Space tumbling target efficient racemization method based on multi-satellite dynamic collaborative reconstruction and electromagnetic field optimization

Abstract

The invention relates to a space tumbling target efficient racemization method based on multi-satellite dynamic collaborative reconstruction and electromagnetic field optimization. The method comprises the steps that the optimal position and attitude of each service satellite are preset; constructing a multi-satellite cooperative formation based on the optimal position and attitude of each service satellite; the multi-satellite cooperative formation is maintained, a stable magnetic field is generated, and electromagnetic racemization is carried out on the space tumbling target; when the angular acceleration modulus is smaller than a preset threshold value, triggering formation approaching and reconstruction; and updating the control law, maintaining the reconstructed new formation configuration, and continuing to perform racemization on the target until the racemization task is completed. According to the invention, through collaborative configuration optimization of a plurality of service satellites carrying high-temperature superconducting coils, an electromagnetic field for racemization is generated and optimized, and efficient racemization of a non-cooperative space tumbling target is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of on-orbit operation of spacecrafts, and particularly to an efficient anti-spin method for space tumbling targets based on multi-satellite dynamic cooperative reconstruction and electromagnetic field optimization. Background Art

[0002] In the tasks of space debris cleaning and malfunctioning spacecraft handling, due to out-of-control attitude and high angular velocity of space free tumbling targets, the subsequent capture operation is extremely difficult and there is a risk of collision. Therefore, it is urgent to achieve safe anti-spin through non-contact means. The electromagnetic anti-spin method is based on the eddy current damping effect, and can generate a braking torque by inducing eddy currents through a magnetic field at a safe distance from the target, avoiding the mechanical collision risk of contact anti-spin, and becoming the preferred anti-spin scheme in current on-orbit anti-spin.

[0003] In the prior art, Kadaba et al. proposed the anti-spin principle of inducing eddy currents in the target skin using an external DC magnetic field, Sugai et al. verified the braking performance of the electromagnetic anti-spin system through experiments, Yu et al. used two satellites for electromagnetic formation flight to enhance the magnetic field intensity, and Wan et al. proposed a multi-coil anti-spin method. However, the prior art has the following defects: ① The anti-spin efficiency decreases significantly as the relative angular velocity of the target decreases, because a single or fixed formation configuration cannot dynamically adapt to the attenuation of the target angular velocity, resulting in a weakening of the eddy current torque; ② There is no established optimal formation reconstruction criterion for multi-satellite cooperation, making it difficult to maintain high-efficiency torque output during the anti-spin process; ③ The research on electromagnetic coupling constraints and energy optimization strategies between service spacecrafts is insufficient, resulting in a long anti-spin time and high energy consumption.

[0004] None of the related technical documents have solved the problem of efficiency decline caused by angular velocity attenuation during the anti-spin process. There is an urgent need for a method that can dynamically optimize the formation configuration and maintain efficient anti-spin. Summary of the Invention

[0005] The object of the present invention is to provide an optimal electromagnetic anti-spin method and system based on multi-satellite cooperation to solve the problems in the prior art that the electromagnetic anti-spin efficiency of space tumbling targets decreases with the attenuation of angular velocity and the formation configuration lacks dynamic optimization. Through the optimal configuration design and dynamic reconstruction of multi-satellite formation, an expected anti-spin magnetic field and torque are continuously generated when the target angular velocity attenuates, achieving fast anti-spin with optimal energy and solving the technical problems of low anti-spin efficiency and high energy consumption in the prior art.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] An efficient anti-spin method for space tumbling targets based on multi-satellite dynamic cooperative reconstruction and electromagnetic field optimization, comprising:

[0008] Presetting the optimal positions and attitudes of each service satellite;

[0009] Construct a multi-satellite collaborative formation based on the optimal positions and attitudes of each service satellite;

[0010] Maintain the multi-satellite collaborative formation, generate a stable magnetic field, and perform electromagnetic despin on the space tumbling target;

[0011] When the angular acceleration modulus is less than a preset threshold, trigger formation approaching and reconstruction;

[0012] Update the control law, maintain the new formation configuration after reconstruction, and continue to despin the target until the despin task is completed.

[0013] Optionally, presetting the optimal positions and attitudes of each service satellite includes:

[0014] Calculate the best position vector r i of each service satellite, that is, the optimal position of the service satellite, where the best position vector satisfies a preset threshold; the preset threshold is r i ·ω t (t0) = 0, ω t is the target angular velocity, and t0 is the initial time;

[0015] Determine the service satellite attitude through the coordinate transformation matrix to make the coil axis perpendicular to the target angular velocity direction, where e x , e y , e z are the reference frame unit vectors.

[0016] Based on the optimal positions and attitudes of each service satellite, construct an information flow adjacency matrix A, and design a nonlinear control law through the consensus theory to make the satellite converge to the desired circular formation; where e i is the error between the actual state and the desired state of the satellite, K p , K d are positive definite matrices, is the satellite attitude change rate.

[0017] Optionally, the constructed multi-satellite collaborative formation is:

[0018] Multiple service satellites are evenly distributed on a circle centered on the target centroid with a radius R, and the included angle θ between the central axes of adjacent satellites is 2π / n, where n is the number of satellites, satisfying the far-field dipole constraint.

[0019] Optionally, maintaining the multi-satellite collaborative formation, generating a stable magnetic field, and performing electromagnetic despin on the space tumbling target includes:

[0020] Maintain the multi-satellite collaborative formation, and the high-temperature superconducting coil generates a constant magnetic field B, inducing an electromagnetic eddy current torque T eddy = ηM(ω t× B), where ω t is the target angular velocity, η is the magnetic tensor efficiency factor, and M is the target magnetic tensor;

[0021] The electromagnetic eddy current torque acts on the space tumbling target. Based on the attitude dynamics of the space tumbling target the target angular velocity parameter can be reduced, where J t is the moment of inertia of the space tumbling target, and is the target angular acceleration.

[0022] Optionally, when the angular acceleration modulus is less than a preset threshold, triggering formation approaching and reconstruction includes:

[0023] Select some service satellites to approach along the direction of the target centroid, and update the position vector r i ′ = r i -δ·e r , where δ is the approaching distance and e r is the unit vector in the direction of the target centroid, and the distance between the coil and the target is reduced to increase the magnetic field strength;

[0024] Based on the energy optimal criterion minE = E formation + E maintain + E reconfig + E post-maintain , calculate the energy consumption at each stage, determine the optimal reconstruction timing and the number of satellites, and update the formation information flow by adjusting the information flow adjacency matrix A; where E reconfig is the energy consumed by the electromagnetic despin formation reconstruction, E formation is the energy consumed to achieve the despin formation configuration, E maintain is the energy required to maintain the formation configuration after the electromagnetic despin formation reconstruction, E post-maintain is the energy consumed to maintain the despin formation configuration before reconstruction.

[0025] Optionally, the new multi-satellite cooperative formation configuration after reconstruction is:

[0026] Multiple service satellites are evenly distributed on a circle centered on the target centroid with a radius R′, and the included angle θ′ between the central axes of adjacent satellites is 2π / n′, where n′ is the number of satellites in the new cooperative formation, satisfying the far-field dipole constraint.

[0027] Optionally, updating the control law to maintain the new formation configuration after reconstruction includes:

[0028] Recalculate the information flow adjacency matrix A according to the new position after reconstruction, optimize the control parameters to maintain formation cooperation, ensure that the central axis of the high-temperature superconducting coil after reconstruction is still perpendicular to the current target angular velocity direction, and maintain the new multi-satellite cooperative formation.

[0029] The beneficial effects of the present invention are:

[0030] Compared with the existing electromagnetic despin technology, in this invention example, through the optimal configuration design and dynamic reconfiguration of multi-satellite cooperative formation, the problems of the attenuation of eddy current torque and the reduction of despin efficiency caused by the decrease of the relative angular velocity of the target during the despin process are effectively solved; the optimal reconfiguration criterion established based on the attenuation characteristics of the target angular velocity, combined with the energy-optimal strategy, determines the best reconfiguration timing and satellite configuration, minimizing the formation adjustment and maintenance energy consumption while improving the despin efficiency; by introducing the far-field dipole constraint and the non-linear control law based on the consensus theory, the electromagnetic coupling interference between multi-satellites is processed and cooperative control is realized, enhancing the adaptability of the system to space tumbling targets with different moments of inertia and shapes, providing a safe, efficient and energy-optimized despin solution for space non-cooperative targets, and having significant engineering application value and technological progressiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0032] Figure 1 Schematic diagram of the change before and after the formation reconfiguration of the service satellite in the embodiment of the present invention (taking a five-satellite formation as an example);

[0033] Figure 2 Schematic diagram of the optimal initial formation configuration in the embodiment of the present invention;

[0034] Figure 3 Schematic diagram of the curve of the angular acceleration modulus change (without formation reconfiguration) in the embodiment of the present invention;

[0035] Figure 4 Schematic diagram of the optimal formation configuration after the formation reconfiguration in the embodiment of the present invention;

[0036] Figure 5 Schematic diagram of the comparison of the curves of the angular velocity modulus change in the embodiment of the present invention;

[0037] Figure 6 Schematic diagram of the comparison of the curves of the angular acceleration modulus change in the embodiment of the present invention;

[0038] Figure 7 Schematic diagram of the flow of an efficient despin method for space tumbling targets based on multi-satellite dynamic cooperative reconfiguration and electromagnetic field optimization in the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0039] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0040] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0041] To achieve efficient electromagnetic despinning for the space tumbling target, this embodiment proposes an optimal configuration design and dynamic reconfiguration method based on multi-satellite cooperation. This method analyzes the influence of the relative pose between the service satellite and the target on the despinning efficiency, constructs the optimal position and attitude constraints for the multi-satellite formation, and designs the formation reconfiguration criterion according to the target angular velocity decay characteristics. The changes before and after the formation reconfiguration are as Figure 1 shown. The specific technical solutions are as follows:

[0042] The system of this embodiment includes multiple service satellites equipped with high-temperature superconducting (HTS) coils. Each satellite connects the coil through a single-link mechanism. The origin of its fixed coordinate system is located at the center of the coil, and the axis points to the target centroid along the central axis of the coil. The target attitude dynamics equation is where the electromagnetic eddy current torque T eddy = ηM(ω t × B), η is the magnetic tensor efficiency factor, M is the target magnetic tensor, and B is the magnetic field generated by the HTS coil.

[0043] As Figure 7 shown, an efficient despinning method for space tumbling targets based on multi-satellite dynamic cooperation reconfiguration and electromagnetic field optimization proposed in this embodiment mainly includes the following steps:

[0044] Preset the optimal positions and attitudes of each service satellite;

[0045] Based on the optimal positions and attitudes of each service satellite, construct a multi-satellite cooperative formation;

[0046] Maintain the multi-satellite cooperative formation, generate a stable magnetic field, and perform electromagnetic despinning on the space tumbling target;

[0047] When the angular acceleration modulus is less than the preset threshold, trigger formation approach and reconfiguration;

[0048] Update the control law, maintain the new formation configuration after reconfiguration, and continue to despin the target until the despinning task is completed.

[0049] Furthermore, presetting the optimal positions and attitudes of each service satellite includes:

[0050] Calculate the optimal position vector r of each service satellite i , that is, the optimal position of the service satellite, where the optimal position vector satisfies a preset threshold;

[0051] Determine the attitude of the service satellite through the coordinate transformation matrix to make the coil axis perpendicular to the target angular velocity direction, where e x , e y , e z is the reference frame unit vector.

[0052] Specifically, in this embodiment, the optimal position and attitude design of a single satellite: Set the central axis of the HTS coil to pass through the target centroid and be located in the vertical plane of the target angular velocity ω t , that is, satisfy r i ·ω t =0 (r i is the coil center position vector). Define the reference frame, whose axis coincides with ω t , and determine the attitude of the service satellite through the coordinate transformation matrix to make the coil axis perpendicular to the target angular velocity direction, where e x , e y , e z is the reference frame unit vector.

[0053] Furthermore, constructing a multi-satellite cooperative formation includes:

[0054] Based on the optimal positions and attitudes of the service satellites, construct the information flow adjacency matrix A, and design a non-linear control law through the consensus theory to make the satellites converge to the desired circular formation.

[0055] Specifically, in this embodiment, the multi-satellite cooperative formation configuration design: Multiple service satellites are evenly distributed on a circle centered on the target centroid with a radius R, and the included angle θ between the central axes of adjacent satellites is 2π / n (n is the number of satellites), satisfying the far-field dipole constraint. Construct the information flow adjacency matrix A, and design a non-linear control law through the consensus theory where e i is the error between the actual state and the desired state of the satellite, K p , K d is a positive definite matrix, to achieve formation position and attitude coordination.

[0056] Furthermore, maintaining the multi-satellite cooperative formation, generating a stable magnetic field, and performing electromagnetic despin on the space tumbling target includes:

[0057] Maintain the multi-satellite cooperative formation, the high-temperature superconducting coil generates a constant magnetic field B, and induces an electromagnetic eddy current torque T eddy =ηM(ω t× B), where ω t is the target angular velocity, η is the magnetic tensor efficiency factor, and M is the target magnetic tensor.

[0058] The electromagnetic eddy current torque acts on the space tumbling target. Based on the attitude dynamics of the space tumbling target the target angular velocity parameter can be reduced, where J t is the moment of inertia of the space tumbling target, and is the target angular acceleration.

[0059] When the angular acceleration modulus is less than the preset threshold, the formation approach and reconstruction are triggered, including:

[0060] Select some service satellites to approach along the direction of the target centroid, and update the position vector r i ′ = r i -δ·e r , where δ is the approach distance and e r is the unit vector in the direction of the target centroid, and the distance between the coil and the target is reduced to increase the magnetic field strength;

[0061] Based on the energy optimal criterion minE = E formation +E maintain +E reconfig +E post-maintain , calculate the energy consumption at each stage, determine the optimal reconstruction timing and the number of satellites, and update the formation information flow by adjusting the information flow adjacency matrix A.

[0062] Specifically, in this embodiment, the optimal formation reconstruction criterion: when the target angular acceleration modulus (preset threshold), reconstruction is triggered. Select some satellites to approach along the direction of the target centroid, and update the position vector r i ′ = r i -δ·e r (δ is the approach distance and e r is the unit vector in the direction of the target centroid), and the distance between the coil and the target is reduced to increase the magnetic field strength. Based on the energy optimal criterion minE = E formation +E maintain +E reconfig +E post-maintain , calculate the energy consumption at each stage, determine the optimal reconstruction timing and the number of satellites, where E reconfig is the energy consumed by the electromagnetic despin formation reconstruction, E formation is the energy consumed to achieve the despin formation configuration, E maintain is the energy required to maintain the formation configuration after the electromagnetic despin formation reconstruction, E post-maintain is the energy consumed to maintain the despin formation configuration before reconstruction, and update the formation information flow by adjusting the adjacency matrix A.

[0063] Furthermore, update the control law to maintain the newly reconstructed formation configuration, including:

[0064] Recalculate the information flow adjacency matrix A based on the newly reconstructed positions, optimize the control parameters to maintain formation cooperation, ensure that the central axis of the high-temperature superconducting coil remains perpendicular to the current target angular velocity direction after reconstruction, and maintain the new multi-satellite collaborative formation.

[0065] Specifically, the despin mission in this embodiment is divided into four stages: ① Formation establishment stage, determining the initial position and attitude through single-satellite and multi-satellite optimization algorithms; ② Despin stage before reconstruction, maintaining the initial formation to generate a stable magnetic field and performing electromagnetic despin on the space tumbling target; ③ Formation reconstruction stage, triggering the approaching strategy according to the threshold and updating the control law; ④ Despin stage after reconstruction, maintaining the new formation configuration through the nonlinear control law until the target angular velocity converges to zero.

[0066] This embodiment proposes multi-satellite collaborative configuration optimization: establishing a position constraint where the central axis of the coil is perpendicular to the target angular velocity through mathematical derivation, and forming an annular formation to maximize the initial despin torque;

[0067] Dynamic reconstruction strategy: an adaptive approaching mechanism based on the angular acceleration threshold to solve the problem of the eddy current torque decline caused by the attenuation of the target angular velocity;

[0068] Energy optimal and cooperative control: designing the control law in combination with the consensus theory to handle the electromagnetic coupling interference between satellites, minimizing the energy consumption during the despin process, and enhancing the system robustness.

[0069] Next, this embodiment selects the following data for experiments.

[0070] I. Implementation Environment and Parameter Configuration

[0071] 1. Space tumbling target:

[0072] The target is set as a 72-faceted failed satellite, approximated as a sphere, and the material of the spherical shell is hard aluminum alloy. The relevant parameters of the target are shown in Table 1 below.

[0073] Table 1 Space Tumbling Target Parameters

[0074]

[0075] 2. Service satellite system:

[0076] Configure 5 service satellites carrying high-temperature superconducting (HTS) coils, and set the mass of each service satellite as m i = 761.533 kg, and the moment of inertia J i = diag(3027.016, 3251.025, 3244.98) (kg·m 2 ), in Σ siThe position vector in the coordinate system is ρ csi = [-2, 0, 0] T m. In addition, N c = 1000, R c = 1m, i c = 100A. Other parameter settings are shown in Table 2 below.

[0077] Table 2 Parameters of the empty service satellite

[0078]

[0079]

[0080] 3. Other parameters

[0081] The specific settings of the time nodes are as follows: t0 = 0s, t1 = 800s, t3 - t2 = 600s. In the stage from t0 to t1, the target is in a free tumbling state. When t = t1, it is necessary to reach the calculated optimal configuration. At this time, ω t (t1) = [54.69, 46.96, -80] T (° / s), so e t = [0.51, 0.44, -0.74] T , in addition I x r = [0, -0.86, -0.51] T , I y r = [-0.86, 0.26, -0.44] T , I z r = [0.51, 0.43, -0.74] T .

[0082] II. Implementation steps

[0083] Stage 1: Establishment of the despun formation configuration (t0 ≤ t ≤ t1)

[0084] Configuration arrangement: Perform optimal configuration on the multi-satellite formation configuration. When the number of service satellites is 5, there is Φ opt = 72°, The calculated optimal configuration scheme is as follows Figure 2 as shown.

[0085] Single-satellite optimization: Calculate the best position vector r i of each satellite, satisfying r i ·ω t (t0) = 0, that is, the coil central axis is located in the vertical plane (y - z plane) of the target initial angular velocity.

[0086] Multi-satellite collaboration: through the adjacency matrix

[0087]

[0088] Construct an information flow network and adopt a consensus control law to enable the satellite to quickly converge to the desired circular formation (where K p = diag(0.15, 0.30, 0.15), K d = diag(0.1, 0.2, 0.1)).

[0089] Phase 2: Non-reconstructed despin (t1 ≤ t ≤ t2)

[0090] Maintain the initial formation configuration. The HTS coil generates a constant magnetic field B, inducing an eddy current torque T eddy = ηM(ω t × B), where the magnetic tensor efficiency factor η = 0.85.

[0091] The electromagnetic eddy current torque acts on the space tumbling target. Based on the attitude dynamics of the space tumbling target it is possible to reduce the target angular velocity parameter, where J t is the moment of inertia of the space tumbling target, and is the target angular acceleration.

[0092] As Figure 3 shown is the curve of the target angular acceleration change. Obviously, as the electromagnetic despin process progresses, the decrease in the target angular velocity causes the induced eddy current torque to decrease, resulting in a rapid decrease in the target angular acceleration and leading to an extremely low despin efficiency. Therefore, it is extremely necessary to reconstruct the formation of the despin satellite.

[0093] To improve the despin efficiency, formation reconstruction must be carried out. Set the angular acceleration threshold as When the angular acceleration modulus is reached, trigger the formation reconstruction. According to the angular acceleration change in the despin working condition before formation reconstruction, t2 = 8035s and t3 = t2 + 600 = 8635s can be determined.

[0094] Phase 3: Despin formation reconstruction (t2 ≤ t ≤ t3)

[0095] Reconstruction strategy: Service satellite No. 1 and service satellite No. 3 approach the space tumbling target, while service satellite No. 2, service satellite No. 4, and service satellite No. 5 remain in their original positions. As Figure 4 shown is the optimal formation configuration after formation reconstruction. Service satellite No. 1 and service satellite No. 3 also adopt the optimized configuration scheme of the multi-satellite formation system, with Φ opt = 180° and

[0096] Control law adjustment: Recalculate the adjacency matrix A according to the new position, optimize the control parameters to maintain formation cooperation, and ensure that the coil central axis after reconstruction is still perpendicular to the current target angular velocity direction.

[0097] Stage 4: Despinning after reconstruction (t3 ≤ t ≤ t4)

[0098] In the new formation configuration, the magnetic field strength increases as the satellite approaches the target, the eddy current torque increases significantly, and the target angular velocity decays rapidly.

[0099] Continuously monitor the target angular velocity. After about 8.693 hours, the target angular velocity ω t Basically converges to 0, and the despinning task is achieved.

[0100] As Figure 5 and Figure 6 shown are the curves of the angular velocity and angular acceleration modulus changes without formation reconstruction and with formation reconstruction. The comparison between the two fully demonstrates the improvement effect of formation reconstruction on the despinning efficiency. Through formation reconstruction, the despinning time is reduced from 49.36 hours to 8.693 hours, a reduction of 82.39%. Or rather, the despinning efficiency is increased by 4.68 times, verifying the adaptability of dynamic reconstruction to the decay of the target angular velocity.

[0101] Compared with the existing electromagnetic despinning technology, in this embodiment, through the optimal configuration design and dynamic reconstruction of multi-satellite cooperative formation, the problem of the reduction of the eddy current torque and the decrease of the despinning efficiency due to the reduction of the relative angular velocity of the target during the despinning process is effectively solved; the optimal reconstruction criterion established based on the decay characteristics of the target angular velocity, combined with the energy-optimal strategy, determines the best reconstruction timing and satellite configuration, minimizing the formation adjustment and maintenance energy consumption while improving the despinning efficiency; by introducing the far-field dipole constraint and the nonlinear control law based on the consensus theory, the electromagnetic coupling interference between multi-satellites is processed and cooperative control is achieved, enhancing the adaptability of the system to space tumbling targets with different moments of inertia and shapes, providing a safe, efficient and energy-optimized despinning solution for space non-cooperative targets, and having significant engineering application value and technological progressiveness.

[0102] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. An efficient despin method for space tumbling targets based on multi-satellite dynamic collaborative reconstruction and electromagnetic field optimization, characterized in that Including: Presetting the optimal positions and attitudes of each service satellite; Based on the optimal positions and attitudes of each service satellite, constructing a multi-satellite cooperative formation; Maintaining the multi-satellite cooperative formation, generating a stable magnetic field, and performing electromagnetic despin on the space tumbling target; When the angular acceleration modulus is less than the preset threshold, triggering formation approaching and reconstruction; Updating the control law, maintaining the new formation configuration after reconstruction, and continuing to perform despin on the target until the despin task is completed.

2. The efficient despin method for spatial tumbling targets based on multi-satellite dynamic cooperative reconstruction and electromagnetic field optimization according to claim 1, characterized in that Presetting the optimal positions and attitudes of each service satellite includes: Calculate the optimal position vector r of each service satellite i , that is, the optimal position of the service satellite, where the optimal position vector satisfies a preset threshold; the preset threshold is r i ·ω t (t0) = 0, ω t is the target angular velocity, and t0 is the initial time; Through the coordinate transformation matrix Determine the attitude of the service satellite so that the coil axis is perpendicular to the direction of the target angular velocity, where e x , e y , e z Is the unit vector of the reference frame.

3. The efficient despin method for space tumbling targets based on multi-satellite dynamic collaborative reconstruction and electromagnetic field optimization according to claim 1, characterized in that, Constructing a multi-satellite cooperative formation includes: Based on the optimal positions and attitudes of each service satellite, construct the information flow adjacency matrix A, and design a non-linear control law through the consensus theory to make the satellites converge to the desired circular formation; where, e i is the error between the actual state and the desired state of the satellite, and K p , K d is a positive definite matrix, is the rate of change of the satellite attitude.

4. The efficient despin method for space tumbling targets based on multi-satellite dynamic collaborative reconstruction and electromagnetic field optimization according to claim 3, wherein The constructed multi-satellite cooperative formation is: Multiple service satellites are evenly distributed on a circle with the target centroid as the center and a radius of R, and the included angle θ between the central axes of adjacent satellites is 2π / n, where n is the number of satellites, satisfying the far-field dipole constraint.

5. The high-efficiency despin method for space tumbling targets based on multi-satellite dynamic collaborative reconstruction and electromagnetic field optimization according to claim 1, characterized in that Maintaining the multi-satellite cooperative formation, generating a stable magnetic field, and performing electromagnetic despin on the space tumbling target includes: Maintain the multi-star cooperative formation. The high-temperature superconducting coil generates a constant magnetic field B, inducing an electromagnetic eddy current torque T on the target. eddy = ηM(ω t × B), where ω t is the angular velocity of the target, η is the magnetic tensor efficiency factor, and M is the magnetic tensor of the target. The electromagnetic eddy current torque acts on the space tumbling target, based on the attitude dynamics of the space tumbling target can reduce the target angular velocity parameter, where J t is the moment of inertia of the space tumbling target, is the target angular acceleration.

6. The efficient despin method for spatial tumbling targets based on multi-satellite dynamic cooperative reconstruction and electromagnetic field optimization according to claim 1, characterized in that, When the angular acceleration modulus is less than the preset threshold, triggering formation reconstruction includes: Select some service satellites to approach along the direction of the target centroid and update the position vector r i ′ = r i -δ·e r , where δ is the approaching distance and e r is the unit vector in the direction of the target centroid, and reduce the distance between the coil and the target to increase the magnetic field strength; Based on the energy-optimal criterion minE = E formation + E maintain + E reconfig + E post-maintain , calculate the energy consumption at each stage, determine the optimal reconstruction time and the number of satellites, and update the formation information flow by adjusting the information flow adjacency matrix A; where E reconfig is the energy consumed for the electromagnetic despin formation reconstruction, E formation is the energy consumed to achieve the despin formation configuration, E maintain is the energy required to maintain the formation configuration after the electromagnetic despin formation reconstruction, E post-maintain is the energy consumed to maintain the despin formation configuration before reconstruction.

7. The efficient despin method for space tumbling targets based on multi-satellite dynamic cooperative reconstruction and electromagnetic field optimization according to claim 6, characterized in that The new configuration of the multi-satellite cooperative formation after reconstruction is: Multiple service satellites are evenly distributed on a circle with the target centroid as the center and a radius of R′, and the included angle θ′ between the central axes of adjacent satellites is 2π / n′, where n′ is the number of satellites in the new cooperative formation, satisfying the far-field dipole constraint.

8. The efficient despin method for spatial tumbling targets based on multi-satellite dynamic collaborative reconstruction and electromagnetic field optimization according to claim 1, characterized in that, Updating the control law, maintaining the new formation configuration after reconstruction, and continuing to perform despin on the target includes: Recalculating the information flow adjacency matrix A according to the new positions after reconstruction, optimizing the control parameters to maintain formation cooperation, ensuring that the central axis of the high-temperature superconducting coil after reconstruction is still perpendicular to the current target angular velocity direction, and maintaining the new multi-satellite cooperative formation.

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