A spacecraft formation control method based on a predetermined time convergence strategy

Abstract

This invention proposes a spacecraft formation control method based on a predetermined time convergence strategy, comprising: during the first inter-satellite communication, a spacecraft selects corresponding configuration parameters and reconfiguration time according to an onboard plan and transmits this information to other spacecraft in the formation for confirmation; the spacecraft obtains its own position and velocity information in the inter-satellite relative coordinate system according to the onboard navigation system, and subtracts it from the expected position and velocity at that moment during the configuration reconfiguration process; and broadcasts its own state deviation information through the inter-satellite communication equipment; while transmitting its own state deviation information, the spacecraft receives state deviation information transmitted by other spacecraft; and calculates its own expected three-axis velocity change rate; broadcasts its own expected velocity change rate through the inter-satellite communication equipment; and calculates its own expected three-axis acceleration change rate; repeating the above steps until the spacecraft reaches the predetermined reconfiguration completion time.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, and specifically relates to a spacecraft formation control method based on a predetermined time convergence strategy. Background Technology

[0002] A spacecraft swarm is a collection of spacecraft with similar orbital information that are located close to each other. Most of the spacecraft participating in the swarm are small or microsatellites, which have advantages such as low cost, simple manufacturing, and high substitutability. By sharing information among the spacecraft, spacecraft swarms can achieve space missions that are difficult for a single spacecraft to accomplish, such as ultra-long baseline interferometric imaging, large-area stereo imaging, and real-time positioning and navigation.

[0003] Maintaining and reconfiguring the spacecraft's spatial configuration is fundamental to completing space missions. The main cooperative control methods are categorized into centralized and distributed systems. Centralized control strategies place high demands on the host satellite's computing and communication capabilities, resulting in lower system robustness compared to distributed systems. In distributed control strategies, all satellites are equal and can exchange cooperative information with neighboring nodes, autonomously calculating their own control variables. Distributed control systems are more robust, remaining functionally unaffected even if some satellites in the formation fail. Common distributed formation control strategies are mostly basic consensus convergence strategies, derived from traditional PID algorithms, which converge over infinite time. Consistency control algorithms employing finite-time convergence strategies can generally only prove convergence within a finite time (upper limit unknown) or within a specified time limit.

[0004] Most common spacecraft formation control strategies cannot constrain configuration control time, or only consider the formation completing reconfiguration and stabilization within a limited time. In situations such as changes in Earth observation targets, rapid formation reconfiguration after obstacle avoidance, or other specific circumstances, we need to have a clear grasp of the formation configuration stabilization time. Summary of the Invention

[0005] In view of this, the present invention provides a spacecraft formation control method based on a predetermined time convergence strategy to solve the problem of achieving spacecraft formation consistency convergence within a defined time when spacecraft formations undergo changes in Earth observation targets or rapid formation reconfiguration after obstacle avoidance. The method includes:

[0006] Step S1: During the first inter-satellite communication, a spacecraft selects the corresponding configuration parameters and reconfiguration time according to the on-board plan and transmits them to other spacecraft in the formation for confirmation;

[0007] Step S2: The spacecraft obtains its own position and velocity information in the inter-satellite relative coordinate system according to the on-board navigation system, and subtracts it from the expected position and velocity at that moment during the configuration reconstruction process; calculates the state deviation information including the position and velocity deviation of the spacecraft, and broadcasts its own state deviation information through the inter-satellite communication equipment;

[0008] Step S3: While transmitting its own state deviation information, the spacecraft receives state deviation information transmitted by other spacecraft; calculates its own expected three-axis velocity change rate; and broadcasts its expected velocity change rate through inter-satellite communication equipment.

[0009] Step S4: While broadcasting its own desired rate of change of velocity information, the spacecraft receives desired rate of change of velocity information from other spacecraft; and calculates its own desired triaxial acceleration rate of change.

[0010] Step S5: The spacecraft determines whether the predetermined reconfiguration completion time has been reached. If it has not been reached, steps S2 to S5 are repeated. If it has been reached, it means that the configuration has achieved consistent convergence and the control process ends.

[0011] Specifically, in step S1, the satellites adopt a circular formation configuration in space, and their positions and velocities satisfy the following parametric equations:

[0012]

[0013] Where r is the formation radius, μ is the formation phase, and n is the circular orbital angular velocity of the formation reference spacecraft.

[0014] Specifically, in step S2, the spacecraft's position deviation information and velocity deviation information, the position deviation information X ei and speed deviation information V ei The specific calculation formula is as follows:

[0015]

[0016] Among them, X i V represents the spacecraft's position information. i The velocity information of the spacecraft is represented by a 3D vector, where i represents the i-th spacecraft in the formation.

[0017] Specifically, step S3 further includes:

[0018] While transmitting its own state deviation information, the spacecraft also receives state deviation information from other spacecraft; after receiving the state deviation information, it calculates its desired triaxial velocity change rate using the following formula.

[0019] in k = x, y, z represent the three coordinate axes, which are the spacecraft's position information X. i The specific form of the three-dimensional vector; i, j = 1, 2, ..., n; j ≠ i; i and j represent the i-th spacecraft and the j-th spacecraft in the formation, respectively; when the i-th spacecraft receives the state deviation information of the j-th spacecraft, that is, when there is information exchange between the two, a ij =1, otherwise a ij =0; α is the configuration pre-determined coefficient, n is the total number of spacecraft in the formation, η vki Custom coefficients for spacecraft, t f The predetermined reconstruction completion time is t, where t is the time for calculating the expected rate of change of velocity.

[0020] Specifically, step S4 further includes: while transmitting its own desired rate of change of velocity information, the spacecraft in the spacecraft formation receives desired rate of change of velocity information transmitted by other spacecraft; and calculates its own desired triaxial acceleration rate of change according to the following formula.

[0021] in, k = x, y, z represent the three coordinate axes; V' eki To calculate velocity, the formula for its three-dimensional vector is: This represents the three-dimensional vector form of the corresponding quantity; β is a predetermined coefficient, and i and j represent the i-th and j-th spacecraft in the formation, respectively; finally, the three-axis control quantity of the i-th spacecraft can be calculated by the following formula:

[0022]

[0023] in, Let γ be the derivative of the desired rate of change of velocity, k = x, y, z represent the three coordinate axes respectively, and γ be a predetermined coefficient.

[0024] Specifically, step S5 further includes: the three-axis control quantity of the i-th spacecraft can be calculated by the following formula:

[0025]

[0026] in, Let x be the derivative of the desired rate of change of velocity, and k = x, y, z represent the three coordinate axes respectively.

[0027] Beneficial effects:

[0028] 1) In view of the problem that the reconfiguration time of spacecraft formation cannot be determined, this invention discloses a spacecraft formation control method with a predetermined time convergence strategy. Under the action of this control law, the spacecraft formation can theoretically achieve consistent convergence at any predetermined time.

[0029] 2) In this invention, while the spacecraft is transmitting its own state deviation information, it is also receiving state deviation information transmitted by other spacecraft, which ensures the accurate estimation of state deviation in the spacecraft formation.

[0030] 3) In this invention, while spacecraft in a spacecraft formation are sending out their own desired rate of change information, they will also receive the desired rate of change information from other spacecraft, thus ensuring an accurate estimate of the desired speed of spacecraft in the spacecraft formation.

[0031] 4) In this invention, the three-axis control variation is obtained by estimating the expected three-axis acceleration variation rate of the spacecraft in the spacecraft formation, which ensures the accurate calculation and estimation of the three-axis control variation of the spacecraft. Attached Figure Description

[0032] Figure 1 This is a flowchart of the specific implementation of the present invention on a single spacecraft. In the diagram, "other satellites" refers to other spacecraft in the spacecraft formation that establish stable communication with the local satellite.

[0033] Figure 2 This is the communication topology of the four-star formation configuration exemplified in this invention. A dot represents a star, and a solid line represents stable communication between two stars.

[0034] Figure 3 This is a three-dimensional trajectory diagram of the four-star formation configuration reconstruction process exemplified in this invention;

[0035] Figure 4 This is a diagram illustrating the convergence process of the three-axis position deviation of the first star in the four-star formation configuration reconstruction process exemplified by this invention.

[0036] Figure 5 This is a diagram illustrating the convergence process of the three-axis velocity deviation of the first star in the four-star formation configuration reconstruction process exemplified by this invention.

[0037] Figure 6 This is a three-axis acceleration diagram of the first star in the four-star formation configuration reconstruction process exemplified by this invention. Detailed Implementation

[0038] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0039] This invention provides a spacecraft formation control method based on a predetermined time convergence strategy disclosed in this embodiment, such as... Figure 1 As shown, the specific implementation steps are as follows:

[0040] Step 1: Determine the formation configuration

[0041] When spacecraft formation needs to reconfigure, it is essential to ensure stable inter-satellite communication. During the initial inter-satellite communication, the spacecraft formation should follow the onboard plan to select the corresponding configuration parameters and reconfiguration time, and transmit this information to other spacecraft in the formation for confirmation, achieving a basic consensus on the formation's spacecraft configuration. This consensus should remain unchanged throughout the entire formation reconfiguration process.

[0042] like Figure 2 As shown, satellite 1 in the formation can communicate with satellites 2 and 3; satellite 2 can communicate with satellites 1 and 4; satellite 3 can communicate with satellites 1 and 4; and satellite 4 can communicate with satellites 2 and 3. The initial and desired configuration parameters of each satellite are shown in the table below:

[0043] Table 1 Formation Configuration Parameters

[0044]

[0045] The satellites are configured in a circular formation in space, and their positions and velocities satisfy the following parametric equations:

[0046]

[0047] Where r is the formation radius, μ is the formation phase, and n is the circular orbital angular velocity of the reference spacecraft in the formation. In this example, it is set to 0.001083077788451 rad / s.

[0048] Step 2: State Deviation Calculation and Broadcast

[0049] Step 2.1: Calculation of State Deviation

[0050] The i-th spacecraft in the spacecraft formation obtains its own position and velocity information in the inter-satellite relative coordinate system based on the on-board navigation system, and calculates the position deviation information X of the i-th spacecraft by subtracting it from the expected position and velocity at that moment during the configuration reconfiguration process. ei and speed deviation information V ei .

[0051] The status deviation of stars 1-4 in a four-star formation is calculated by the following formula.

[0052]

[0053] Among them, X i =[x i y i z i ] T V represents the spacecraft's position information. i =[v xi vyi v zi ] T The velocity information of the spacecraft is represented as a 3D vector. The subscripts i = 1, 2, 3, 4 indicate the i-th spacecraft in the formation, and X... ci V represents the desired position of the spacecraft. ci This represents the desired velocity of the spacecraft. The subscript i has the same meaning and is calculated by the formula in step 1.

[0054] Step 2.2: Broadcasting Status Deviation Information

[0055] The i-th spacecraft in the spacecraft formation broadcasts its position and velocity deviation information via inter-satellite communication equipment.

[0056] Step 3: Calculation and broadcast of the desired rate of change of velocity

[0057] Step 3.1: Calculation of the desired rate of change of velocity

[0058] The i-th spacecraft in the spacecraft formation, while transmitting its own state deviation information, will simultaneously receive state deviation information transmitted by the j-th spacecraft. After receiving the state deviation information, the i-th spacecraft calculates its desired triaxial velocity change rate using the following formula.

[0059]

[0060] The parameters for the expected rate of change of velocity of the four satellites forming the formation are shown in the table below.

[0061] Table 2 Parameters of Expected Rate of Change of Velocity

[0062]

[0063] Step 3.2: Broadcasting the desired rate of change of velocity

[0064] The i-th spacecraft in the spacecraft formation broadcasts its desired rate of change of velocity information via inter-satellite communication equipment.

[0065] Step 4: Calculation and Execution of Control Variables

[0066] The i-th spacecraft in the spacecraft formation, while transmitting its own desired rate of change of velocity, will simultaneously receive the desired rate of change of velocity information transmitted by the j-th spacecraft. Upon receiving the information, the i-th spacecraft calculates its own desired triaxial acceleration rate of change using the following formula.

[0067]

[0068] Table 3 Parameters of Desired Rate of Change of Acceleration

[0069]

[0070] Finally, the three-axis control parameters of the i-th spacecraft can be calculated using the following formula:

[0071]

[0072] in, Let x, y, z be the derivative of the desired rate of change of velocity, and let k = x, y, z represent the three coordinate axes respectively.

[0073] The control quantity is converted into a control command for the actuator and output to the actuator. The conversion relationship varies depending on the actuator, which is not within the scope of this patent claim and therefore will not be described in detail.

[0074] Step 5: Control total time judgment

[0075] During the implementation of the control quantity, determine whether the predetermined reconfiguration completion time t has been reached. f If the target is not reached, repeat steps 2 to 5; if the target is reached, it means that the configuration has achieved consistent convergence and the control flow ends.

[0076] Assuming the actuators can perfectly reproduce the calculated control quantities, a digital simulation platform demonstrates that the 4-star formation achieved formation configuration convergence within 2000 seconds, consistent with the preset timing. For details, see [link to simulation]. Figure 3 The configuration convergence process of the first star in the formation, as follows: Figure 4-6 As shown. The convergence process of other satellite configurations within the formation is almost identical to that of the first satellite, and will not be described in detail here.

[0077] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0078] It will be apparent to those skilled in the art that the embodiments of the present invention are not limited to the details of the exemplary embodiments described above, and that the embodiments of the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the embodiments of the present invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the embodiments of the present invention is defined by the appended claims rather than the foregoing description. Therefore, all variations falling within the meaning and scope of equivalents of the claims are intended to be encompassed within the embodiments of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims. Furthermore, it is clear that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units, modules, or devices recited in the system, apparatus, or terminal claims may also be implemented by the same unit, module, or device through software or hardware. The terms "first," "second," etc., are used to indicate names and do not indicate any particular order.

[0079] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention and are not intended to limit them. Although the embodiments of the present invention have been described in detail with reference to the above preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the embodiments of the present invention should not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A spacecraft formation control method based on a predetermined time convergence strategy, characterized in that, include: Step S1: During the first inter-satellite communication, a spacecraft selects the corresponding configuration parameters and reconfiguration time according to the on-board plan and transmits them to other spacecraft in the formation for confirmation; Step S2: The spacecraft obtains its own position and velocity information in the inter-satellite relative coordinate system according to the on-board navigation system, and subtracts it from the expected position and velocity at that moment during the configuration reconstruction process; calculates the state deviation information including the position and velocity deviation of the spacecraft, and broadcasts its own state deviation information through the inter-satellite communication equipment; Step S3: While transmitting its own state deviation information, the spacecraft receives state deviation information transmitted by other spacecraft; calculates its own expected three-axis velocity change rate; and broadcasts its expected velocity change rate through inter-satellite communication equipment. Step S4: While broadcasting its own desired rate of change of velocity information, the spacecraft receives desired rate of change of velocity information from other spacecraft; and calculates its own desired triaxial acceleration rate of change. Step S5: The spacecraft determines whether the predetermined reconfiguration completion time has been reached. If it has not been reached, steps S2 to S5 are repeated. If it has been reached, it means that the configuration has achieved consistent convergence and the control process ends. Step S3 further includes: While transmitting its own state deviation information, the spacecraft also receives state deviation information from other spacecraft; after receiving the state deviation information, it calculates its desired triaxial velocity change rate using the following formula. in k = x, y, z represent the three coordinate axes, which are the spacecraft's position information X. i The specific form of the three-dimensional vector; i, j = 1, 2, ..., n; j ≠ i; i and j represent the i-th spacecraft and the j-th spacecraft in the formation, respectively; when the i-th spacecraft receives the state deviation information of the j-th spacecraft, that is, when there is information exchange between the two, a ij =1, otherwise a ij =0; α is the configuration pre-determined coefficient, n is the total number of spacecraft in the formation, η vki Custom coefficients for spacecraft, t f The predetermined reconstruction completion time is t, where t is the time for calculating the expected rate of change of velocity. Step S4 further includes: while transmitting its own desired rate of change of velocity information, the spacecraft in the spacecraft formation receives desired rate of change of velocity information transmitted by other spacecraft; and calculates its own desired triaxial acceleration rate of change according to the following formula. in, k = x, y, z represent the three coordinate axes; V' eki To calculate velocity, the formula for its three-dimensional vector is: This represents the three-dimensional vector form of the corresponding quantity; β is a predetermined coefficient, and i and j represent the i-th and j-th spacecraft in the formation, respectively; finally, the three-axis control quantity of the i-th spacecraft can be calculated by the following formula: in, Let γ be the derivative of the desired rate of change of velocity, k = x, y, z represent the three coordinate axes respectively, and γ be a predetermined coefficient.

2. The spacecraft formation control method based on a predetermined time convergence strategy as described in claim 1, characterized in that, In step S1, the satellites adopt a circular formation configuration in space, and their positions and velocities satisfy the following parametric equations: Where r is the formation radius, μ is the formation phase, and n is the circular orbital angular velocity of the formation reference spacecraft.

3. The spacecraft formation control method based on a predetermined time convergence strategy as described in claim 1 or 2, characterized in that, In step S2, the spacecraft's position deviation information and velocity deviation information, position deviation information X ei and speed deviation information V ei The specific calculation formula is as follows: Among them, X i V represents the spacecraft's position information. i The velocity information of the spacecraft is represented by a 3D vector, X. ci V represents the desired position of the spacecraft. ci Let i represent the desired velocity of the spacecraft, and let i represent the i-th spacecraft in the formation.

4. The spacecraft formation control method based on a predetermined time convergence strategy as described in claim 1, characterized in that, Step S5 further includes: the three-axis control quantity of the i-th spacecraft can be calculated by the following formula: in, Let x, y, z be the derivative of the desired rate of change of velocity, and let k = x, y, z represent the three coordinate axes respectively.

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