target-firing strategy and the first control pulse.

[0074] Specifically, the formation motion equations under the circular restricted three-body model are first established, that is, the virtual equilibrium point rotation system is defined. A virtual spacecraft SC0 is placed at the center of the initial formation configuration, and active control acceleration is applied. To keep it stationary in the rotational system of the Sun's geological center, a local vertical and horizontal coordinate system is set with it as the center. The virtual equilibrium point rotational system is stationary relative to the rotational system of the Sun's geological center.

[0075] Let ρ = (x, y, z) T This indicates that the virtual spacecraft SC0 rotates at a virtual equilibrium point. In the position, a0 is the acceleration of the virtual spacecraft SC0 in the inertial frame, then The spacecraft dynamics equations in the system are:

[0076]

[0077] a0=(-1+μcosθ,-μsinθ,0) T (3)

[0078] Where V is the potential energy function, and equation (1) is dimensionless using the following units:

[0079]

[0080] Furthermore, a Taylor expansion near SC0 linearizes the spacecraft dynamics in the approximate circularly restricted three-body problem. The department contains:

[0081]

[0082] in, The parameters in equation (5) are the spacecraft state parameters, and are as follows:

[0083]

[0084] Let δx be the relative state of a follower spacecraft to its host spacecraft in a formation of multiple spacecraft. Then, the linearly approximated equations of motion for the formation are:

[0085]

[0086] The formation represented by equations (5) and (6) is a linear time-invariant system, and its state can be obtained from the state transition matrix Φ(t, t0):

[0087]

[0088] δx(t)=Φ(t,t0)δx(t0); (8)

[0089] in,

[0090] Secondly, based on the desired position and the formation motion equation, the first control pulse is determined. That is, the target aiming method can be used to determine the pulse at each control, and the velocity increment at the initial moment can be determined by the desired state at the end, thereby avoiding the error divergence between the desired trajectory and the target trajectory due to the randomness of the pulse direction.

[0091] make Let ρ be the state transition matrix and its submatrices. e Desired position of the main star, δρ e To determine the desired position of the star relative to the primary star, the first control pulse can be obtained from the linearized equations of formation motion under the circular restricted three-body model:

[0092]

[0093] Furthermore, based on the preset target acquisition strategy and the first control pulse, the second control pulse is determined. Gravitational wave detection missions have extremely stringent requirements for maintaining formation configuration and orbit determination accuracy, while linearization can introduce relative errors on the order of 10. -3 Therefore, preliminary design within a linearized circularly restricted three-body model is insufficient to characterize the control laws. Considering both computational efficiency and model accuracy, the circularly restricted three-body nonlinear model outperforms both the linearized and two-body models, while its computational efficiency far surpasses that of high-precision dynamical models that consider gravitational perturbations from all large celestial bodies. The first control pulse is used as an initial value guess, and the second control pulse under the nonlinear model is determined through a pre-defined targeting strategy. It is important to note that, unlike the two-body model where the reachable domain is the entire space, Φ... rvThe area near an integer multiple of half a cycle is singular, meaning there are unreachable positions in the linearized restricted three-body model. In the corresponding nonlinear three-body model, even if the point is reachable, the maneuvering impulse is large. Therefore, to avoid singularities and unreachable situations, it is necessary to limit the duration of the control segment.

[0094] The pre-defined target acquisition strategy is a numerical method used to solve boundary value problems. The basic idea is to "guess" an initial condition, and based on this guess, check whether the system response satisfies the boundary conditions through numerical integration or simulation. If not, the guess is adjusted, and the process is repeated until a suitable solution is found.

[0095] In step S102, a hierarchical control topology is established based on the control pulse calculation model, and the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flights are determined according to the hierarchical control topology.

[0096] Specifically, low-frequency, high-precision formation holding control can be defined as a mixed-integer optimization problem, where the number of pulses is an integer, and the pulse timing and pulse size are real numbers. Assuming that each spacecraft in the formation is controlled simultaneously to reduce the control frequency, a virtual spacecraft SC is also set up. c Guiding the overall movement of the detector formation. When conducting gravitational wave observations, it is necessary to ensure the configurational stability of the detectors rather than their absolute positions; therefore, it is feasible for the formation to deviate from its desired location. For gravitational wave detectors deployed in heliocentric orbits, due to the influence of Earth's gravity, their overall movement will gradually drift, and their long-term motion will be constrained. The horseshoe-shaped region in the system, and the overall shift of the formation, especially the change in the distance from the formation center to the sun, has an adverse effect on the stability of the configuration. Therefore, it is necessary to properly control the overall position of the formation.

[0097] Considering the relaxation control of the formation center position, the virtual spacecraft SC c Located at a virtual equilibrium point, it does not satisfy the equations of uncontrolled spaceflight dynamics and represents an ideal orbit; the virtual spacecraft SC c Control is achieved through low-frequency pulses, satisfying the dynamic equations and representing the desired orbit. The actual formation center is the geometric center of the three spacecraft, which does not satisfy space dynamics; its trajectory is the actual orbit. Since the formation scale is much smaller than the distance between the stars and the sun, the desired trajectory can be used to approximate the actual formation trajectory. SC0 ​​and SC c Forming a virtual "master-slave" structure formation, SC c The tracking of SC0 motion, taking into account both orbital deviation and fuel consumption, and top-level control, namely the problem of maintaining control over the overall absolute position of the formation, can be expressed as shown in equation (11).

[0098] In some embodiments, the overall position control strategy for multiple spacecraft formation flights is as follows:

[0099]

[0100] st||δR c || max ≤δR c0

[0101] δθ c0 ≤δθ c ≤δθ c1

[0102] t ci ≤t c(i+1) (i = 1, 2, ..., N-1);

[0103] Wherein, δR c For virtual spacecraft SC c The change in distance to the Sun, δθ c For virtual spacecraft SC c The amount of change in the Earth's angle that lags behind; ΔV ci For loading in the virtual spacecraft SC c The i-th pulse on the signal, N represents the total number of pulses, w c1 w c2 w c3 For the corresponding weighting coefficient, t ci To load the i-th pulse into the virtual spacecraft SC c The moment above.

[0104] Studies have found that δR c The hysteresis angle has a significant impact on configuration stability and is constrained by stability indices, while the hysteresis angle has a smaller impact on stability. Furthermore, the larger the hysteresis angle, the less the formation is affected by Earth's gravity, resulting in a more stable configuration. Therefore, δθ c Mainly affected by the lag distance D trail Constraints.

[0105] Therefore, by optimizing the top-level control strategy, a desired trajectory of the formation center can be obtained, which represents the desired position of the entire spacecraft formation that satisfies dynamic constraints.

[0106] In step S103, a cooperative control topology is established, the control strategy for the formation configuration is optimized based on the cooperative control topology, and the formation flight of multiple spacecraft is coordinated based on the overall position control strategy of multiple spacecraft formation flight and the optimized formation configuration control strategy.

[0107] Specifically, for the three real spacecraft SC in the probe d In terms of SC cAs a virtual master star, the bottom-level control, i.e., the formation control objective, is to maintain the formation configuration and follow the desired trajectory. Unlike the top-level control, which determines the number of pulse control times N through traversal, to maintain the stability of the gravitational wave detector's formation configuration, the bottom-level control time interval is shorter than the top-level control time interval. This results in a large number of control moments and pulses throughout the entire operating cycle, making overall optimization difficult. The moment when the formation is under overall control, i.e., SC... c The control moment can serve as a natural dividing point, dividing the entire working cycle into several segments, and optimizing each segment sequentially. This reduces the difficulty of solving the problem, and within each segment, the formation can be considered to drift freely without additional control. The optimization index of the underlying control can be directly defined as the weighted sum of the stability indices of the formation configuration. Considering fuel consumption, the optimization problem can be expressed as shown in equation (12):

[0108] In some embodiments, the control strategy for the optimized formation configuration is as follows:

[0109] min J d =w d1 |δL arm | max +w d2 |δθ breath | max +w d3 |V arm | max (12)

[0110]

[0111] st||ΔV djk ||≤ΔV dmax

[0112] t d(k+1) -t dk ≥Δt dmin (k = 1, 2, ..., M) i -1);

[0113] Among them, M i ΔV represents the number of bottom-level control pulses in the i-th segment. djk For the i-th segment loaded on the real spacecraft SC j The kth pulse on, δL arm δθ is the change in arm length. breath V is the change in respiratory angle. arm w is the rate of change of arm length. d1 w d2 w d3 w d4 For the corresponding weighting coefficient, t dkTo load the k-th pulse from the i-th segment into the real spacecraft SC j The moment above.

[0114] It is understandable that, in order to ensure that the gravitational wave detection is not disturbed for a period of time, the time interval between two pulses should be greater than a minimum value. Since the gravitational wave detector is equipped with a field-effect thruster in engineering, the embodiments of this application use pulses to approximate a continuous thrust that is much shorter than the orbital period, so amplitude limitations need to be added.

[0115] The underlying collaborative control integrates two consistency principles: "master-slave" and "virtual structure." The former ensures that the formation follows the top-level SC. c The trajectory ensures the formation maintains an equilateral triangle configuration. The cooperative control strategy proposed in this application relies on the current state to determine the control expectation. Fuel consumption can be allocated by setting the weights of each spacecraft. An example of three identical spacecraft is used for illustration:

[0116] 1) Through the real spacecraft SC d The current state determines the center position of the formation, the formation plane direction, the average orbital radius (distance from the star to the center), and the average orbital phase angle (phase angle of the star's movement in the formation plane);

[0117] 2) Calculate the angular momentum of the "virtual structure" with the formation center as the axis, and determine the rotational velocity of the triangular configuration in the plane;

[0118] 3) Shift the formation center to the SC at the control terminal time. c The location is determined, and the configuration is rotated by the corresponding angle within the formation plane;

[0119] 4) Calculate SC d The corresponding phase angle determines the control terminal time SC. d The nominal expected position;

[0120] 5) Make a small perturbation based on the nominal desired position, introduce the variable to be optimized, and the position after perturbation is the final desired position.

[0121] Therefore, based on the above work, the desired position of each spacecraft in the spacecraft formation for each pulse control can be obtained. By using a pre-set target-firing strategy, the two-point boundary value problem can be solved to obtain the required pulse, effectively reducing the solution space, lowering the problem's difficulty, and improving the solution efficiency. Furthermore, by determining the top-level SC... c Relaxation control and underlying layer through SC d The state determination of the formation configuration motion state makes reasonable use of the formation motion law, avoids inappropriate phase angle transfer and configuration plane rotation, thereby reducing fuel consumption and improving the working life of the detector.

[0122] Furthermore, in some embodiments, after establishing a cooperative control topology and optimizing the control strategy for the formation configuration based on the cooperative control topology, the method further includes: establishing an optimization model for the formation configuration maintenance control strategy based on a preset dynamic model extension algorithm; and performing cooperative control of the formation flight of multiple spacecraft based on the optimization model for the formation configuration maintenance control strategy.

[0123] Specifically, in the circularly constrained three-body model, global optimization is performed to maintain the control orbit. To avoid infeasible solutions caused by random pulse directions, the optimization variables in this stage are the pulse time and the desired position. In higher-precision models, solving the two-point boundary value problem requires a long computation time. Therefore, the optimization variables can be transformed into the pulse time and pulse magnitude, followed by local optimization. The orbit accuracy is gradually improved through model homotopy iteration, realizing the design of a gravitational wave detection formation maintaining control orbit under a high-precision dynamic model.

[0124]

[0125] Where f0 is the low-precision model, f1 is the high-precision model, and ∈ is the homotopy parameter, which can vary from 0 to 1.

[0126] This application uses the LISA gravitational wave detection project as an example. This project comprises a gravitational wave detector consisting of three spacecraft deployed in near-Earth orbit, orbiting the Sun and lagging behind Earth by approximately 20°. The arm length of the approximately equilateral triangle configuration they form is approximately 2.5 million kilometers, and the expected operational period is 10 years. In the optimized control strategy, the average control interval is 89.0715 days, the minimum control interval is 47.1430 days, the total velocity increment of the three spacecraft is 703.8025 m / s, and the change in the formation configuration stability index is approximately 15% of the requirement. This achieves a significant improvement in the sensitivity of the space gravitational wave detector at a relatively low cost. The application of a high-precision, low-frequency formation configuration maintenance control strategy optimization design method reduces the optimization difficulty at each stage, improves the problem-solving efficiency, and significantly enhances the geometric stability of the formation configuration through low-frequency active control, thereby improving the accuracy of gravitational wave detection.

[0127] The collaborative control method for multiple spacecraft formation flight proposed in this application establishes a control pulse calculation model driven by control expectations. Based on this model, a hierarchical control topology can be established, and the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flight can be determined according to the hierarchical control topology. By establishing a collaborative control topology, the control strategy for the formation configuration can be optimized, and the overall position control strategy and optimized formation configuration control strategy of multiple spacecraft formation flight can be used to collaboratively control the flight of multiple spacecraft formations. Therefore, by using the control pulse calculation model to perform hierarchical optimization design of the overall position and formation configuration of the formation, low-frequency collaborative control of spacecraft formations can be achieved. This solves the problems of complex variables and excessive computation time required for designing control strategies in existing technologies, and improves the detection accuracy of space gravitational waves.

[0128] Next, referring to the accompanying drawings, a cooperative control device for the formation flight of multiple spacecraft according to an embodiment of this application is described.

[0129] Figure 2 This is a block diagram of a collaborative control device for multiple spacecraft formation flight according to an embodiment of this application.

[0130] like Figure 2 As shown, the collaborative control device 10 for the formation flight of multiple spacecraft includes: a setup module 100, a determination module 200, and a control module 300.

[0131] Among them, module 100 is used to establish a calculation model of the control pulse driven by the desired control.

[0132] The determination module 200 is used to establish a hierarchical control topology based on the control pulse calculation model, and to determine the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flights according to the hierarchical control topology.

[0133] The control module 300 is used to establish a cooperative control topology, optimize the control strategy of the formation configuration based on the cooperative control topology, and coordinate the flight of multiple spacecraft in formation based on the overall position control strategy of multiple spacecraft formation flight and the optimized formation configuration control strategy.

[0134] Furthermore, in some embodiments, after optimizing the control strategy for the formation configuration based on the cooperative control topology, the control module 300 is also used for:

[0135] Based on the pre-defined dynamic model extension algorithm, an optimization model for the formation configuration maintenance control strategy is established.

[0136] Based on the formation configuration maintenance control strategy optimization model, the coordinated control of multiple spacecraft formation flight is carried out.

[0137] Furthermore, in some embodiments, the establishment module 100 is specifically used for:

[0138] Based on the circular restricted three-body model, the equations of formation motion are established;

[0139] The first control pulse is determined based on the desired position and the formation motion equation;

[0140] Based on the preset target-hitting strategy and the first control pulse, the second control pulse is determined.

[0141] Furthermore, in some embodiments, the overall position control strategy for multiple spacecraft formation flights is as follows:

[0142]

[0143] st||δR c || max ≤δR c0

[0144] δθ c0 ≤δθ c ≤δθ c1

[0145] t ci ≤t c(i+1) (i = 1, 2, ..., N-1);

[0146] Wherein, δR c For virtual spacecraft SC c The change in distance to the Sun, δθ c For virtual spacecraft SC c The amount of change in the Earth's angle that lags behind; ΔV ci For loading in the virtual spacecraft SC c The i-th pulse on the signal, N represents the total number of pulses, w c1 w c2 w c3 For the corresponding weighting coefficient, t ci To load the i-th pulse into the virtual spacecraft SC c The moment above.

[0147] Furthermore, in some embodiments, the control strategy for the optimized formation configuration is as follows:

[0148]

[0149] st||ΔV djk ||≤ΔV dmax

[0150] t d(k+1) -t dk ≥Δt dmin (k = 1, 2, ..., M) i -1);

[0151] Among them, M i ΔV represents the number of bottom-level control pulses in the i-th segment. djk For the i-th segment loaded on the real spacecraft SC j The kth pulse on, δL arm δθ is the change in arm length. breath V is the change in respiratory angle. arm w is the rate of change of arm length. d1 w d2 w d3 w d4 For the corresponding weighting coefficient, t dk To load the k-th pulse from the i-th segment into the real spacecraft SC j The moment above.

[0152] It should be noted that the explanation of the above-mentioned embodiment of the cooperative control method for multiple spacecraft formation flight also applies to the cooperative control device for multiple spacecraft formation flight in this embodiment, and will not be repeated here.

[0153] According to the cooperative control device for multiple spacecraft formation flight proposed in the embodiments of this application, by establishing a control pulse calculation model driven by control expectations, a hierarchical control topology can be established based on the control pulse calculation model. Based on the hierarchical control topology, the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flight can be determined respectively. By establishing a cooperative control topology, the control strategy for the formation configuration can be optimized based on the cooperative control topology. Furthermore, based on the overall position control strategy and the optimized formation configuration control strategy, the multiple spacecraft formation flight can be cooperatively controlled. Therefore, by using the control pulse calculation model to perform hierarchical optimization design of the overall position and formation configuration of the formation, low-frequency cooperative control of spacecraft formations can be achieved. This solves the problems of complex variables and excessively long calculation time required for designing control strategies in existing technologies, and improves the detection accuracy of space gravitational waves.

[0154] Figure 3 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include:

[0155] The memory 301, the processor 302, and the computer program stored on the memory 301 and capable of running on the processor 302.

[0156] When the processor 302 executes the program, it implements the cooperative control method for multiple spacecraft formation flight provided in the above embodiments.

[0157] Furthermore, electronic devices also include:

[0158] Communication interface 303 is used for communication between memory 301 and processor 302.

[0159] The memory 301 is used to store computer programs that can run on the processor 302.

[0160] The memory 301 may include high-speed RAM (Random Access Memory) memory, and may also include non-volatile memory, such as at least one disk storage.

[0161] If the memory 301, processor 302, and communication interface 303 are implemented independently, then the communication interface 303, memory 301, and processor 302 can be interconnected via a bus to complete communication between them. The bus can be an ISA (Industry Standard Architecture) bus, a PCI (Peripheral Component Interconnect) bus, or an EISA (Extended Industry Standard Architecture) bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 3 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0162] Optionally, in a specific implementation, if the memory 301, processor 302, and communication interface 303 are integrated on a single chip, then the memory 301, processor 302, and communication interface 303 can communicate with each other through an internal interface.

[0163] Processor 302 may be a CPU (Central Processing Unit), an ASIC (Application Specific Integrated Circuit), or one or more integrated circuits configured to implement embodiments of this application.

[0164] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for coordinated control of multiple spacecraft formation flight.

[0165] This invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method for coordinated control of multiple spacecraft formation flight.

[0166] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0167] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0168] Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limitations on the present application. Ordinary technicians in this field can change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A method for coordinated control of multiple spacecraft flying in formation, characterized in that, Includes the following steps: Establish a calculation model for control impulses driven by control expectations; Based on the control pulse calculation model, a hierarchical control topology is established, and the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flights are determined according to the hierarchical control topology. A cooperative control topology is established, the control strategy of the formation configuration is optimized based on the cooperative control topology, and the formation flight of the multiple spacecraft is coordinated and controlled based on the overall position control strategy of the multiple spacecraft formation flight and the optimized formation configuration control strategy. The overall position control strategy for the formation flight of the multiple spacecraft is as follows: s.t.‖δR c ‖ max ≤δR c0 dth c0 ≤δθ c ≤δθ c1 t ci ≤t c(i+1) (i=1,2,...,n-1); Wherein, δR c For virtual spacecraft SC c The change in distance to the Sun, δθ c For virtual spacecraft SC c The amount of change in the Earth's angle that lags behind; ΔV ci For loading in the virtual spacecraft SC c The i-th pulse on the signal, N represents the total number of pulses, w c1 w c2 w c3 For the corresponding weighting coefficient, t ci To load the i-th pulse into the virtual spacecraft SC c The moment on; The control strategy for the optimized formation configuration is as follows: s.t.||ΔV djk ||≤ΔV dmax t d(k+1) -t dk ≥Δt dmin (k=1,2,...,M i -1); Among them, M i ΔV represents the number of bottom-level control pulses in the i-th segment. djk For the i-th segment loaded on the real spacecraft SC j The kth pulse on, δL arm δθ is the change in arm length. breath V is the change in respiratory angle. arm w is the rate of change of arm length. d1 w d2 w d3 w d4 For the corresponding weighting coefficient, t dk To load the k-th pulse from the i-th segment into the real spacecraft SC j The moment above.

2. The method according to claim 1, characterized in that, After establishing the cooperative control topology and optimizing the control strategy for the formation configuration based on the cooperative control topology, the method further includes: Based on the preset dynamic model extension algorithm, an optimization model for the maintenance control strategy of the formation configuration is established; Based on the optimization model of the formation control strategy, the formation flight of the multiple spacecraft is coordinated.

3. The method according to claim 1, characterized in that, The establishment of the control impulse calculation model driven by the desired control includes: Based on the circular restricted three-body model, the equations of formation motion are established; Based on the desired position and the formation motion equation, the first control pulse is determined; Based on the preset target-hitting strategy and the first control pulse, the second control pulse is determined.

4. A collaborative control device for multiple spacecraft flying in formation, characterized in that, The cooperative control method for multiple spacecraft formation flight as described in claim 1, characterized in that the device comprises: Establish a module to build a calculation model for the control pulses driven by the desired control. The determination module is used to establish a hierarchical control topology based on the control pulse calculation model, and to determine the overall position control strategy and formation configuration control strategy for multiple spacecraft formation flights according to the hierarchical control topology. The control module is used to establish a cooperative control topology, optimize the control strategy of the formation configuration based on the cooperative control topology, and coordinate the formation flight of the multiple spacecraft based on the overall position control strategy of the multiple spacecraft formation flight and the optimized formation configuration control strategy.

5. The apparatus according to claim 4, characterized in that, After establishing the cooperative control topology and optimizing the control strategy for the formation configuration based on the cooperative control topology, the control module further includes: Based on the preset dynamic model extension algorithm, an optimization model for the maintenance control strategy of the formation configuration is established; Based on the optimization model of the formation control strategy, the formation flight of the multiple spacecraft is coordinated.

6. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the program to implement the cooperative control method for formation flying of multiple spacecraft as described in any one of claims 1-3.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the cooperative control method for multiple spacecraft formation flight as described in any one of claims 1-3.

8. A computer program product, characterized in that, Includes a computer program, which, when executed by a processor, is used to implement the cooperative control method for flight of multiple spacecraft in formation as described in any one of claims 1-3.

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