Spacecraft formation flying control method using null space projection behavior method

Abstract

This invention proposes a spacecraft formation flight control method utilizing the null-space projection behavior method. First, a spacecraft formation dynamics model and its communication topology network model are established, and control target levels are defined. Second, a desired trajectory is generated based on the null-space behavior control method. Considering mass uncertainty, actuator saturation, and external disturbances, a controller is designed to track the generated desired trajectory. This invention monitors the relative positions and velocities between spacecraft in real time, adjusts the control inputs of each spacecraft, ensures the connectivity of the communication network is not disrupted, avoids collisions with obstacles and other spacecraft, and can achieve the desired configuration of the spacecraft formation according to mission requirements, improving mission efficiency and accuracy. Simultaneously, considering complex environmental factors such as mass uncertainty, actuator saturation, and external disturbances, it achieves efficient, safe, and autonomous control of spacecraft formation flight.

Description

Technical Field

[0001] This invention relates to the field of spacecraft formation control technology, specifically to the use of the null-space projection behavior method to achieve distributed cooperative control of spacecraft formations under communication distance and collision avoidance constraints. Background Technology

[0002] Spacecraft Formation Flying (SFF), as an advanced space technology, has received widespread attention in recent years due to its significant advantages in improving mission flexibility, reliability, and efficiency. SFF is widely used in various fields such as synthetic aperture radar, gravity field detection, space interferometry, and distributed satellite systems. However, with the increasing size of spacecraft formations and the growing complexity of missions, how to achieve effective coordinated control among spacecraft has become a pressing issue.

[0003] In spacecraft formation control, maintaining communication network connectivity, avoiding collisions between spacecraft, and achieving the desired formation configuration are the three core challenges. Traditional control methods, such as virtual structures, pilot-follower methods, and potential function methods, have solved these problems to some extent, but they are inadequate when dealing with complex interactions between multiple spacecraft and adapting to dynamically changing environments.

[0004] In recent years, null-space-based behavioral control methods have been increasingly applied to spacecraft formation control due to their unique advantages in handling multi-task coordinated control problems. Null-space behavioral control methods decompose complex control tasks into multiple sub-tasks, design corresponding behavioral controllers for each sub-task, and then use null-space projection technology to project the velocity components of low-priority tasks into the null space of high-priority tasks, thereby avoiding velocity conflicts and achieving coordinated control between multiple tasks. For example, Chinese patent application CN116280269A discloses an integrated control method for multi-spacecraft formation systems based on predictive behavioral control. This method feeds back the predictive information from the lower-level controllers to the upper-level planning layer. Through null-space behavioral control and model predictive control, it extends traditional single-step planning to multi-step prediction, optimizes future trajectories, and improves spacecraft safety and control objective achievement. However, this method only considers the global tasks of formation maintenance and movement, as well as the local tasks of obstacle avoidance. The tasks are relatively simple, and it cannot cope with complex environmental factors such as mass uncertainty, actuator saturation, and external disturbances. Summary of the Invention

[0005] To address the problems of existing technologies, this invention proposes a spacecraft formation flight control method utilizing the null-space projection behavior method. This method comprehensively solves the problems of maintaining connectivity, obstacle avoidance, and formation configuration control during spacecraft formation flight. By real-time monitoring of the relative positions and velocities between spacecraft, the control inputs of each spacecraft are adjusted to ensure that the connectivity of the communication network is not disrupted, while avoiding collisions with obstacles (including other spacecraft). Furthermore, it can achieve the desired configuration of the spacecraft formation according to mission requirements, improving mission efficiency and accuracy. Simultaneously, considering complex environmental factors such as mass uncertainty, actuator saturation, and external disturbances, this method achieves efficient, safe, and autonomous control of spacecraft formation flight.

[0006] The technical solution of this invention is as follows:

[0007] A spacecraft formation flight control method utilizing the zero-space projection behavior method includes the following steps:

[0008] Step 1: Establish a dynamic model of the spacecraft formation and its communication topology network model, and divide the control target hierarchy;

[0009] Step 2: Generate the desired trajectory based on the null space behavior control method; including the following process:

[0010] Step 2.1: Design three subtasks: connectivity maintenance, obstacle avoidance, and formation configuration, and calculate the expected speed for each subtask:

[0011] Build obstacle avoidance tasks and generate speed:

[0012] Design an obstacle avoidance task function. in Define the location of the nearest obstacle or other spacecraft to spacecraft i, and set the desired obstacle avoidance task function σ. i,od The error was obtained.

[0013] Generation repulsion rate Where k o To increase collision avoidance gain, J i,o The Jacobian matrix corresponding to the obstacle avoidance task;

[0014] Construct a connectivity-preserving task:

[0015] Design a connectivity-maintaining task function. in Set the location of the farthest spacecraft in the neighborhood set of spacecraft i, and define the desired connectivity-preserving task function σ. i,cd The error was obtained.

[0016] Generation attraction speed Where k cTo maintain connectivity gain, J i,c To maintain connectivity, the Jacobian matrix corresponding to the task is preserved;

[0017] Constructing distributed formation configuration tasks:

[0018] Design spacecraft formation configuration mission functions:

[0019]

[0020] And set the desired spacecraft formation configuration mission function σ f,d The error is then defined as follows:

[0021] Formation configuration generation speed Where K f =k f I 3n Let k be the gain matrix. f For formation configuration gain, J f The Jacobian matrix corresponding to the configuration task;

[0022] Step 2.2: Project the velocity of the low-priority task onto the null space of the high-priority task through null space projection, and generate the final desired trajectory;

[0023] Step 3: Considering quality uncertainty, actuator saturation and external disturbances, track the desired trajectory generated in Step 2 through controller design.

[0024] Furthermore, in step 1, the spacecraft formation dynamics model is as follows:

[0025]

[0026] Where m i For the mass of spacecraft i, C i D is the orbital coefficient matrix. i Let n be the position coupling matrix. i For nonlinear gravitational terms, d i For external interference, f i p is the control force vector of the i-th spacecraft; i Let be the position vector of the i-th spacecraft in the relative coordinate system.

[0027] Furthermore, in step 1, the communication topology network model of the spacecraft formation is a dynamic graph created based on the distances between the spacecraft.

[0028] in Let n be the vertex set, and n be the number of spacecraft in the spacecraft formation.

[0029] ε(t) is a dynamically changing set of edges. For an edge (i,j) consisting of spacecraft i and j, if the distance between spacecraft i and j is ||p ij (t)||at (δ) i Within the interval of ,Δ), ​​then (i,j)∈ε(t), where δ i The minimum distance between spacecraft i and obstacles and other spacecraft is set, and Δ is the maximum communication range set; otherwise... The adjacency matrix has the following elements:

[0030]

[0031] Furthermore, in step 1, the control objectives are divided into four levels:

[0032] 1) If the initial distance satisfies ||p ij (0)||<Δ-∈, then maintain throughout the control process

[0033]

[0034] Where ∈ represents the set minimum value;

[0035] 2) All spacecraft maintain distance from obstacles and other spacecraft. as well as

[0036] ||p ij (t)||>δ i ,i∈{1,2,...,n},j∈{1,2,...,N};

[0037] 3) The distance between spacecraft i and j asymptotically converges to the expected value d. ij ;

[0038] 4) The speed of all spacecraft eventually approaches zero.

[0039] Furthermore, in step 2.1, σ is taken. i,od =δ i , σ i,cd =Δ

[0040] Furthermore, in step 2.1, take The unit vector pointing the spacecraft to the nearest obstacle:

[0041]

[0042] Pick Here is a unit vector pointing to the farthest neighbor:

[0043]

[0044] Pick L is the Laplacian matrix corresponding to the dynamic graph.

[0045] Furthermore, in step 2.2, the obstacle avoidance task projection matrix is ​​first defined. The attraction velocity of the connectivity preservation task is projected onto the null space of the obstacle avoidance task; secondly, a joint projection matrix for the safety task is defined. Projecting formation mission velocity into the safe mission null space, where Finally, generate conflict-free expected velocity commands. in For formation configuration speed The configuration velocity corresponding to spacecraft i is determined to ensure obstacle avoidance is prioritized, connectivity is secondary, and configuration is the last priority. The desired trajectory is obtained by integrating the generated conflict-free expected velocity command with the initial position.

[0046] Furthermore, the specific process of step 3 is as follows: Based on the desired trajectory generated in step 2, combined with sliding mode control, anti-saturation compensation, and online parameter estimation, the desired trajectory is tracked.

[0047] Step 3.1: Design the sliding surface and smooth the desired trajectory:

[0048] Define the sliding surface:

[0049]

[0050] In the formula: β>0 is the convergence rate parameter, For position tracking error, For reference speed;

[0051] Step 3.2: Dynamically compensate for saturation and suppress error integrals:

[0052] Design an anti-saturation compensation term q to address actuator saturation constraints. i Its dynamic equation is:

[0053]

[0054] In the formula: The deviation between the actual control force and the virtual control force, γ0 > 0 is used to adjust the compensation rate;

[0055] Step 3.3: Adaptive quality estimation and integrated controller design to track the desired trajectory generated in Step 2:

[0056] The virtual control force is designed as follows:

[0057]

[0058] In the formula: K is a mass-independent dynamic term. i,p and K i,d The gain matrix is ​​symmetric positive definite, and the sliding mode term is -(γ1+γ2)sgn(s i ) used to counteract external disturbances d i quality parameters Online updates via projective adaptive laws:

[0059]

[0060] In the formula: To estimate the error, γ3 > 0 controls the learning rate, and γ4 > 0 suppresses parameter drift.

[0061] Furthermore, in step 3.1, a first-order low-pass filter is introduced.

[0062]

[0063] The equivalent acceleration estimate is obtained by smoothing the reference signal by adjusting the time constant ρ << 1. Thus constraining the upper bound of acceleration

[0064] Beneficial effects

[0065] Compared with the prior art, the beneficial effects of the present invention are:

[0066] 1) This invention designs connectivity-maintaining behavior to enable spacecraft to monitor and adjust their relative positions in real time during formation flight, ensuring that the connectivity of the communication map is not disrupted, thereby guaranteeing the reliability and real-time performance of information transmission and improving the stability and safety of formation flight.

[0067] 2) Existing methods mostly focus on the control of a single task (such as maintaining connectivity or obstacle avoidance). This invention introduces the concept of zero space into spacecraft formation control, realizes coordinated control between multiple tasks, avoids speed conflicts, and improves the overall efficiency of spacecraft formation flight.

[0068] 3) The distributed adaptive controller designed in this invention can adapt to dynamically changing environments by adjusting control parameters, thereby improving the robustness and adaptability of the system and enabling spacecraft formations to be adapted to more complex and changeable space environments.

[0069] 4) By clearly defining the priority of each sub-task and generating conflict-free expected trajectories accordingly, this invention ensures the priority execution of high-priority tasks, realizes orderly coordination and control among multiple tasks, and improves the intelligence level of spacecraft formation flight.

[0070] This invention provides new insights and references for the verification and experimentation of flight control for Chinese spacecraft formations, and is easy to promote and use.

[0071] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0072] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0073] Figure 1 This is a diagram illustrating safe distances and communication maintenance for spacecraft.

[0074] Figure 2 This is a schematic diagram of the inter-spacecraft communication topology network in a specific embodiment;

[0075] Figure 3 This is a comparison of the spacecraft distances in a specific embodiment with and without considering connectivity maintenance tasks; (a) without connectivity maintenance, (b) with connectivity maintenance.

[0076] Figure 4 The images show a comparison of the distances between spacecraft and obstacles in specific embodiments, considering and not considering connectivity maintenance tasks; (a) without connectivity maintenance, (b) with connectivity maintenance.

[0077] Figure 5 These are trajectory diagrams of spacecraft formation flight missions with and without considering connectivity maintenance tasks in specific embodiments; (a) without connectivity maintenance, (b) with connectivity maintenance. Detailed Implementation

[0078] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0079] This embodiment provides a spacecraft formation flight control method utilizing the null-space projection behavior method, systematically solving the problems of connectivity maintenance, obstacle avoidance, and formation configuration control in spacecraft formation flight. The method first decomposes the spacecraft formation task into three sub-tasks and designs corresponding behavior controllers for each. Through null-space projection technology, velocity conflicts between different tasks are effectively avoided, generating conflict-free desired trajectories. Furthermore, a distributed adaptive controller is designed to track these desired trajectories, fully considering complex environmental factors such as mass uncertainty, actuator saturation, and external disturbances, ensuring the robustness and adaptability of the controller, and providing a reliable and valuable reference scheme for spacecraft formation control. Specific steps include:

[0080] Step 1: Establish a spacecraft formation dynamics model and its communication topology network model, and divide the control target hierarchy:

[0081] Step 1.1: Establish a spacecraft formation dynamics model:

[0082] First, establish a relative coordinate system for the spacecraft formation flight, assuming a reference spacecraft orbiting in an elliptical orbit. Then... The origin of the relative coordinate system is located at the center of mass of the reference spacecraft. X r The axis extends from the Earth's center to the reference spacecraft's center of mass, Z. r The axis is parallel to the orbital angular momentum vector, Y r The axis is obtained using the right-hand rule.

[0083] Based on a relative coordinate system, consider a system with n rigid spacecraft. Let p represent the position vector of spacecraft i in the relative coordinate system, where i = 1, ..., n. Also, let p represent the Nn obstacles. i Let i = n+1,...,N. The dynamic model of the spacecraft formation can be described as follows:

[0084]

[0085] Where: m i For the mass of spacecraft i, C i It is the orbital coefficient matrix, D i It is the position coupling matrix, n i For nonlinear gravitational terms, d i For external interference, f i It is the control force vector of the i-th spacecraft.

[0086] Furthermore, assuming the disturbance d i Given an unknown bounded environment, the saturation constraint of the actuator is set as follows:

[0087]

[0088] f i,j Let the actuator of spacecraft i be the control force component in dimension j. The upper bound of the control force of the actuator in dimension j is defined. Let be the virtual control force component of the actuator of spacecraft i in dimension j.

[0089] Step 1.2: Construct a communication topology network model:

[0090] Describe the communication graph between spacecraft using graph theory:

[0091] Traditional picture It is an ordered triple From a set of vertices An edge set ε and an adjacency matrix Composition. A vertex represents a spacecraft, and an edge represents a communication link between two spacecraft. An edge (i,j) is in ε if and only if spacecraft i can obtain the state of spacecraft j. In this case, spacecraft i and j are considered adjacent, and the neighborhood set of spacecraft i is defined as... If for any edge This is called an undirected graph. In the diagram, a path of length M consists of a series of distinct vertices i0, i1, ..., i... M Given that for all k = 0, 1, ..., M-1, these vertices are in ε, and (i k i k+1 In ε. If in In an undirected graph, there is a path between every pair of vertices. This is called a connected graph. The adjacency matrix... Defined as: if (i,j) is in the range, then a ij =1, otherwise a ij =0. Laplace matrix The definition of is:

[0092]

[0093] In this embodiment, a dynamic graph is created based on the distance between spacecraft. The distance between spacecraft i and j is represented by ||p ij (t)|| indicates that in (δ) i Within the interval of ,Δ), ​​then (i,j)∈ε(t), where δ i Let Δ be the minimum distance between spacecraft i and obstacles (including other spacecraft), and let Δ be the maximum communication range. If the distance is outside this range, then... Communication links can also be used Adjacency matrix in Represented as:

[0094]

[0095] Step 1.3: Divide the control target levels:

[0096] The control objectives are clearly divided into four levels:

[0097] 1) If the initial distance satisfies ||p ij (0)||<Δ-∈, then maintain throughout the control process

[0098]

[0099] Where ∈ is a set minimum value, for example, 10. -3 ;

[0100] 2) All spacecraft maintain distance from obstacles and other spacecraft. as well as

[0101] ||p ij (t)||>δ i ,i∈{1,2,...,n},j∈{1,2,...,N};

[0102] 3) The distance between spacecraft i and j asymptotically converges to the expected value d. ij ;

[0103] 4) The speed of all spacecraft eventually approaches zero.

[0104] Step 2: Generate the desired trajectory based on the zero-space behavior control method.

[0105] This step employs a multi-task priority control framework based on the zero-space behavior method, using task variables... and its Jacobian matrix Mapping the control objective to a velocity planning problem, specifically defining the task variable as σ(t) = f(p(t)), its differential relation is: Generating minimum norm velocity solutions using pseudo-inverse methods And through the null space projection operator Redundant degrees of freedom are handled. By prioritizing and integrating the three levels of tasks—obstacle avoidance, connectivity maintenance, and formation configuration—a conflict-free desired trajectory is generated, ensuring both safety and coordination during spacecraft formation flight.

[0106] Step 2.1: Design three subtasks: connectivity maintenance, obstacle avoidance, and formation configuration, and calculate the expected speed for each subtask:

[0107] Build obstacle avoidance tasks and generate speed:

[0108] To address the collision risk between spacecraft and obstacles (including other spacecraft), an obstacle avoidance task function is designed. in Let σ be the location of the nearest obstacle (including other spacecraft) to spacecraft i, and set the desired obstacle avoidance task function σ. i,od In this embodiment, σ is taken. i,od =δ i The error is then defined as follows:

[0109]

[0110] Repulsion velocity is generated using the least squares method. Where k o J is the gain coefficient. i,o For the Jacobian matrix corresponding to the obstacle avoidance task, take... The unit vector pointing the spacecraft to the nearest obstacle:

[0111]

[0112] This speed Only when an obstacle (including other spacecraft) enters the collision avoidance radius δ i When activated, it forces the spacecraft to move away from the obstacle.

[0113] Construct a connectivity-preserving task:

[0114] To prevent communication link breakage, design a connectivity maintenance task function. in Set the location of the farthest spacecraft in the neighborhood set of spacecraft i, and define the desired connectivity-preserving task function σ. i,cd In this embodiment, σ is taken. i,cd =Δ, then the error is defined as follows:

[0115] The attraction velocity is solved by pseudo-inverse equation. Where k c >0 represents the gain, J i,c To obtain the Jacobian matrix corresponding to the connectivity-preserving task, take... Here is a unit vector pointing to the farthest neighbor:

[0116]

[0117] This task is triggered only when the distance to a neighbor is close to the communication radius Δ, ensuring network connectivity.

[0118] Constructing distributed formation configuration tasks:

[0119] To achieve the desired formation configuration, design the spacecraft formation configuration mission function:

[0120]

[0121] And set the desired spacecraft formation configuration mission function σ f,d The error is then defined as follows:

[0122] Speed ​​of formation configuration generated by pseudo-inverse generation Where K f =k f I 3n Let k be the gain matrix.f To set the gain, J f Let Jacobian matrix be the one corresponding to the configuration task. L is the Laplacian matrix corresponding to the dynamic graph. This task only relies on neighbor location information, supports distributed implementation, and avoids the bottleneck of centralized computing.

[0123] Step 2.2: Multi-task priority fusion and null-space projection:

[0124] To avoid task conflicts, the velocity of low-priority tasks is projected into the null space of high-priority tasks through null space projection, thus avoiding velocity conflicts and generating the final desired trajectory.

[0125] First, define the obstacle avoidance task projection matrix. The attraction velocity of the connectivity preservation task is projected onto the null space of the obstacle avoidance task; secondly, a joint projection matrix for the safety task is defined. Projecting formation mission velocity into the safe mission null space, where Finally, generate conflict-free expected velocity commands. in For formation configuration speed The configuration velocity corresponding to spacecraft i is determined to ensure obstacle avoidance is prioritized, connectivity is secondary, and configuration is the last priority. Using the generated conflict-free desired velocity command, combined with the initial position, the desired trajectory can be obtained through integration.

[0126] Step 3: Distributed Adaptive Controller Design. Considering factors such as quality uncertainty, actuator saturation, and external disturbances, the controller is designed to track the desired trajectory generated in Step 2. By constructing a sliding surface and introducing an adaptive law for quality estimation, the robustness and adaptability of the controller are ensured.

[0127] Specifically, based on the desired trajectory generated in step 2, a distributed adaptive control strategy is designed by combining sliding mode control, anti-saturation compensation, and online parameter estimation to solve spacecraft trajectory tracking under conditions of unknown mass, actuator saturation, and external disturbances.

[0128] Step 3.1: Design the sliding surface and smooth the desired trajectory

[0129] To enhance tracking robustness, the sliding surface is first defined:

[0130]

[0131] In the formula: β>0 is the convergence rate parameter, For position tracking error, For reference speed. Due to the desired speed Discontinuity may occur due to task switching; therefore, a first-order low-pass filter is introduced.

[0132]

[0133] The equivalent acceleration estimate is obtained by smoothing the reference signal by adjusting the time constant ρ << 1. Thus constraining the upper bound of acceleration This design effectively suppresses chattering, providing a smooth input to the controller while ensuring... Physical realizability.

[0134] Step 3.2: Dynamically compensate for saturation and suppress error integrals:

[0135] Design an anti-saturation compensation term q to address actuator saturation constraints. i Its dynamic equation is:

[0136]

[0137] In the formula: To compensate for the deviation between the actual control force and the virtual control force, γ0 > 0, the compensation rate is adjusted. This compensator dynamically adjusts q... i The amplitude is adjusted to compensate for accumulated errors caused by saturation in real time, preventing the integral term from diverging. Compensation term q i The introduction of sliding surface s i It can indirectly reflect the saturation effect and prove that it is eventually bounded through stability analysis, thereby improving the controller's adaptability to the nonlinear constraints of the actuator.

[0138] Step 3.3: Adaptive quality estimation and integrated controller design to track the desired trajectory generated in step 2.

[0139] To address the characteristic of spacecraft mass being unknown but slowly changing, the virtual control force is designed as follows:

[0140]

[0141] In the formula: K is a mass-independent dynamic term. i,p and K i,d The gain matrix is ​​symmetric positive definite, and the sliding mode term is -(γ1+γ2)sgn(s i ) used to counteract external disturbances d i Quality parameters Online updates via projective adaptive laws:

[0142]

[0143] In the formula: To estimate the error, γ3 > 0 controls the learning rate, and γ4 > 0 suppresses parameter drift. This control law integrates quality estimation error, disturbance, and tracking error into a robust framework, achieving synergy between parameter adaptation and disturbance suppression.

[0144] The following is a specific example:

[0145] First, determine the reference orbit of the reference spacecraft: semi-major axis a = 6971 km, eccentricity e = 0.02, initial true anomaly angle θ0 = 40°, and Earth's gravitational constant μ = 3.986 × 10⁻⁶. 14 m 3 / s 2 .

[0146] Secondly, the information of the spacecraft participating in the formation flight is determined. In this example, three spacecraft participate in the formation flight with masses m1 = 10 kg, m2 = 12 kg, and m3 = 11 kg, respectively. The initial mass estimates are as follows. Their initial positions are p1(0) = [-10, 10, 0] T m, p2(0) = [0, 15, 0] T m, p3(0) = [-10, 20, 0] T m, desired position is σ f,d =[40,10,0,50,15,0,40,20,0] T m, spacecraft topology network such as Figure 1 As shown. The spacecraft formation environmental information and safe distance are as follows: Figure 2 As shown, the collision avoidance radius δ i =8m, communication radius Δ = 20m, obstacle center coordinates p0[20,20,0] T m.

[0147] Finally, the controller parameters were determined: the behavioral task gains were collision avoidance gain k0 = 1 and connectivity preservation gain k c =1, Formation configuration gain k f =0.02, the sliding control parameters are convergence rate β=1, anti-saturation compensation gain γ0=1, adaptive law parameters γ3=2, γ4=0.5, and the maximum control force constraint is ||f i || ∞ ≤10N. Compared to control methods that only include collision avoidance and formation tasks, without maintaining connectivity, the inter-spacecraft distance is relatively small. Figure 3 As shown, the distance between the spacecraft and the obstacle is as follows: Figure 4 As shown, the spacecraft formation flight process is for example... Figure 5 As shown in the figure. The results demonstrate that this invention achieves orderly coordinated control among multiple tasks, improving the intelligence level of spacecraft formation flight.

[0148] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A spacecraft formation flight control method utilizing the null-space projection behavior method, characterized in that: Includes the following steps: Step 1: Establish a dynamic model of the spacecraft formation and its communication topology network model, and divide the control target hierarchy; Step 2: Generate the desired trajectory based on the null space behavior control method; including the following process: Step 2.1: Design three subtasks: connectivity maintenance, obstacle avoidance, and formation configuration, and calculate the expected speed for each subtask: Build obstacle avoidance tasks and generate speed: Design an obstacle avoidance task function. in Define the location of the nearest obstacle or other spacecraft to spacecraft i, and set the desired obstacle avoidance task function σ. i,od The error was obtained. Generation repulsion rate Where k o To increase collision avoidance gain, J i,o The Jacobian matrix corresponding to the obstacle avoidance task; Construct a connectivity-preserving task: Design a connectivity-maintaining task function. in Set the location of the farthest spacecraft in the neighborhood set of spacecraft i, and define the desired connectivity-preserving task function σ. i,cd The error was obtained. Generation attraction speed Where k c To maintain connectivity gain, J i,c To maintain connectivity, the Jacobian matrix corresponding to the task is preserved; Constructing distributed formation configuration tasks: Design spacecraft formation configuration mission functions: And set the desired spacecraft formation configuration mission function σ f,d The error is then defined as follows: Formation configuration generation speed Where K f =k f I 3n Let k be the gain matrix. f For formation configuration gain, J f The Jacobian matrix corresponding to the configuration task; Step 2.2: Project the velocity of the low-priority task onto the null space of the high-priority task through null space projection, and generate the final desired trajectory; Step 3: Considering quality uncertainty, actuator saturation and external disturbances, track the desired trajectory generated in Step 2 through controller design.

2. The spacecraft formation flight control method using the null-space projection behavior method according to claim 1, characterized in that: In step 1, the spacecraft formation dynamics model is as follows: Where m i For the mass of spacecraft i, C i D is the orbital coefficient matrix. i Let n be the position coupling matrix. i For nonlinear gravitational terms, d i For external interference, f i p is the control force vector of the i-th spacecraft; i Let be the position vector of the i-th spacecraft in the relative coordinate system.

3. The spacecraft formation flight control method using the null-space projection behavior method according to claim 1, characterized in that: In step 1, the communication topology network model of the spacecraft formation is a dynamic graph created based on the distances between the spacecraft. in Let n be the vertex set, and n be the number of spacecraft in the spacecraft formation. ε(t) is a dynamically changing set of edges. For an edge (i,j) consisting of spacecraft i and j, if the distance between spacecraft i and j is ||p ij (t)||at (δ) i Within the interval of ,Δ), ​​then (i,j)∈ε(t), where δ i The minimum distance between spacecraft i and obstacles and other spacecraft is set, and Δ is the maximum communication range set; otherwise... The adjacency matrix has the following elements:

4. The spacecraft formation flight control method using the null-space projection behavior method according to claim 3, characterized in that: In step 1, the control objectives are divided into four levels: 1) If the initial distance satisfies ||p ij (0)||<Δ-∈, then maintain throughout the control process Where ∈ represents the set minimum value; 2) All spacecraft maintain distance from obstacles and other spacecraft. as well as ||p ij (t)||>δ i ,i∈{1,2,...,n},j∈{1,2,...,N}; 3) The distance between spacecraft i and j asymptotically converges to the expected value d. ij ; 4) The speed of all spacecraft eventually approaches zero.

5. The spacecraft formation flight control method using the null-space projection behavior method according to claim 1, characterized in that: In step 2.1, take σ. i,od =δ i , σ i,cd =Δ.

6. The spacecraft formation flight control method using the null-space projection behavior method according to claim 1, characterized in that: In step 2.1, take The unit vector pointing the spacecraft to the nearest obstacle: Pick Here is a unit vector pointing to the farthest neighbor: Pick L is the Laplacian matrix corresponding to the dynamic graph.

7. The spacecraft formation flight control method using the null-space projection behavior method according to claim 1, characterized in that: In step 2.2, the obstacle avoidance task projection matrix is ​​first defined. The attraction velocity of the connectivity preservation task is projected onto the null space of the obstacle avoidance task; secondly, a joint projection matrix for the safety task is defined. Projecting formation mission velocity into the safe mission null space, where Finally, generate conflict-free expected velocity commands. in For formation configuration speed The configuration velocity corresponding to spacecraft i is determined to ensure obstacle avoidance is prioritized, connectivity is secondary, and configuration is the last priority. The desired trajectory is obtained by integrating the generated conflict-free expected velocity command with the initial position.

8. The spacecraft formation flight control method using the null-space projection behavior method according to claim 1, characterized in that: Step 3 involves the following steps: Based on the desired trajectory generated in Step 2, combined with sliding mode control, anti-saturation compensation, and online parameter estimation, the desired trajectory is tracked. Step 3.1: Design the sliding surface and smooth the desired trajectory: Define the sliding surface: In the formula: β>0 is the convergence rate parameter, For position tracking error, For reference speed; Step 3.2: Dynamically compensate for saturation and suppress error integrals: Design an anti-saturation compensation term q to address actuator saturation constraints. i Its dynamic equation is: In the formula: The deviation between the actual control force and the virtual control force, γ0 > 0 is used to adjust the compensation rate; Step 3.3: Adaptive quality estimation and integrated controller design to track the desired trajectory generated in Step 2: The virtual control force is designed as follows: In the formula: K is a mass-independent dynamic term. i,p and K i,d The gain matrix is ​​symmetric positive definite, and the sliding mode term is -(γ1+γ2)sgn(s i ) used to counteract external disturbances d i quality parameters Online updates via projective adaptive laws: In the formula: To estimate the error, γ3 > 0 controls the learning rate, and γ4 > 0 suppresses parameter drift.

9. A spacecraft formation flight control method using the null-space projection behavior method according to claim 8, characterized in that: In step 3.1, a first-order low-pass filter is introduced. The equivalent acceleration estimate is obtained by smoothing the reference signal by adjusting the time constant ρ << 1. Thus constraining the upper bound of acceleration

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