A Method for Generating Microsatellite Cluster Configuration Strategies and Cooperative Trajectory Planning for Dynamic Missions

Abstract

A method for generating configuration strategies and coordinating trajectory planning for microsatellite swarms in dynamic missions is presented. This method relates to the fields of spacecraft on-orbit mission planning and swarm flight control. Addressing the problem that when microsatellites are released from the same platform, the initial distance is close to zero, leading to infeasible trajectory planning solutions and difficulty in adapting to dynamic missions, this method first matches terminal configuration strategies from a strategy library based on mission requirements; then establishes a relative dynamic model based on the Hill equation; with the goal of minimizing energy consumption, an optimal control model is constructed using a progressive constraint strategy, ensuring that the minimum relative distance constraint between satellites smoothly increases from zero to a nominal value during the separation phase; finally, the model is discretized using the pseudospectral method, and the coordinating trajectory is obtained. This invention resolves the contradiction between separation safety and cooperative maneuvering under initial zero-distance conditions, exhibiting strong mission adaptability and applicability to on-orbit servicing, space rescue, target reconnaissance and tracking, and other fields.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a method for generating microsatellite cluster configuration strategies and coordinating trajectory planning for dynamic missions. Background Technology

[0002] With the development of space missions such as on-orbit servicing, space rescue, and target reconnaissance and tracking, spacecraft platforms capable of carrying and releasing multiple microsatellites have gradually become an important direction for research and application. These platforms release multiple microsatellites in orbit to form temporary clusters, enabling the microsatellites to coordinate and maneuver within a nearby orbit to perform missions, and then return to the platform for unified management after mission completion. This model combines the advantages of centralized scheduling and distributed execution, possessing high flexibility and scalability, and can better adapt to sudden and complex mission scenarios, and is considered an important future development trend in on-orbit servicing technology.

[0003] However, trajectory planning for microsatellite swarms faces unique constraints under the aforementioned mission modes. Since multiple microsatellites are typically released from the same spacecraft platform, their initial relative positions may overlap or be extremely close. Furthermore, during coordinated maneuvers, a strict minimum safe distance requirement must be met to prevent collisions. Existing trajectory planning methods often employ static path constraints to directly impose minimum distance limitations. When the initial relative distance is zero or extremely small, this can easily lead to an infeasible solution in the initial optimization model, making it difficult to generate feasible coordinated trajectories and hindering the application of such platforms in practical missions.

[0004] On the other hand, with the increasing complexity and diversity of mission scenarios, microsatellite constellations need to possess strong dynamic mission adaptability. Different missions have different requirements for the spatial geometric distribution that the constellation needs to achieve at the moment of mission execution, meaning that the terminal configuration needs to be adjusted according to mission requirements. In existing technologies, configuration selection and trajectory planning often lack a unified strategy-driven mechanism. When the configuration is determined unreasonably, it will not only reduce mission execution efficiency but may also increase collision risk or lead to mission failure. Furthermore, after determining the terminal configuration, planning cooperative trajectories for multiple satellites to simultaneously satisfy dynamic constraints, collision avoidance constraints, and optimization objectives is itself a complex optimization problem with high dimensions and strong constraints. Traditional planning methods are insufficient in efficiency and stability when dealing with such problems.

[0005] To address the aforementioned complex constraints, the pseudospectral method has been gradually introduced into the field of aerospace trajectory optimization due to its numerical advantages in handling terminal and path constraints. However, in scenarios where microsatellites are released from the same location, there is still a lack of mature and universal solutions for effectively handling the contradiction between initial distance constraints and safe separation requirements within the optimal control framework such as the pseudospectral method. Therefore, there is an urgent need for a collaborative trajectory planning method for microsatellite swarms that can meet dynamic mission requirements and comprehensively consider terminal configuration requirements, relative dynamic characteristics, and separation safety constraints, in order to improve the feasibility, stability, and practicality of trajectory planning. Summary of the Invention

[0006] To address the problems in existing technologies where trajectory planning for microsatellite clusters is infeasible when the initial relative distance is close or zero during release from the same platform, the difficulty in simultaneously satisfying separation safety and coordinated maneuvering requirements, and the inability of terminal configurations to flexibly adapt to dynamic mission needs, this invention proposes the following solutions: A method for generating microsatellite constellation configuration strategies and co-trajectory planning for dynamic missions includes: S1. Obtain the dynamic mission requirements of the spacecraft platform carrying microsatellites in orbit; S2. Based on the dynamic task requirements, match the target terminal configuration strategy from the preset terminal configuration strategy library. S3. Based on the target terminal configuration strategy, determine the terminal configuration geometric parameters corresponding to the microsatellite cluster; S4. Based on the Hill equation, establish a relative dynamic model of the microsatellite cluster relative to the spacecraft platform; S5. Based on the terminal configuration geometric parameters and relative dynamics model, with the goal of minimizing energy consumption and considering the condition that the initial relative distance of the microsatellite cluster is zero, an optimal control model is constructed using a progressive constraint strategy. S6. The optimal control model is discretized and solved using the pseudospectral method to obtain the microsatellite cluster cooperative trajectory that satisfies the target terminal configuration strategy.

[0007] Furthermore, the terminal configuration strategy library mentioned in S2 includes straight configuration strategy, coplanar surround configuration strategy, vertical observation configuration strategy, tilted configuration strategy, spatial configuration strategy and custom configuration strategy.

[0008] Furthermore, the terminal configuration geometric parameters described in S3 are transformed into final-state constraints in the optimal control model, and the final-state constraints are expressed as follows: , in, It is the terminal time.

[0009] Furthermore, the relative dynamic model described in S4 is transformed into dynamic constraints in the optimal control model, and these dynamic constraints are expressed as follows: , in, It is a state vector. It is a control vector. It is a system matrix. It is a control matrix. For the relative motion of the microsatellite cluster, it is a continuous time variable.

[0010] Furthermore, the progressive constraint strategy described in S5 includes a separation phase and a normal phase. In the separation phase, the minimum relative distance constraint value between each microsatellite gradually increases from 0; in the normal phase, the minimum relative distance constraint value between each microsatellite remains at a preset nominal value.

[0011] Furthermore, in the separation stage, the minimum relative distance constraint value increases smoothly exponentially with the pseudospectral method configuration point index until it reaches the nominal value at a preset critical configuration point.

[0012] Furthermore, the exponential growth rate is controlled by a constraint tightening rate coefficient, which is set according to the thrust and separation safety requirements of each microsatellite.

[0013] Furthermore, the placement point of the pseudospectral method described in S6 is located in the interval Above, and through a linear time mapping relationship with the actual time interval. correspond.

[0014] Furthermore, all constraints of the optimal control model are uniformly discretized at the configuration point, and the corresponding nonlinear programming problem is constructed and solved.

[0015] Furthermore, within the pseudospectral method discretization framework, the minimum relative distance constraint between microsatellites is determined in the 1st... At each pseudospectral configuration point, the following relationship is applied: , , , in, and These are the minimum relative distance and the maximum relative distance, respectively. It is the constraint tightening rate coefficient. It is the critical configuration point in the transition phase.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The microsatellite cluster configuration strategy generation and collaborative trajectory planning method for dynamic missions described in this invention obtains dynamic mission requirements in orbit and matches them with terminal configuration strategies accordingly. This enables the microsatellite cluster to form a spatial geometric distribution corresponding to the mission objectives at the time of mission execution. This avoids the situation in the prior art where the configuration is fixed for a long time or relies on manual preset, making it difficult to adapt to sudden missions. This allows the cluster to complete configuration adjustments according to mission requirements when performing different missions such as rescue and tracking.

[0017] The microsatellite cluster configuration strategy generation and collaborative trajectory planning method for dynamic missions described in this invention solves the problem by taking the terminal configuration geometric parameters as final-state constraints and integrating them with the relative dynamics model into the optimal control framework. This allows configuration design and trajectory planning to be completed in the same calculation process, avoiding the repeated correction problem caused by determining the configuration first and then planning the trajectory separately in the prior art. This method controls the overall maneuver energy consumption while meeting the terminal configuration requirements.

[0018] The microsatellite cluster configuration strategy generation and cooperative trajectory planning method for dynamic missions described in this invention introduces progressive distance constraints during the trajectory planning process, so that the minimum relative distance between microsatellites gradually increases from zero in the initial separation stage. This avoids the situation where no feasible solution is obtained by directly applying static safety distance constraints when the initial relative distance is close to or zero, thus enabling microsatellites to complete separation and cooperative maneuvers while meeting safety requirements.

[0019] The microsatellite cluster configuration strategy generation and cooperative trajectory planning method for dynamic missions described in this invention utilizes the pseudospectral method to uniformly discretize and solve the optimal control model that includes terminal configuration constraints, dynamic constraints, and distance constraints. This enables multiple microsatellites to obtain cooperative trajectories that meet the requirements under complex constraints, avoiding the problem of solution failure or unstable results that is prone to occur in traditional methods under strong constraints of multiple satellites.

[0020] This invention has the ability to generate microsatellite cluster terminal configurations for dynamic missions and achieve safe cooperative trajectory planning under conditions where the initial relative distance is close or zero. It can complete multi-satellite cooperative maneuvers under the premise of satisfying relative dynamic constraints and safe distance constraints, and is applicable to fields such as on-orbit servicing, space rescue, target reconnaissance and tracking, and multi-microsatellite cooperative flight control. Attached Figure Description

[0021] Figure 1 This is a simulation flowchart of the method described in the implementation method; Figure 2 It is the trajectory of the microsatellite in the inertial coordinate system described in the implementation method; Figure 3It is the trajectory of the microsatellite in the main spacecraft coordinate system of the method described in the implementation method; Figure 4 This is a graph showing the changes in performance indicators of the method described in the implementation method; Figure 5 This is a graph showing the relative distance changes of microsatellites according to the method described in the implementation method; Figure 6 This is a graph showing the changes in microsatellite control quantities according to the method described in the implementation embodiment; Figure 7 These are simulation results of the linear configuration strategy described in the implementation method; Figure 8 These are simulation results of the coplanar configuration strategy of the method described in the implementation method; Figure 9 These are simulation results of the spatial configuration strategy of the method described in the implementation method; Figure 10 These are simulation results of the tilt configuration strategy described in the implementation method. Detailed Implementation

[0022] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] Implementation Method 1 A method for generating microsatellite constellation configuration strategies and co-trajectory planning for dynamic missions includes: S1. Obtain the dynamic mission requirements of the spacecraft platform carrying microsatellites in orbit; S2. Based on the dynamic task requirements, match the target terminal configuration strategy from the preset terminal configuration strategy library. S3. Based on the target terminal configuration strategy, determine the terminal configuration geometric parameters corresponding to the microsatellite cluster; S4. Based on the Hill equation, establish a relative dynamic model of the microsatellite cluster relative to the spacecraft platform; S5. Based on the terminal configuration geometric parameters and relative dynamics model, with the goal of minimizing energy consumption and considering the condition that the initial relative distance of the microsatellite cluster is zero, an optimal control model is constructed using a progressive constraint strategy. S6. The optimal control model is discretized and solved using the pseudospectral method to obtain the microsatellite cluster cooperative trajectory that satisfies the target terminal configuration strategy.

[0024] By acquiring the dynamic mission requirements of the spacecraft platform in orbit and matching the corresponding terminal configuration strategy according to the dynamic mission requirements, the configuration planning of the microsatellite cluster can be directly centered around the specific mission objectives. This avoids the problem of using a fixed configuration and needing frequent manual adjustments when the mission changes, and ensures that the configuration generation process is consistent with the actual mission requirements.

[0025] Furthermore, the terminal configuration strategy library mentioned in S2 includes straight configuration strategy, coplanar surround configuration strategy, vertical observation configuration strategy, tilted configuration strategy, spatial configuration strategy and custom configuration strategy.

[0026] By pre-building a terminal configuration strategy library containing multiple configuration forms and matching the target configuration strategy from it before mission execution, microsatellite clusters can quickly determine the required spatial distribution form according to different mission types, reducing the complexity of temporary configuration design and facilitating timely configuration determination in the event of sudden mission changes or frequent switching.

[0027] Furthermore, the terminal configuration geometric parameters described in S3 are transformed into final-state constraints in the optimal control model, and the final-state constraints are expressed as follows: , in, It is the terminal time.

[0028] Based on the target terminal configuration strategy, the terminal configuration geometric parameters of the microsatellite cluster are determined, and these geometric parameters are used as constraints for subsequent trajectory planning. This ensures that the trajectory planning results accurately meet the expected configuration requirements at the terminal moment, avoiding the need to correct the terminal position after the trajectory planning is completed.

[0029] Furthermore, the relative dynamic model described in S4 is transformed into dynamic constraints in the optimal control model, and these dynamic constraints are expressed as follows: , in, It is a state vector. It is a control vector. It is a system matrix. It is a control matrix. For the relative motion of the microsatellite cluster, it is a continuous time variable.

[0030] By establishing a relative dynamic model of the microsatellite cluster relative to the spacecraft platform based on the Hill equation, the trajectory planning process can be carried out directly within the relative motion framework, reducing unnecessary coordinate transformations and modeling complexity, and facilitating a unified description of the motion state of each microsatellite in multi-satellite collaborative scenarios.

[0031] Furthermore, the progressive constraint strategy described in S5 includes a separation phase and a normal phase. In the separation phase, the minimum relative distance constraint value between each microsatellite gradually increases from 0; in the normal phase, the minimum relative distance constraint value between each microsatellite remains at a preset nominal value.

[0032] By unifying the terminal configuration geometric parameters and relative dynamics model into the optimal control model, and solving the trajectory with the goal of minimizing energy consumption, the generated cooperative trajectory satisfies the dynamics and configuration requirements while avoiding unnecessary maneuvers, thereby controlling the overall energy consumption level.

[0033] Furthermore, in the separation stage, the minimum relative distance constraint value increases smoothly exponentially with the pseudospectral method configuration point index until it reaches the nominal value at a preset critical configuration point.

[0034] By introducing a progressive constraint strategy that combines the separation phase and the normal phase into the optimal control model, microsatellites can gradually increase their spacing when the initial relative distance is close to or zero, thus avoiding the problem of the model having no feasible solution due to directly applying a fixed minimum safe distance constraint.

[0035] Furthermore, the exponential growth rate is controlled by a constraint tightening rate coefficient, which is set according to the thrust and separation safety requirements of each microsatellite.

[0036] By utilizing the minimum relative distance constraint that gradually increases with the pseudospectral method configuration point index during the separation phase, the process of changing the safe distance between microsatellites becomes smoother, reducing the impact of constraint abrupt changes on the trajectory planning solution process, which is beneficial for obtaining continuous and feasible separation trajectories.

[0037] Furthermore, the placement point of the pseudospectral method described in S6 is located in the interval Above, and through a linear time mapping relationship with the actual time interval. correspond.

[0038] By setting the constraint tightening rate coefficient according to the thrust capability and separation safety requirements of the microsatellite, the growth rate of the minimum relative distance constraint is matched with the actual separation capability, thus avoiding the situation where the trajectory becomes unattainable due to excessively rapid constraint growth.

[0039] Furthermore, all constraints of the optimal control model are uniformly discretized at the configuration point, and the corresponding nonlinear programming problem is constructed and solved.

[0040] By setting configuration points within the normalized interval using the pseudospectral method and mapping them to actual flight times, the continuous-time optimal control problem can be transformed into a discrete form for processing. This facilitates the unified consideration of various constraints during numerical computation. Furthermore, within the pseudospectral method discretization framework, the minimum relative distance constraint between microsatellites is determined in the 1st... At each pseudospectral configuration point, the following relationship is applied: , , , in, and These are the minimum relative distance and the maximum relative distance, respectively. It is the constraint tightening rate coefficient. It is the critical configuration point in the transition phase.

[0041] The dynamic constraints, terminal constraints, and distance constraints are uniformly discretized at each pseudospectral method configuration point, and the corresponding nonlinear programming problem is constructed and solved. This allows the cooperative trajectories of multiple microsatellites to be obtained within the same computational framework, avoiding inconsistencies caused by step-by-step solutions.

[0042] Implementation Method 2 This invention proposes a method for generating microsatellite cluster configuration strategies and co-trajectory planning for spacecraft platforms carrying microsatellites, which is oriented towards dynamic missions and seeks the optimal trajectory with the lowest energy consumption for different terminal configurations.

[0043] like Figure 1 As shown, Hill's Equation is first chosen to describe the relative motion between the satellite cluster and the spacecraft platform, establishing a corresponding relative dynamics model of the spacecraft. This relative dynamics model forms the basis for subsequent trajectory planning and serves as the dynamic constraint in the optimization problem.

[0044] If the spacecraft platform that releases microsatellites is the main spacecraft, and the cluster of microsatellites is the secondary spacecraft, then the state equations of the two-body relative dynamic system based on Hill's equations are as follows:

[0045] In the formula —The orbital angular velocity of the main spacecraft, ,in The distance from the center of mass of the main spacecraft to the center of the Earth. The gravitational constant of Earth; —The position vector of the secondary spacecraft in the coordinate system of the primary spacecraft, that is, the relative position vector between the secondary spacecraft and the primary spacecraft. The three-axis components, .

[0046] —Control quantities applied to the secondary spacecraft The three-axis components, .

[0047] The system state equations can be written in state-space form as shown below, and used as a relative dynamic model for subsequent optimization:

[0048] In the formula —State vector, ; —Control vector, ; —The continuous-time variable of the relative motion of microsatellite clusters; —The system matrix describes the natural dynamic characteristics of the system; —The control matrix describes the effect of control inputs on the system state. The expression is

[0049]

[0050] Based on this relative dynamics model, an optimal control model for collaborative trajectory planning of microsatellite clusters can be constructed. The core of this model lies in determining the corresponding optimization objectives and constraint functions (terminal configuration, mutual collision avoidance, etc.) according to dynamic mission requirements. Among them, equation (2) will serve as the dynamic constraint describing the satellite motion, while the terminal configuration constraint directly determines the efficiency of the cluster in completing its mission.

[0051] To meet the diverse needs of dynamic missions (such as emergency rescue, 3D reconnaissance, and refueling), a pre-configured terminal configuration strategy library containing various typical configurations and supporting custom generation is required for microsatellite constellations. Different configuration strategies correspond to different spatial geometric distributions and mission capabilities, forming the basis of mission execution constraints. During mission planning, specific terminal configuration strategies are first matched or generated from this library based on mission requirements. Commonly used terminal formation configuration strategies include: (1) Straight line configuration (follow-fly configuration) strategy All satellites maintain a near-linear configuration with the target spacecraft, sharing the same orbital root numbers, with differences only in their true anomaly angles. This strategy is relatively simple to control and fuel-efficient, making it suitable for missions such as continuous on-orbit surveillance and target tracking.

[0052] (2) Coplanar surrounding configuration strategy All satellites and the target spacecraft are positioned in the same orbital plane, forming a circular distribution in relative motion. This strategy provides a continuous lateral observation angle of the target and is suitable for missions requiring stable relative positions, such as long-term close-range surveillance and communication relay.

[0053] (3) Vertical observation configuration strategy The satellite constellation is mainly distributed along the normal direction of the target's orbital plane. This strategy effectively covers the top and bottom "blind spots" of the target, providing a unique observation perspective and is suitable for special surveillance missions with a focus on observing specific directions.

[0054] (4) Tilted configuration strategy The satellite constellation maintains an approximately straight line with the target, but is distributed within a plane inclined to the orbit. This strategy combines along-orbit and trans-orbit observation capabilities, enabling multi-angle space environment monitoring, but it has high control complexity.

[0055] (5) Spatial configuration strategy Satellites form specific spatial geometric configurations around the target, such as cubes, tetrahedrons, or spheres. This strategy provides an omnidirectional, three-dimensional observation or operational interface, making it ideal for complex tasks such as high-precision three-dimensional reconnaissance, three-dimensional positioning, or collaborative acquisition / maintenance.

[0056] (6) Custom configuration strategy In addition to the strategies mentioned above, custom terminal configuration strategies can be dynamically generated based on the unique requirements of a specific mission and the number of available satellites to maximize mission efficiency.

[0057] Based on the selected terminal configuration strategy, the desired terminal six-element number for each satellite relative to the target position can be determined, and this number can be converted into the desired terminal relative position using a transformation function. and speed These geometric parameters are directly translated into final-state constraints in the optimal control model. For models containing... The final-state constraints of a cluster of satellites can be uniformly expressed as:

[0058] In the formula —Terminal time.

[0059] The remaining constraints can be expressed as follows: Initial state constraints (located in the same position as the main spacecraft):

[0060] In the formula —Initial time.

[0061] Thrust constraint:

[0062] In the formula —Maximum acceleration.

[0063] Relative distance constraints

[0064] In the formula —Minimum relative distance and maximum relative distance.

[0065] Choosing energy consumption as the optimization function, it is expressed as follows:

[0066] Therefore, using equation (7) as the objective function and equations (2) to (6) as the constraint functions, an optimal control model for collaborative trajectory planning of microsatellite clusters is constructed.

[0067] To numerically solve this continuous optimal control model, this invention employs a pseudospectral method for discretization and solution. The core idea is to approximate the state and control variables over a series of collocation points using a global interpolation polynomial, thereby transforming the differential form of the dynamic equation constraints into algebraic constraints and the continuous optimal control model into a nonlinear programming optimization problem. Since the optimization problem includes terminal constraints, a pseudospectral method capable of explicitly handling boundary points is required. This implementation uses the Lobatto pseudospectral method (LPM). Given the number of discrete points, the parameters of the LPM can be pre-calculated as follows:

[0068]

[0069]

[0070] In the formula —Number of discrete points; — An Nth-order Legendre polynomial ; —Discrete collocation points, for the equation The root, plus two endpoints; —Configure point weights; —Differential matrix, for 1-order matrix.

[0071] The collocation points used in the pseudospectral method are all located in the interval Therefore, it is necessary to convert the actual time to correspond one-to-one with the configuration points, as shown in the following formula:

[0072] In the formula —Configuration points; —The corresponding actual time, These are the start time and the end time, respectively.

[0073] The optimization variables consist of two parts: state variables and control variables. The state variables are the three-axis positions and velocities of each auxiliary spacecraft in the master spacecraft coordinate system, totaling six variables. The control variables are the three-axis control inputs of each auxiliary spacecraft, totaling three variables. The state variables and control variables are interconnected through equation (2). The optimization variables are then placed at the configuration point... By performing a discrete approximation, the following discrete sequence is obtained:

[0074] Therefore, equation (2) can be expressed as:

[0075] In the formula —Number of microsatellites.

[0076] The optimization function can be discretized using the pseudospectral method as follows:

[0077] In the formula —Pseudospectral method for setting point weights; The constraint function is divided into two parts: state equation constraints and other constraints. The state equation constraints can be obtained from equation (13) and discretized using the pseudospectral method.

[0078] The core of this transformation lies in the discretization of the derivative terms in the formula, which is implemented as follows:

[0079] Therefore, the entire formula becomes:

[0080] In the formula —Pseudospectral differential matrix; Other constraints are also obtained directly from their respective continuous forms (3) to (6) at each placement point, as shown in (17) to (20): Initial state constraints:

[0081] Final state constraints:

[0082] Thrust Constraints: To facilitate further thrust analysis, the control variables can be normalized, with the maximum control variable set to 1, and the coefficient matrix multiplied by the maximum acceleration coefficient for compensation. The thrust constraints and compensation of the coefficient matrix are as follows:

[0083] In the formula —Maximum acceleration.

[0084] Relative distance constraint: To address the previously mentioned path constraint problem, special handling of the relative distance constraint is required during discretization. To ensure the feasibility of the optimization problem, this invention employs an incremental constraint strategy: in the initial separation stage, the minimum distance constraint value... Starting from 0, indexed by configuration point. It increases smoothly according to an exponential law until it reaches a critical point. After reaching the nominal value This strategy is specifically implemented in a discrete framework as follows:

[0085]

[0086]

[0087] In the formula —Minimum relative distance and maximum relative distance; —Constraint tightening rate coefficient; —The critical placement point in the transition phase. Placement points before this point are in the separation phase, where the minimum distance constraint gradually tightens. Placement points after this point are in the normal phase, where the minimum distance constraint is a fixed value. Parameters and It can be customized according to the mission's requirements for separation security and speed.

[0088] By discretizing the system variables, objective function, and constraint functions of the optimal control model using the pseudospectral method, the continuous trajectory planning problem can be transformed into a nonlinear programming problem, which can then be solved using a mature optimization solver. Different terminal configuration strategies will affect the given final-state constraints in the constraint functions, thus impacting the optimization process and results.

[0089] Implementation Method 3 This embodiment verifies the method for generating configuration strategies and coordinating trajectory planning for microsatellite clusters in dynamic missions through numerical simulation. This embodiment integrates the technical solutions described in the preceding embodiments, and, in conjunction with specific orbital parameters, configuration strategy settings, and calculation processes, illustrates the feasibility and effectiveness of the method in typical mission scenarios, serving as a specific implementation and technical evidence of the method in this patent.

[0090] In this embodiment, the spacecraft platform and the microsatellite cluster are assumed to be in the same spatial position at the initial moment, meaning that the initial relative positions of each microsatellite and the spacecraft platform are consistent. The initial six-element orbits of the spacecraft platform and the microsatellite cluster are selected as follows:

[0091] The corresponding target position orbital six-element number is selected as follows:

[0092] The above settings are used to describe a typical mission scenario in which a cluster of microsatellites completes coordinated maneuvers by changing phase while maintaining its orbital altitude and shape.

[0093] In this embodiment, the number of microsatellites is set to The number of discrete points in the pseudospectral method is set to Terminal time set to The maximum acceleration, minimum relative distance, and maximum relative distance of the microsatellite are limited by preset acceleration and distance constraints, respectively, with the constraint tightening rate coefficient set to... The critical placement point for the asymptotic distance constraint is set as follows: The above parameter settings are used to numerically solve the cooperative trajectory of a microsatellite cluster while ensuring separation safety.

[0094] The relative dynamics model used in this embodiment is based on the Hill equation, and its state-space form is shown below:

[0095] By describing the relative motion state of microsatellites in the orbital coordinate system of the main spacecraft, the dynamic constraints of multiple microsatellites can be modeled and processed within a unified coordinate framework, which facilitates the subsequent introduction of dynamic constraints into the optimal control model.

[0096] To verify the method's responsiveness to different dynamic mission requirements, this embodiment sets up five terminal configuration strategies corresponding to typical mission scenarios: diamond configuration strategy, straight configuration strategy (follow-flying), coplanar configuration strategy, spatial configuration strategy, and inclined configuration strategy. Each strategy is executed by a cluster of four microsatellites. The terminal orbital root number parameters for each configuration strategy are set as follows: The parameters corresponding to the rhombus configuration strategy are:

[0097] The parameters corresponding to the linear configuration strategy are:

[0098] The parameters corresponding to the coplanar configuration strategy are:

[0099] The parameters corresponding to the spatial configuration strategy are:

[0100] The parameters corresponding to the tilt configuration strategy are:

[0101] In this embodiment, take , Under the above parameter conditions, the pseudospectral method is used to discretize and solve the optimal control model, which includes terminal configuration constraints, relative dynamic constraints, and asymptotic distance constraints. The simulation results are as follows: Figures 2 to 10 As shown.

[0102] in, Figures 2 to 6 Simulation results for implementing a diamond configuration strategy for microsatellite clusters. Figure 2 The orbital trajectories of the four microsatellites at the last two discrete points in the inertial coordinate system are given. It can be seen that the cluster forms the expected rhomboid spatial structure at the terminal moment, which meets the configuration requirements. Figure 3 This is used to transform the relative motion trajectory to the main spacecraft coordinate system, and to characterize the relative motion relationship between the microsatellite and the spacecraft platform.

[0103] From the perspective of optimization process, Figure 4 The performance index convergence curve shown indicates that, under the set parameter conditions, the optimization process can proceed stably, and the performance index gradually converges during the iteration process. Figure 5 The curves showing the relative distance between microsatellites over time demonstrate that the relative distance changes smoothly and continuously, always meeting the preset minimum relative distance constraint. Figure 6 As shown in the control quantity variation curve, the control quantities of each microsatellite in the three-axis directions did not exceed the preset thrust constraint.

[0104] To further verify the applicability of this method under different task requirements, Figures 7 to 10 Terminal trajectory results are presented under linear, coplanar, spatial, and tilted configuration strategies. Simulation results show that, under different terminal configuration strategies, cooperative trajectories satisfying the corresponding terminal geometric constraints can be generated, indicating that the proposed method can adapt to various typical dynamic mission scenarios and complete cooperative trajectory planning for microsatellite clusters.

[0105] The above detailed description of the technical solution provided by the present invention is intended to highlight the advantages and benefits of the technical solution provided by the present invention. However, the above detailed embodiments are not intended to limit the scope of protection of the present invention. Any reasonable modifications and improvements to the present invention, recombination of embodiments, and equivalent substitutions based on the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0106] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims disclosed in the present invention can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in the disclosure of the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle scope of the present invention should be considered to fall within the protection scope of the present invention.

[0107] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for generating microsatellite constellation configuration strategies and coordinating trajectory planning for dynamic missions, characterized in that, include: S1. Obtain the dynamic mission requirements of the spacecraft platform carrying microsatellites in orbit; S2. Based on the dynamic task requirements, match the target terminal configuration strategy from the preset terminal configuration strategy library. S3. Based on the target terminal configuration strategy, determine the terminal configuration geometric parameters corresponding to the microsatellite cluster; S4. Based on the Hill equation, establish a relative dynamic model of the microsatellite cluster relative to the spacecraft platform; S5. Based on the terminal configuration geometric parameters and relative dynamics model, with the goal of minimizing energy consumption and considering the condition that the initial relative distance of the microsatellite cluster is zero, an optimal control model is constructed using a progressive constraint strategy. S6. The optimal control model is discretized and solved using the pseudospectral method to obtain the microsatellite cluster cooperative trajectory that satisfies the target terminal configuration strategy.

2. The method according to claim 1, characterized in that, The terminal configuration strategy library mentioned in S2 includes straight configuration strategy, coplanar surround configuration strategy, vertical observation configuration strategy, tilted configuration strategy, spatial configuration strategy and custom configuration strategy.

3. The method according to claim 1, characterized in that, The terminal configuration geometric parameters described in S3 are converted into final-state constraints in the optimal control model, and the final-state constraints are expressed as follows: ， in, It is the terminal time.

4. The method according to claim 1, characterized in that, The relative dynamic model described in S4 is transformed into dynamic constraints in the optimal control model, and these dynamic constraints are expressed as follows: ， in, It is a state vector. It is a control vector. It is a system matrix. It is a control matrix. For the relative motion of the microsatellite cluster, it is a continuous time variable.

5. The method according to claim 1, characterized in that, The progressive constraint strategy described in S5 includes a separation phase and a normal phase. In the separation phase, the minimum relative distance constraint value between each microsatellite gradually increases from 0. During normal operation, the minimum relative distance constraint between each microsatellite remains at the preset nominal value.

6. The method according to claim 5, characterized in that, During the separation phase, the minimum relative distance constraint value increases smoothly exponentially with the pseudospectral method configuration point index until it reaches the nominal value at a preset critical configuration point.

7. The method according to claim 6, characterized in that, The exponential growth rate is controlled by a constraint tightening rate coefficient, which is set according to the thrust and separation safety requirements of each microsatellite.

8. The method according to claim 1, characterized in that, The placement point of the pseudospectral method described in S6 is located in the interval Above, and through a linear time mapping relationship with the actual time interval. correspond.

9. The method according to claim 8, characterized in that, At the configuration point, all constraints of the optimal control model are discretized uniformly, and the corresponding nonlinear programming problem is constructed and solved.

10. The method according to claim 1, characterized in that, Within the pseudospectral method discretization framework, the minimum relative distance constraint between microsatellites is in the... At each pseudospectral configuration point, the following relationship is applied: ， ， ， in, and These are the minimum relative distance and the maximum relative distance, respectively. It is the constraint tightening rate coefficient. It is the critical configuration point in the transition phase.

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