Multi-spacecraft cooperative rendezvous control method for communication time delay

Abstract

The invention discloses a communication delay-oriented multi-spacecraft cooperative rendezvous control method, which comprises the following steps of: firstly, respectively designing two delay state predictors for each follower spacecraft, and effectively solving the problem of transmission delay of output states between adjacent spacecrafts induced by communication bandwidth constraints; based on two time delay state predictors, designing a distributed composite state observer to perform real-time estimation on state information, control input, relative state of the observer and the leader and unknown sum disturbance of the leader; and a distributed cooperative rendezvous controller is designed by using an estimated output value of the distributed composite state observer, so that no-error tracking of the follower spacecraft on the state of the leader is realized while the total disturbance is inhibited, and cooperative rendezvous of the whole spacecraft cluster is realized. According to a cooperative control strategy proposed for a spacecraft cluster system, autonomous cooperative rendezvous of spacecraft clusters is realized by using less transmission information with time delay, and the method can be widely applied to other multi-agent formation cooperative systems.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft cluster cooperative control, and relates to a distributed cooperative control strategy and method for multiple spacecraft, particularly a multi-spacecraft cooperative rendezvous control method oriented towards communication delay. Background Technology

[0002] With the rapid advancement of modern aerospace technology, the functions of space systems in various countries have become increasingly powerful, finding widespread application in fields such as meteorological monitoring, scientific exploration, resource surveying, navigation and communication, military reconnaissance, and space warfare. While traditional single-satellite technology has been continuously improved and developed, it has also brought problems such as complex structures, long development cycles, high manufacturing and maintenance costs, and poor system reliability. To overcome the bottlenecks of single-satellite technology and meet the increasingly complex demands of space missions, countries have begun to explore and develop new satellite application models. This involves using multiple low-cost, simple, and short-development-cycle modular satellite structures to communicate and collaborate through inter-satellite communication networks to complete space missions. This not only compensates for the functional limitations of single satellites but also utilizes lightweight and flexible microsatellites to replace large and complex spacecraft, significantly increasing the scale and capabilities of the entire system. It provides a large measurement baseline and attack / defense area, greatly expanding the application scope and mission objectives, thus enabling efficient completion of space missions such as military security situation assessment, regional multi-dimensional positioning and target guidance, and space collaborative encirclement. Furthermore, modular spacecraft can achieve autonomous rendezvous in space through collaborative control, forming large spacecraft similar to space stations to perform complex space missions.

[0003] The key technology for autonomous rendezvous of modular spacecraft is the consensus and cooperative control of the swarm. Consistency refers to the convergence of the states of all modular spacecraft to the same position over time, thus enabling the swarm to combine. In recent years, due to the widespread application of swarm systems in practice, such as satellite attitude alignment, multi-robot formation, sensor network estimation, and power management in smart grids, the consensus problem of swarms has received increasing attention, and significant research results have been achieved. Moradi et al. proposed a sliding mode control protocol to achieve asymptotically robust consensus convergence for the leader-follower consensus problem of a time-delay linear variable parameter model; Liu et al. studied the consensus problem of nonlinear singular swarm systems with external disturbances, eliminating the impact of disturbances while achieving the consensus goal; Mohammadi et al. proposed a method for estimating position and velocity and used this method to design a control law for a nonlinear swarm system, ultimately achieving the leader-follower consensus goal; and He et al. designed a novel finite-time consensus protocol for the distributed consensus control problem of a second-order leaderless swarm with external bounded disturbances.

[0004] However, in achieving state consistency of spacecraft swarms in complex space environments, spacecraft nodes are not only affected by uncertainties such as internal propulsion systems and modeling errors, but also inevitably experience transmission delays due to the inherent bandwidth constraints of the network, which facilitates information exchange between spacecraft. This leads to system response lag and affects actual rendezvous operations. Furthermore, space network bandwidth is limited. Therefore, how to utilize as little communication information as possible to overcome the impact of transmission delays on system response speed while effectively suppressing the impact of uncertainties within and outside the spacecraft swarm on the accuracy of coordinated control, and to achieve real-time, high-precision autonomous rendezvous, is the key technical problem that this invention patent aims to solve and overcome. Summary of the Invention

[0005] Purpose of the invention: In order to overcome the above shortcomings, the purpose of this invention is to provide a multi-spacecraft cooperative rendezvous control method oriented towards communication delay. By utilizing as little communication information as possible with time delay, it is possible to achieve real-time estimation of all information of the leader and its own unmeasurable state, as well as active suppression of total disturbances, and finally realize the control strategy for cooperative rendezvous of spacecraft clusters to meet engineering applications.

[0006] Technical solution: In order to achieve the above objectives, the present invention provides a multi-spacecraft cooperative rendezvous control method for communication delay, characterized by the following steps: S1): Establishing a multi-spacecraft dynamics model under communication delay, considering cooperative rendezvous control between spacecraft during the model establishment process, including 1 leader and N followers; An undirected topology is proposed for this multi-spacecraft configuration. Used to indicate the communication relationships between spacecraft; in, Represents a set of nodes; Represents the set of edges; If two spacecraft are connected by an edge, they are considered adjacent spacecraft, and adjacent spacecraft can communicate with each other; edges in an undirected topology. Indicates cold weather and spacecraft Information can be exchanged between them; Represents the connection matrix, if ,but ,otherwise ; Due to the complexity of the space environment and the strong nonlinearity induced by state coupling and structural flexibility inherent in spacecraft, the system model of each follower is a nonlinear system containing unknown terms. The dynamics model of a follower is shown below: (1) In the formula, ; The distance of the virtual spacecraft relative to the Earth's center. and These represent the semi-major diameter and eccentricity of the reference orbit, respectively. For the tracker spacecraft orbital radius, The true anomaly angle of the reference orbit. is the Earth's gravitational constant. For the tracker spacecraft In the LVLH reference frame Position information on the coordinate axes To act on External disturbance forces along the coordinate axes, To be applied to Control forces along the coordinate axes; Define variables , , and ; Considering the communication delay between adjacent spacecraft, system (1) can be rewritten as: (2) In the formula, Indicates spacecraft The measurement output status; Indicates spacecraft Status information is transmitted to adjacent spacecraft j via a communication network; Indicates follower spacecraft The designed state observer monitors the leader's output state in The estimated value of the time; Indicates spacecraft Communication delay with spacecraft j; Indicates action on spacecraft The sum of disturbances; Assume the dynamic model of the leader spacecraft is as follows: (3) In the formula, This indicates the position information of the leader spacecraft on each coordinate axis in the LVLH reference frame; To act on External disturbance forces along the coordinate axes, To be applied to Control forces along the coordinate axes; Define variables , Similarly, considering the information transmission delay between the leader spacecraft and the adjacent follower spacecraft, system (3) can be rewritten as: (4) In the formula, Indicates the measurement output status of the leader spacecraft; This indicates that the leader spacecraft transmits information to its adjacent follower spacecraft via a communication network. Status information; Represents leader spacecraft and follower spacecraft Inter-communication latency; Indicates the control inputs of the leader spacecraft; This represents the sum of disturbances acting on the leader spacecraft; Let the state tracking error variable of the i-th follower spacecraft relative to the leader be: , Combining equations (2) and (4), the tracking error system between the i-th follower spacecraft and the leader spacecraft can be obtained as follows: (5); S2): Design a delay state predictor for the first... The follower spacecraft is designed with two time-delay state predictors, S21): First, in order to predict the follower spacecraft's state... exist To estimate the leader's output state at any given time, a time-delay state predictor is designed, as follows: (6) Among them, Indicates the first A follower spacecraft in The estimated value of the leader's output state at any given time; For the first A follower spacecraft in relation to the leader's state The estimated value; The output value of the delay state predictor is the first one, i.e., the first... A follower spacecraft exist The predicted value of the leader's output state estimate at any given time; S22): Secondly, follower spacecraft In order to predict To determine the output state of the leader at any given time, design a delay state predictor 2, which takes the following form: (7) In the formula, The output value of the second delay state predictor, i.e., the first... A follower spacecraft in The predicted value of the leader's output status at any given time; S3): Design a distributed cooperative rendezvous control strategy: First, obtain the leader's state information; second, overcome the influence of unknown nonlinear terms in the follower's own system on tracking accuracy. Therefore, based on the time-delay state predictor 1 and time-delay state predictor 2 in S2), a novel distributed cooperative rendezvous control strategy is designed, as follows: For the first... A distributed composite state observer is designed for a follower spacecraft, and its specific form is as follows: (8) In the formula, Indicates the first A follower spacecraft in relation to the leader's state The estimated value; Indicates the first Follower spacecraft and leader tracking error status The estimated value; , All parameters are adjustable; Indicates the first The error of a follower spacecraft's state estimate to the leader compared to its neighboring spacecraft. Indicates the first The tracking error of a follower spacecraft in relation to the leader's output state; No. A follower spacecraft only utilizes the spacecraft adjacent to it. Estimates of the leader's output state and the leader's output status This allows for the monitoring of the leader's state. and the relative error state with respect to the leader Real-time estimation; To achieve autonomous rendezvous between the follower and leader spacecraft, a distributed cooperative rendezvous controller of the following form is designed using the output value of the distributed composite observer of the i-th follower spacecraft: (9) In the formula, This refers to the adjustable gain parameter of the controller; This represents the expected value of the relative information between the i-th follower spacecraft and the leader spacecraft.

[0007] Therefore, under the above control strategy, the original nonlinear tracking error system between each follower spacecraft and the leader will be transformed into a linear dynamic system, which effectively suppresses the influence of the total disturbance on the system and ultimately achieves that each tracking error state tends to zero, thus realizing real-time cooperative rendezvous control between multiple spacecraft.

[0008] The multi-spacecraft cooperative rendezvous control method for communication delay described in this invention, in step S2) Represents the total disturbance acting on spacecraft i, where .

[0009] In S2) of the present invention Represents the sum of perturbations acting on the leader spacecraft, where: .

[0010] As can be seen from the above technical solution, the present invention has the following beneficial effects: 1. The multi-spacecraft cooperative rendezvous control method for communication delay described in this invention designs two delay state predictors. By utilizing the delay information transmitted between adjacent spacecraft j and the leader, as well as the velocity level state information output by spacecraft i's own observer, the method predicts in real time the estimated value of the output state of spacecraft j adjacent to spacecraft i and the actual output state of the leader.

[0011] 2. This invention also designs a distributed autonomous cooperative rendezvous control strategy, which uses only the estimated value of the leader's output state by the adjacent spacecraft j and the leader's actual output state to estimate all states of the leader and the tracking error state, and feedforward compensation to suppress the influence of the sum disturbance on the rendezvous accuracy. Attached Figure Description

[0012] Figure 1 This is a flowchart of a multi-spacecraft cooperative rendezvous control method for communication delay according to the present invention; Figure 2 This is a block diagram of the multi-spacecraft cooperative rendezvous control strategy for communication delay in this invention; Figure 3 This is a diagram of the undirected topology for inter-spacecraft communication in this invention. Figure 4 This is a curve showing the state change of a spacecraft cluster along the X-axis under the influence of the design scheme of this invention. Figure 5 This is the control input variation curve of the spacecraft cluster in the X-axis direction under the action of the design scheme of this invention; Figure 6 This is a curve showing the state change of the spacecraft cluster along the X-axis when the time delay state predictor is ignored in this invention. Detailed Implementation

[0013] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0014] Example 1 like Figure 1 The method for multi-spacecraft cooperative rendezvous control oriented to communication delay includes the following steps: S1): Establish a multi-spacecraft dynamics model under communication delay. The model establishment process considers the cooperative rendezvous control between spacecraft, including 1 leader and N followers; An undirected topology is proposed for this multi-spacecraft configuration. Used to indicate the communication relationships between spacecraft; in, Represents a set of nodes; Represents the set of edges; If two spacecraft are connected by an edge, they are considered adjacent spacecraft, and adjacent spacecraft can communicate with each other; edges in an undirected topology. Indicates cold weather and spacecraft Information can be exchanged between them; Represents the connection matrix, if ,but ,otherwise Furthermore, follower spacecraft adjacent to the leader can obtain the leader's output state, but the leader cannot obtain the follower spacecraft's state information. When adjacent to the leader ,otherwise .

[0015] Due to the complexity of the space environment and the strong nonlinearity induced by state coupling and structural flexibility inherent in spacecraft, the system model of each follower is a nonlinear system containing unknown terms. The dynamics model of a follower is shown below: (1) In the formula, ; The distance of the virtual spacecraft relative to the Earth's center. and These represent the semi-major diameter and eccentricity of the reference orbit, respectively. For the tracker spacecraft orbital radius, The true anomaly angle of the reference orbit. is the Earth's gravitational constant. For the tracker spacecraft In the LVLH reference frame Position information on the coordinate axes To act on External disturbance forces along the coordinate axes, To be applied to Control forces along the coordinate axes; Define variables , , and ; Considering the communication delay between adjacent spacecraft, system (1) can be rewritten as: (2) In the formula, Indicates spacecraft The measurement output status; Indicates spacecraft Status information is transmitted to adjacent spacecraft j via a communication network; Indicates follower spacecraft The designed state observer monitors the leader's output state in The estimated value of the time; Indicates spacecraft Communication delay with spacecraft j; Indicates action on spacecraft The sum of disturbances; in .

[0016] Assume the dynamic model of the leader spacecraft is as follows: (3) In the formula, This indicates the position information of the leader spacecraft on each coordinate axis in the LVLH reference frame; To act on External disturbance forces along the coordinate axes, To be applied to Control forces along the coordinate axes; Define variables , Similarly, considering the information transmission delay between the leader spacecraft and the adjacent follower spacecraft, system (3) can be rewritten as: (4) In the formula, Indicates the measurement output status of the leader spacecraft; This indicates that the leader spacecraft transmits information to its adjacent follower spacecraft via a communication network. Status information; Represents leader spacecraft and follower spacecraft Inter-communication latency; Indicates the control inputs of the leader spacecraft; This represents the sum of perturbations acting on the leader spacecraft; where: Let the first The state tracking error variable of each follower spacecraft relative to the leader: , Combining equations (2) and (4), we can obtain the first... The tracking error system between the follower spacecraft and the leader is shown below: (5); S2): Design a delay state predictor for the first... The follower spacecraft is designed with two time-delay state predictors, S21): First, in order to predict the follower spacecraft's state... exist To estimate the leader's output state at any given time, a time-delay state predictor is designed, as follows: (6) Among them, Indicates the first A follower spacecraft in The estimated value of the leader's output state at any given time; For the first A follower spacecraft in relation to the leader's state The estimated value; The output value of the delay state predictor is the first one, i.e., the first... A follower spacecraft exist The predicted value of the leader's output state estimate at any given time; S22): Secondly, follower spacecraft In order to predict To determine the output state of the leader at any given time, design a delay state predictor 2, which takes the following form: (7) In the formula, The output value of the second delay state predictor, i.e., the first... A follower spacecraft in The predicted value of the leader's output status at any given time; S3): Design a distributed cooperative rendezvous control strategy: First, obtain the leader's state information; second, overcome the influence of unknown nonlinear terms in the follower's own system on tracking accuracy. Therefore, based on the time-delay state predictor 1 and time-delay state predictor 2 in S2), a novel distributed cooperative rendezvous control strategy is designed, as follows: For the first... A distributed composite state observer is designed for a follower spacecraft, and its specific form is as follows: (8) In the formula, Indicates the first A follower spacecraft in relation to the leader's state The estimated value; Indicates the first Follower spacecraft and leader tracking error status The estimated value; , All parameters are adjustable; Indicates the first The error of a follower spacecraft's state estimate to the leader compared to its neighboring spacecraft. Indicates the first The tracking error of a follower spacecraft in relation to the leader's output state; No. A follower spacecraft only utilizes the spacecraft adjacent to it. Estimates of the leader's output state and the leader's output status This allows for the monitoring of the leader's state. and the relative error state with respect to the leader Real-time estimation; To achieve autonomous rendezvous between the follower and leader spacecraft, utilizing the... Based on the output values ​​of a distributed composite observer for a follower spacecraft, design a distributed cooperative rendezvous controller of the following form: (9) In the formula, This refers to the adjustable gain parameter of the controller; Indicates the first The expected value of relative information between a follower spacecraft and a leader spacecraft.

[0017] Example 2 This embodiment is the same as the multi-spacecraft cooperative rendezvous control method for communication delay in Embodiment 1.

[0018] The following example illustrates the autonomous rendezvous control among six spacecraft, including one leader and five follower spacecraft.

[0019] This embodiment presents a multi-spacecraft cooperative rendezvous control method oriented towards communication delay, comprising the following steps: S1): Establish a multi-spacecraft dynamics model under communication delay. The model establishment process considers the cooperative rendezvous control between spacecraft, including 1 leader and N followers. An undirected topology is proposed for this multi-spacecraft configuration. Used to indicate the communication relationships between spacecraft; in, Represents a set of nodes; Represents the set of edges; If two spacecraft are connected by an edge, they are considered adjacent spacecraft, and adjacent spacecraft can communicate with each other; edges in an undirected topology. Indicates cold weather and spacecraft Information can be exchanged between them; Represents the connection matrix, if ,but ,otherwise Furthermore, follower spacecraft adjacent to the leader can obtain the leader's output state, but the leader cannot obtain the follower spacecraft's state information. When adjacent to the leader ,otherwise .

[0020] The undirected topology among the five follower spacecraft is as follows: Figure 3 As shown, the connection matrix can be obtained. ,and , .

[0021] Due to the complexity of the space environment and the strong nonlinearity induced by state coupling and structural flexibility inherent in spacecraft, the system model of each follower is a nonlinear system containing unknown terms. The dynamics model of a follower is shown below: (1) In the formula, ; The distance of the virtual spacecraft relative to the Earth's center. and These represent the semi-major diameter and eccentricity of the reference orbit, respectively. For the tracker spacecraft orbital radius, The true anomaly angle of the reference orbit. is the Earth's gravitational constant. For the tracker spacecraft In the LVLH reference frame Position information on the coordinate axes To act on External disturbance forces along the coordinate axes, To be applied to Control forces along the coordinate axes; Define variables , , and ; Considering the communication delay between adjacent spacecraft, system (1) can be rewritten as: (2) In the formula, Indicates spacecraft The measurement output status; Indicates spacecraft Status information is transmitted to adjacent spacecraft j via a communication network; Indicates follower spacecraft The designed state observer monitors the leader's output state in The estimated value of the time; Indicates spacecraft Communication delay with spacecraft j; Indicates action on spacecraft The sum of disturbances; in .

[0022] Assume the dynamic model of the leader spacecraft is as follows: (3) In the formula, This indicates the position information of the leader spacecraft on each coordinate axis in the LVLH reference frame; To act on External disturbance forces along the coordinate axes, To be applied to Control forces along the coordinate axes; Define variables , Similarly, considering the information transmission delay between the leader spacecraft and the adjacent follower spacecraft, system (3) can be rewritten as: (4) In the formula, Indicates the measurement output status of the leader spacecraft; This indicates that the leader spacecraft transmits information to its adjacent follower spacecraft via a communication network. Status information; Represents leader spacecraft and follower spacecraft Inter-communication latency; Indicates the control inputs of the leader spacecraft; This represents the sum of perturbations acting on the leader spacecraft; where: In this example, the eccentricity is set to... , The initial state of the spacecraft is set as follows: , External interference is set as follows: .

[0023] Let the first The state tracking error variable of each follower spacecraft relative to the leader: , Combining equations (2) and (4), we can obtain the first... The tracking error system between the follower spacecraft and the leader is shown below: (5); The purpose is to allow the follower spacecraft Achieve autonomous rendezvous and docking with the leader spacecraft, i.e., track error status. It approaches zero.

[0024] S2): Design a delay state predictor for the first... The follower spacecraft is designed with two time-delay state predictors, S21): First, in order to predict the follower spacecraft's state... exist To estimate the leader's output state at any given time, a time-delay state predictor is designed, as follows: (6) Among them, Indicates the first A follower spacecraft in The estimated value of the leader's output state at any given time; For the first A follower spacecraft in relation to the leader's state The estimated value; The output value of the delay state predictor is the first one, i.e., the first... A follower spacecraft exist The predicted value of the leader's output state estimate at any given time; In this embodiment, a transmission delay is assumed. ; S22): Secondly, follower spacecraft In order to predict To determine the output state of the leader at any given time, design a delay state predictor 2, which takes the following form: (7) In the formula, The output value of the second delay state predictor, i.e., the first... A follower spacecraft in The predicted value of the leader's output state at any given time; in this embodiment, a transmission delay is assumed. ; S3): Design a distributed cooperative rendezvous control strategy: First, obtain the leader's state information; second, overcome the influence of unknown nonlinear terms in the follower's own system on tracking accuracy. Therefore, based on the time-delay state predictor 1 and time-delay state predictor 2 in S2), a novel distributed cooperative rendezvous control strategy is designed, as follows: For the first... A distributed composite state observer is designed for a follower spacecraft, and its specific form is as follows: (8) In the formula, Indicates the first A follower spacecraft in relation to the leader's state The estimated value; Indicates the first Follower spacecraft and leader tracking error status The estimated value; , All parameters are adjustable; Indicates the first The error of a follower spacecraft's state estimate to the leader compared to its neighboring spacecraft. Indicates the first The tracking error of a follower spacecraft in relation to the leader's output state; In this example, the adjustable gain parameter is set to... .

[0025] No. A follower spacecraft only utilizes the spacecraft adjacent to it. Estimates of the leader's output state and the leader's output status This allows for the monitoring of the leader's state. and the relative error state with respect to the leader Real-time estimation; To achieve autonomous rendezvous between the follower and leader spacecraft, utilizing the... Based on the output values ​​of a distributed composite observer for a follower spacecraft, design a distributed cooperative rendezvous controller of the following form: (9) In the formula, This refers to the adjustable gain parameter of the controller; Indicates the first The expected value of relative information between a follower spacecraft and a leader spacecraft.

[0026] In this example, the adjustable gain parameter of the controller is assumed to be... Expected value of relative information between follower and leader spacecraft .

[0027] Under the aforementioned control strategy, the original nonlinear tracking error system between each follower spacecraft and the leader will be transformed into a linear dynamic system, which effectively suppresses the influence of the total disturbance on the system and ultimately achieves that each tracking error state approaches zero, thus realizing real-time cooperative rendezvous control among multiple spacecraft.

[0028] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0029] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A multi-spacecraft cooperative rendezvous control method oriented towards communication delay, characterized in that: include: The following steps are taken: S1): Establish a multi-spacecraft dynamics model under communication delay. During the model establishment process, the cooperative rendezvous control between spacecraft is considered, including 1 leader and N followers; No. The dynamics model of a follower is shown below: （1） In the formula, , , , , ; The distance of the virtual spacecraft relative to the Earth's center. and These represent the semi-major diameter and eccentricity of the reference orbit, respectively. The orbital radius of the tracker spacecraft, The true anomaly angle of the reference orbit. is the Earth's gravitational constant. For the tracker spacecraft in the LVLH reference frame Position information on the coordinate axes To act on External disturbance forces along the coordinate axes, To be applied to Control forces along the coordinate axes; Define variables , , and ; Considering the communication delay between adjacent spacecraft, system (1) can be rewritten as: （2） In the formula, Indicates spacecraft The measurement output status; Indicates spacecraft Transmitted to adjacent spacecraft via communication network Status information; Indicates follower spacecraft The designed state observer monitors the leader's output state in The estimated value of the time; Indicates spacecraft With spacecraft Inter-communication latency; Indicates action on spacecraft The sum of disturbances; Assume the dynamic model of the leader spacecraft is as follows: （3） In the formula, This indicates the position information of the leader spacecraft on each coordinate axis in the LVLH reference frame; To act on External disturbance forces along the coordinate axes, To be applied to Control forces along the coordinate axes; Define variables , Similarly, considering the information transmission delay between the leader spacecraft and the adjacent follower spacecraft, system (3) can be rewritten as: （4） In the formula, Indicates the measurement output status of the leader spacecraft; This indicates that the leader spacecraft transmits information to its adjacent follower spacecraft via a communication network. Status information; Represents leader spacecraft and follower spacecraft Inter-communication latency; Indicates the control inputs of the leader spacecraft; This represents the sum of disturbances acting on the leader spacecraft; Let the first The state tracking error variable of each follower spacecraft relative to the leader: ， Combining equations (2) and (4), we can obtain the first... The tracking error system between the follower spacecraft and the leader is shown below: （5）； S2): Design a delay state predictor for the first... The follower spacecraft is designed with two time-delay state predictors, S21): First, in order to predict the follower spacecraft's state... exist To estimate the leader's output state at any given time, a time-delay state predictor is designed, as follows: (6); in, Indicates the first A follower spacecraft in The estimated value of the leader's output state at any given time; For the first A follower spacecraft in relation to the leader's state The estimated value; The output value of the delay state predictor is the first one, i.e., the first... A follower spacecraft exist The predicted value of the leader's output state estimate at any given time; S22): Secondly, follower spacecraft In order to predict To determine the output state of the leader at any given time, design a delay state predictor 2, which takes the following form: （7） In the formula, The output value of the second delay state predictor, i.e., the first... A follower spacecraft in The predicted value of the leader's output status at any given time; S3): Design a distributed cooperative rendezvous control strategy: First, obtain the leader's state information; second, overcome the influence of unknown nonlinear terms in the follower's own system on tracking accuracy. Therefore, based on the time-delay state predictor 1 and time-delay state predictor 2 in S2), a novel distributed cooperative rendezvous control strategy is designed, as follows: For the first... A distributed composite state observer is designed for a follower spacecraft, and its specific form is as follows: （8） In the formula, Indicates the first A follower spacecraft in relation to the leader's state The estimated value; Indicates the first Follower spacecraft and leader tracking error status The estimated value; , All parameters are adjustable; Indicates the first The error of a follower spacecraft's state estimate to the leader compared to its neighboring spacecraft. Indicates the first The tracking error of a follower spacecraft in relation to the leader's output state; No. A follower spacecraft only utilizes the spacecraft adjacent to it. Estimates of the leader's output state and the leader's output status This allows for the monitoring of the leader's state. and the relative error state with respect to the leader Real-time estimation; To achieve autonomous rendezvous between the follower and leader spacecraft, utilizing the... Based on the output values ​​of a distributed composite observer for a follower spacecraft, design a distributed cooperative rendezvous controller of the following form: (9) In the formula, This refers to the adjustable gain parameter of the controller; Indicates the first The expected value of relative information between a follower spacecraft and a leader spacecraft.

2. The multi-spacecraft cooperative rendezvous control method for communication delay as described in claim 1, characterized in that: In the process of establishing the multi-spacecraft dynamics model under communication delay in S1), an undirected topology is given for the multi-spacecraft. Used to indicate the communication relationships between spacecraft; in, Represents a set of nodes; Represents the set of edges; If two spacecraft are connected by an edge, they are considered adjacent spacecraft, and adjacent spacecraft can communicate with each other; edges in an undirected topology. Indicates cold weather and spacecraft Information can be exchanged between them; Represents the connection matrix, if ,but ,otherwise .

3. The multi-spacecraft cooperative rendezvous control method for communication delay as described in claim 1, characterized in that: In S2) Indicates action on spacecraft The sum of disturbances, where: 。 4. The multi-spacecraft cooperative rendezvous control method for communication delay as described in claim 1, characterized in that: In S2) Represents the sum of perturbations acting on the leader spacecraft, where: 。

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