An ER-PSO algorithm-based whole-process task planning method and system for a drag-free satellite

Abstract

The present application relates to aerospace technology field, propose a kind of based on ER-PSO algorithm's no tow satellite whole process mission planning method and system, comprising: establish three satellite system whole process dynamics model;Based on three satellite system whole process dynamics model, set design variable, constraint condition and fitness function, obtain no tow satellite whole process mission planning model;For no tow satellite whole process mission planning model, based on ER-PSO algorithm, the task planning problem is solved, and preliminary optimization result is obtained;Based on preliminary optimization result, the fitness function of the particle of the top three in fitness function reconstruction is reconstructed in the process of ER-PSO algorithm solution, obtain the shortest time of three satellites synchronous into scientific measurement mode and the time of three satellites into each mode of three satellite system whole process, complete mission planning.The present application realizes the shortest time optimization of three satellite system synchronous into scientific measurement mode, improves the systematicness, coordination and time efficiency of mission planning.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace technology, and in particular to a full-process task planning method and system for a drag-free satellite based on an ER-PSO algorithm. BACKGROUND

[0002] With the maturation of gravitational wave detection technology, as the core carrier for realizing high-precision space detection, the working principle and the phased control mode before entering the scientific measurement mode of the drag-free satellite have gradually become clear. However, as a highly complex multi-mode coupled system, the drag-free satellite covers multi-dimensional task requirements such as inter-satellite cooperation and intra-satellite precise control, and the importance of its full-process task planning is increasingly prominent. The current research still has significant gaps: the academic circle focuses on deepening the control theory under single task mode, lacks overall planning of the switching time sequence and task connection of the satellite in each operation mode from the global perspective of the system, and is difficult to meet the needs of precise control of the full process for gravitational wave detection tasks.

[0003] In the prior art, the traditional satellite task planning paradigm is centered on external task driving, such as imaging satellites based on different observation targets to carry out parallel task scheduling, and to realize attitude and orbit adjustment by tracking external targets. Although the basic task time sequence arrangement is realized, in actual application, the global optimization ability under multiple constraint conditions is insufficient, the coordination accuracy of complex mode switching is low, and most of them use simple independent mode processing method, ignoring the coupling relationship analysis between modes. It is difficult to accurately realize the optimal cooperative control of the multi-satellite system within a limited time in high-precision scenarios such as gravitational wave detection, especially the search efficiency of the global optimal solution under multiple constraint conditions and the accuracy of processing complex constraint relationships are low. SUMMARY

[0004] Therefore, the present application provides a full-process task planning method and system for a drag-free satellite based on an ER-PSO (Experience Replay - Particle Swarm Optimization, improved particle swarm optimization algorithm based on experience pool replay) algorithm, which solves the problem that the prior art is difficult to accurately realize the optimal cooperative control of the multi-satellite system within a limited time in high-precision scenarios such as gravitational wave detection, especially the search efficiency of the global optimal solution under multiple constraint conditions and the accuracy of processing complex constraint relationships are low.

[0005] The technical scheme of the present application is implemented as follows: in a first aspect, the present application provides a full-process task planning method for a drag-free satellite based on an ER-PSO algorithm, comprising the following steps:

[0006] establishing a three-satellite system full-process dynamics model, the three-satellite system full-process dynamics model being used for gravitational wave detection of the drag-free satellite;

[0007] Based on the Samsung system full-process dynamics model, design variables, constraints and fitness functions are set to obtain the drag-free satellite full-process mission planning model.

[0008] For the aforementioned dragless satellite full-process mission planning model, the mission planning problem is solved based on the ER-PSO algorithm, and preliminary optimization results are obtained;

[0009] Based on the preliminary optimization results, the fitness functions of the top three particles in terms of fitness during the ER-PSO algorithm solution process are reconstructed to obtain the shortest time for the three satellites to enter the scientific measurement mode simultaneously and the time for the three satellites to enter each mode of the entire three-satellite system process, thus completing the mission planning.

[0010] Based on the above technical solutions, preferably, the establishment of a full-process dynamic model of a three-satellite system for gravitational wave detection without dragging satellites includes:

[0011] The Samsung system's entire process is designed with various modes, including attitude adjustment mode, quality release capture mode, high resolution mode, and drag-free control mode.

[0012] Dynamic models were performed for each mode of the Samsung system to construct the dynamic model involved in the entire mission planning of the gravitational wave detection satellite.

[0013] A full-process dynamic model of the three-satellite system for gravitational wave detection was constructed based on the collaborative operation of each satellite and its mode, and the triggering time of each working mode of each satellite was extracted as an independent input parameter interface.

[0014] Based on the above technical solutions, preferably, the attitude adjustment mode includes: initializing the orbital six elements and attitude Euler angles of the three satellites, determining the construction method of the initial body coordinate system of each satellite, and setting a specific target coordinate system for each satellite during the attitude adjustment process to achieve mutual tracking and attitude alignment between the satellites.

[0015] Based on the above technical solutions, preferably, the dynamic modeling includes: describing the relationship between angular acceleration, moment of inertia and control torque using attitude dynamics equations, quantifying the attitude using quaternion differential equations, and constructing an attitude adjustment control system through attitude error calculation formulas and PID controller equations.

[0016] The motion state of the inspection mass in the cavity coordinate system is characterized by the dynamic equation. Based on the interference force generated by the electrostatic levitation force on the satellite, the motion of the inspection mass is regulated by the PID control strategy.

[0017] The input parameter interface includes the release and capture time of each inspection mass in each satellite, the start time of high-resolution mode control for each inspection mass, and the start time of drag-free mode control for each satellite, comprising 15 input parameter interfaces.

[0018] Based on the above technical solutions, preferably, the step of establishing a drag-free satellite full-process mission planning model based on the Samsung system full-process dynamics model includes setting design variables, constraints, and fitness functions, including:

[0019] The trigger times of each satellite's operating mode extracted from the full-process dynamic model of the Samsung system are used as design variables;

[0020] Setting constraints includes the logic for the mode triggering sequence and the logic for the mode triggering time;

[0021] The fitness function is set as the sum of the times when each satellite enters the scientific measurement mode, resulting in a drag-free satellite full-process mission planning model. The scientific measurement mode is defined as the satellite being in drag-free control mode and the sensitive axis displacement being less than [a certain value]. and non-sensitive axis displacement less than .

[0022] Based on the above technical solutions, preferably, the design variables include the release and capture time of each inspection mass in each satellite, the start time of each inspection mass in each satellite to perform high-resolution mode control, and the start time of each satellite to perform drag-free mode control, including 15 input parameter interfaces.

[0023] The mode triggering sequence logic is as follows: the release capture time of each inspection quality is less than the time of each inspection quality performing high-resolution mode control, and the time of each inspection quality performing high-resolution mode control is less than the time of each satellite starting to perform drag-free mode control.

[0024] The mode triggering time logic is as follows: the release time of each inspection quality is greater than the simulation start time, and the time for each satellite to perform drag-free mode control is less than the simulation end time.

[0025] Based on the above technical solutions, preferably, the task planning problem for the dragless satellite full-process mission planning model is solved using the ER-PSO algorithm to obtain preliminary optimization results, including:

[0026] Initialize the particle swarm, perform iterative optimization according to the basic process of the particle swarm optimization algorithm, and obtain the fitness value of each particle by updating the particle velocity and position.

[0027] The particle swarm optimization process is improved based on the experience pool replay mechanism. The global search capability and convergence performance of the particle swarm optimization algorithm are enhanced by the real-time update and maintenance mechanism of the experience pool, and preliminary optimization results are obtained.

[0028] Based on the above technical solutions, preferably, the particle swarm initialization includes: setting the particle swarm size, maximum number of iterations, inertia weight and learning factor, and randomly initializing the position and velocity of each particle within the constraints of the design variables;

[0029] The iterative optimization process includes: calculating the new position and new velocity of each particle according to the particle velocity update formula and the position update formula; calculating the fitness value corresponding to the position of each particle based on the drag-free satellite full-process mission planning model; updating the individual optimal position and the global optimal position; and repeating the iteration until the convergence condition is met.

[0030] The experience pool replay mechanism includes: establishing an experience pool to store historical excellent solutions, setting the experience pool capacity and update strategy; during particle swarm optimization, adding excellent particles that meet the conditions to the experience pool; when a particle gets stuck in a local optimum, selecting historical excellent solutions from the experience pool to guide the search direction of the current particle.

[0031] The real-time update and maintenance mechanism of the experience pool includes: sorting the solutions in the experience pool according to their fitness values, and removing poor solutions when the experience pool is full using an elimination strategy.

[0032] Based on the above technical solutions, preferably, the fitness function of the top three particles in fitness ranking during the ER-PSO algorithm solution process is reconstructed based on the preliminary optimization results to obtain the shortest time for the three satellites to simultaneously enter the scientific measurement mode and the corresponding time for each satellite to enter each mode, thus completing the mission planning, including:

[0033] The fitness values ​​of all particles during the ER-PSO algorithm iteration are statistically analyzed and sorted in ascending order. The three particles with the smallest fitness values ​​are selected as candidate optimal solutions. The selected particles are verified to meet the constraints. If they do not meet the constraints, the next particle with a smaller fitness value is selected to replace them, so as to ensure that the three selected particles are all feasible solutions.

[0034] Based on the position information of the three candidate particles, the evaluation weights and evaluation indicators of the fitness function are reset, and the evaluation weight of the three-star synchronization performance is increased to obtain the reconstructed fitness function.

[0035] The reconstructed fitness function is substituted into the full-process dynamic model of the three-satellite system for simulation calculation. The reconstruction fitness values ​​of the three candidate solutions are compared, and the solution with the smallest reconstruction fitness value is selected as the final mission planning scheme. The corresponding optimal time series for each satellite to enter each mode is output.

[0036] Secondly, the present invention also provides a drag-free satellite end-to-end mission planning system based on the ER-PSO algorithm, the system comprising:

[0037] The dynamics model construction module is used to establish a full-process dynamics model of the Samsung system, which is used to detect gravitational waves on dragless satellites.

[0038] The planning model construction module is used to set design variables, constraints and fitness functions based on the full-process dynamic model of the Samsung system to obtain a drag-free satellite full-process mission planning model.

[0039] The preliminary optimization module is used to solve the mission planning problem based on the ER-PSO algorithm for the entire process mission planning model of the towless satellite, and obtain preliminary optimization results.

[0040] The mission planning module is used to reconstruct the fitness function of the top three particles in fitness ranking during the ER-PSO algorithm solution process based on the preliminary optimization results, so as to obtain the shortest time for the three satellites to enter the scientific measurement mode simultaneously and the time for the three satellites to enter each mode of the three-satellite system in the whole process, and complete the mission planning.

[0041] The drag-free satellite full-process mission planning method and system based on the ER-PSO algorithm of the present invention has the following advantages over the prior art:

[0042] (1) By establishing a full-process dynamic model of the three-satellite system without dragging, the complete workflow of each satellite from attitude adjustment to scientific measurement is incorporated into a unified planning framework. Combined with the global optimization capability and experience pool replay mechanism of the ER-PSO algorithm, it can efficiently solve complex multivariate optimization problems under the premise of satisfying multiple constraints. Furthermore, by reconstructing the fitness function of excellent particles, the quality of the solution is further improved. Finally, the shortest time optimization for the three-satellite system to enter the scientific measurement mode simultaneously is achieved, which improves the systematicness, coordination and time efficiency of mission planning.

[0043] (2) By establishing a full-process dynamic model of the three-star system, reasonably setting design variables, constraints and fitness functions, a complete mission planning model is constructed to ensure that each mission link of the satellite strictly follows the time-series dependency relationship, effectively avoiding the chaos and conflict of mission links. With the unique particle velocity and direction calculation method and the real-time update and maintenance of the experience pool, a better solution can be found quickly, greatly shortening the solution time of mission planning, improving mission execution efficiency, accelerating the mission planning process, saving a lot of valuable time for the gravitational wave detection mission, and enabling the satellite to enter the scientific measurement mode more quickly.

[0044] (3) Detailed and accurate dynamic modeling was performed on various modes of the three-star gravitational wave detection system, including attitude adjustment mode, test mass release and capture mode, high resolution mode, and drag-free control mode. In attitude adjustment mode, the satellite's orbital root numbers, attitude Euler angles, target coordinate system, and related attitude dynamic equations were defined. In other modes, specific dynamic equations and control processes were also given, laying a precise model foundation for mission planning, improving the accuracy of mission planning, and better meeting the stringent requirements of precise control throughout the entire process for gravitational wave detection missions. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a flowchart of a drag-free satellite full-process mission planning method based on the ER-PSO algorithm according to the present invention;

[0047] Figure 2 A schematic diagram illustrating the initialization satellite attitude mode provided in an embodiment of the present invention;

[0048] Figure 3 A schematic diagram illustrating the initialization satellite attitude mode provided in an embodiment of the present invention;

[0049] Figure 4 This is a schematic diagram of the satellite's internal coordinate system provided in an embodiment of the present invention;

[0050] Figure 5 A schematic diagram of the test mass release capture mode provided in an embodiment of the present invention;

[0051] Figure 6 A schematic diagram of a high-resolution mode provided in an embodiment of the present invention;

[0052] Figure 7 This is a schematic diagram of the drag-free control mode provided in an embodiment of the present invention;

[0053] Figure 8 This is a schematic diagram of the ER-PSO algorithm provided in this embodiment of the invention when the experience pool is not full.

[0054] Figure 9 This is a schematic diagram of the ER-PSO algorithm after the experience pool is filled, provided in an embodiment of the present invention.

[0055] Figure 10This diagram illustrates the optimization results of drag-free satellite mission planning based on the PSO algorithm and the ER-PSO algorithm, as provided in embodiments of the present invention. Detailed Implementation

[0056] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0057] Please see Figure 1 This invention provides a drag-free satellite full-process mission planning method based on the ER-PSO algorithm, including the following steps:

[0058] A full-process dynamic model of the Samsung system is established, which is used for gravitational wave detection of dragless satellites.

[0059] Based on the Samsung system full-process dynamics model, design variables, constraints and fitness functions are set to obtain the drag-free satellite full-process mission planning model.

[0060] For the aforementioned dragless satellite full-process mission planning model, the mission planning problem is solved based on the ER-PSO algorithm, and preliminary optimization results are obtained;

[0061] Based on the preliminary optimization results, the fitness functions of the top three particles in terms of fitness during the ER-PSO algorithm solution process are reconstructed to obtain the shortest time for the three satellites to enter the scientific measurement mode simultaneously and the time for the three satellites to enter each mode of the entire three-satellite system process, thus completing the mission planning.

[0062] Specifically, this embodiment establishes a full-process dynamic model of the three-satellite system without dragging, incorporating the complete workflow of each satellite from attitude adjustment to scientific measurement into a unified planning framework. Combining the global optimization capability and experience pool replay mechanism of the ER-PSO algorithm, it can efficiently solve complex multivariate optimization problems under multiple constraints. Furthermore, by reconstructing the fitness function of excellent particles, the quality of the solution is further improved, ultimately achieving the shortest time optimization for the three-satellite system to simultaneously enter the scientific measurement mode, thus improving the systematicness, coordination, and time efficiency of mission planning.

[0063] This invention fully considers various constraints, including mode triggering sequence logic and mode triggering time logic, ensuring the feasibility of satellite mission planning under various practical limitations. This comprehensive and detailed constraint setting allows the planning scheme to flexibly adapt to complex situations during satellite operation. Furthermore, the experience pool replay mechanism in the ER-PSO algorithm plays a crucial role. It records information during particle motion and retains valuable particle information by continuously updating and maintaining the experience pool. This enables the algorithm to better suit the characteristics of mission planning problems, quickly finding effective solutions even when facing complex and ever-changing mission requirements, thus significantly improving the system's overall adaptability to different mission scenarios and environmental changes.

[0064] This invention constructs a systematic drag-free satellite mission planning framework that integrates core elements such as timeline arrangement, action sequence design, constraint analysis, and planning scheme optimization. It delves into the intrinsic relationships between constraints, action sequences, time mapping, and mission planning. This innovative framework provides new theoretical support and technical pathways for gravitational wave detection missions, contributing to the advancement of gravitational wave detection technology to a higher level. Furthermore, through efficient and precise mission planning, drag-free satellites can operate more stably and smoothly enter scientific measurement mode, effectively reducing the risk of detection failure due to unreasonable mission planning and improving the success rate of gravitational wave detection missions.

[0065] The mission planning focus of drag-free satellites shifts to precise internal operations, exhibiting a significant serial mission characteristic—each mission segment, such as satellite attitude alignment, quality release and acquisition, high-resolution mode control, drag-free state maintenance, and scientific measurement mode activation, must strictly follow temporal dependencies and dynamically adjust control strategies by tracking internal quality checks.

[0066] The full-process mission planning model for drag-free satellites needs to comprehensively cover all key stages of the mission lifecycle, integrating core elements such as timeline arrangement, action sequence design, constraint analysis, and planning scheme optimization. By deeply exploring the intrinsic relationship between constraints, action sequences, time mapping, and mission planning, the model achieves overall coordination and optimization of the entire drag-free satellite mission execution process, providing theoretical support and technical pathways for improving the efficiency and success rate of gravitational wave detection missions.

[0067] The establishment of a full-process dynamic model for the three-satellite system for gravitational wave detection without dragging satellites includes:

[0068] The proposed Samsung system includes various modes throughout the entire process, including attitude adjustment mode, quality release capture mode, high resolution mode, and drag-free control mode.

[0069] Dynamic models were performed for each mode of the Samsung system to construct the dynamic model involved in the entire mission planning of the gravitational wave detection satellite.

[0070] A full-process dynamic model of the three-satellite system for gravitational wave detection was constructed based on the collaborative operation of each satellite and its mode, and the triggering time of each working mode of each satellite was extracted as an independent input parameter interface.

[0071] The attitude adjustment mode includes: initializing the orbital root numbers and attitude Euler angles of the three satellites, and clarifying the construction method of the initial body coordinate system of each satellite. During the attitude adjustment process, a specific target coordinate system is set for each satellite to achieve mutual tracking and attitude alignment between satellites. The relationship between elements such as angular acceleration, moment of inertia, and control torque is described using attitude dynamics equations; attitude is quantitatively described using quaternion differential equations; and a complete attitude adjustment control system is constructed through attitude error calculation formulas and PID controller equations to ensure that the satellite attitude can be accurately adjusted to the target state.

[0072] In one specific embodiment, the orbital six elements of satellite 1 are initialized as follows: the semi-major axis is... m, eccentricity 0, orbital inclination 74.39°, right ascension of ascending node 0°, argument of perigee 211.58°, mean perigee 30°, initialize the attitude Euler angles of satellite 1 as follows: In attitude Euler angles, the three angles represent the rotation angles around the z-axis, y-axis, and x-axis of the satellite orbit coordinate system, respectively.

[0073] The initial orbit of satellite 2 has six roots and a semi-major axis of [value missing]. m, eccentricity 0, orbital inclination 74.39°, right ascension of ascending node 0°, argument of perigee 211.58°, mean perigee 150°, initialize the attitude Euler angles of satellite 2 as follows: ;

[0074] The initial orbit of satellite 3 has six roots and a semi-major axis of [value missing]. m, eccentricity 0, orbital inclination 74.39°, right ascension of ascending node 0°, argument of perigee 211.58°, mean perigee 270°, initialize the attitude Euler angles of satellite 3 as follows: ;

[0075] The satellite's body coordinate system is reversed in its x and z axes compared to the initialized coordinate system. The y-axis is determined by the right-hand rule. Specifically, the initial body coordinate system of satellite 1 is described as a rotation of 4.156 rad around the z-axis of the satellite orbit coordinate system, a rotation of -2.132 rad around the y-axis of the satellite orbit coordinate system, and a rotation of 1.275 rad around the x-axis of the satellite orbit coordinate system to obtain a transition coordinate system. The x and z axes of the transition coordinate system are reversed, and the y-axis is determined using the right-hand rule to obtain a new coordinate system. The initial body coordinate system of satellite 2 is described as a rotation of 1.023 rad around the z-axis of the satellite orbit coordinate system, and a rotation of 1.023 rad around the x-axis of the satellite orbit coordinate system. The initial coordinate system of satellite 3 is described as follows: Rotating the y-axis by -0.598 rad and the x-axis around the satellite orbit coordinate system by 2.14 rad, a transition coordinate system is obtained. Reversing the x and z axes of the transition coordinate system and applying the right-hand rule to the y-axis, a new coordinate system is obtained. Figure 2 As shown.

[0076] Satellite 1 ( The target coordinate system in the control process is the transition coordinate system obtained by rotating the transition coordinate system 30° counterclockwise around the y-axis, with the direction from satellite 1 to satellite 2 as the positive x-axis of the transition coordinate system, the y-axis of the satellite 2 orbit coordinate system as the y-axis of the transition coordinate system, and the z-axis of the transition coordinate system determined according to the right-hand rule.

[0077] Satellite 2 ( The target coordinate system in the control process is the transition coordinate system obtained by rotating the transition coordinate system 30° counterclockwise around the y-axis, with the direction from satellite 2 to satellite 3 as the positive x-axis of the transition coordinate system, the y-axis of the satellite 3 orbit coordinate system as the y-axis of the transition coordinate system, and the z-axis of the transition coordinate system determined according to the right-hand rule.

[0078] Satellite 3 ( The target coordinate system in the control process is the transition coordinate system obtained by rotating it counterclockwise by 30° around the y-axis, with the direction from Satellite 3 to Satellite 1 as the positive x-axis of the transition coordinate system, the y-axis of the orbital coordinate system of Satellite 1 as the y-axis of the transition coordinate system, and the z-axis of the transition coordinate system determined according to the right-hand rule. That is, the three satellites track each other until their attitudes are aligned. This mode involves an attitude control loop, and the specific attitude dynamics equations are as follows:

[0079] ;

[0080] ;

[0081] ;

[0082] in, Represents the angular acceleration vector, I Represents the moment of inertia matrix, The inverse matrix representing the moment of inertia, Represents the control torque vector, Represents the disturbance torque vector, The antisymmetric matrix representing the angular velocity vector. Indicates the satellite's angular velocity;

[0083] Attitudes are described in quaternion form, and the specific quaternion differential equation is as follows:

[0084] ;

[0085] ;

[0086] ;

[0087] in, Representing quaternions Represents the angular velocity matrix. Denotes the derivative of a quaternion. Representing quaternion expressions respectively The coefficients in the text, , , This represents the angular velocity components of a rigid body about the three orthogonal axes of its body coordinate system;

[0088] The formula for calculating attitude error is:

[0089] ;

[0090] in, For error quaternions, Find the inverse of the target quaternion. For the current quaternion, Represents the multiplication operation of quaternions.

[0091] Attitude error vector The calculation formula is:

[0092] ;

[0093] ;

[0094] ;

[0095] in, Represents the rotation axis vector. Indicates the rotation angle. , , Representing the error quaternions respectively exist The coefficients in the directions of the three orthogonal bases.

[0096] The PID controller equation is:

[0097] ;

[0098] in, Represents the control torque vector. Represents the proportional gain coefficient. Represents the integral gain coefficient. Represents the differential gain coefficient. This represents the attitude error vector, specifically... , , The satellite's maximum control torque is .

[0099] Based on the above equations, a dynamic model of the satellite in "attitude adjustment mode" can be constructed. A schematic diagram after attitude alignment is shown below. Figure 3 As shown.

[0100] The inspection mass release and capture mode includes the following: at a certain moment, the inspection mass is released from the clamping mechanism, and its release velocity and displacement are closely related to the satellite's angular velocity and described based on a specifically defined cavity coordinate system. In this mode, the motion state of the inspection mass in the cavity coordinate system is characterized by dynamic equations, while also considering the interference force generated by the electrostatic levitation force on the satellite. The displacement of the inspection mass in the cavity coordinate system is used as the error, and a PID control strategy is employed to effectively regulate the motion of the inspection mass, thereby constructing a corresponding dynamic model.

[0101] In one specific embodiment, at a certain moment, the test mass is released from the clamping mechanism and released in the cavity coordinate system. Its release velocity and displacement are considered to be related to the satellite's angular velocity, specifically the release velocity. , It should be noted that both the velocity and displacement are defined based on the cavity coordinate system corresponding to the inspection mass. The cavity coordinate system of inspection mass 1 is defined as obtained by rotating the satellite body coordinate system 60° clockwise around the y-axis, and the cavity coordinate system of inspection mass 2 is defined as obtained by rotating the satellite body coordinate system 60° counterclockwise around the y-axis. The coordinate system diagram is shown below. Figure 4 As shown, the dynamic equations involved in this mode are:

[0102] ;

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] in, , , These represent the x, y, and vertices of the inspection quality 1 in its cavity coordinate system. , , These represent the horizontal, vertical, and axial coordinates of the inspection quality 2 in its cavity coordinate system. , , These represent the displacements of the inspection mass 1 along the x, y, and z axes of its cavity coordinate system. , , These represent the displacements of the inspection mass 2 along the x, y, and z axes of its cavity coordinate system, respectively. , , These represent the accelerations of the test mass 1 along the x-axis, y-axis, and z-axis of its cavity coordinate system, respectively. , , These are the accelerations of the test mass 2 along the x-axis, y-axis, and z-axis of its cavity coordinate system, respectively. , , These represent the electrostatic negative stiffness coefficients of the test mass along the x-axis, y-axis, and z-axis of the cavity coordinate system, respectively. and These represent the angular velocity vector and angular acceleration mass of the satellite's body coordinate system relative to the geocentric inertial coordinate system, respectively. , , These represent the forces acting on the satellite along the x, y, and z axes in the cavity coordinate system of test mass 1, respectively. , , These represent the forces acting on the inspection mass 1 along the x, y, and z axes in its cavity coordinate system, respectively. , , These represent the forces acting on the satellite in the x, y, and z axes of the cavity coordinate system of the test mass 2, respectively. , , These represent the forces acting on the inspection mass 2 along the x, y, and z axes in its cavity coordinate system, respectively. Indicates the mass of the satellite, This indicates the quality of inspection quality 1. This indicates the quality of inspection quality 2.

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] in, This represents the forces acting on the satellite in its body coordinate system. , , , , , These represent the forces acting on inspection mass 1 and inspection mass 2 in their respective cavity coordinate systems along the x-axis, y-axis, and z-axis directions. This represents the rotation matrix from the satellite body coordinate system to the satellite cavity coordinate system 1; This represents the rotation matrix from the satellite body coordinate system to the satellite cavity coordinate system 2.

[0114] In this mode, the satellite is subjected to interference forces generated by electrostatic levitation, specifically expressed as follows:

[0115] ;

[0116] in, The interference force generated by the electrostatic levitation force on the satellite and Let these represent the position vectors of test mass 1 and test mass 2 relative to the satellite's centroid, respectively. and These represent the forces acting on inspection mass 1 and inspection mass 2 in the cavity coordinate system, respectively.

[0117] The specific control process uses the displacement of the mass in the cavity coordinate system as the error for PID control. A schematic diagram of this mode is shown below. Figure 5 As shown, based on the above equations, a dynamic model of the satellite under the "test mass release capture mode" can be constructed.

[0118] The high-resolution mode includes the following: the control equations for this mode are basically the same as those for the test mass release and capture mode, but there are significant differences in actual operation. In the test mass release and capture mode, the electrostatic levitation force is relatively large, the noise generated is also more obvious, and the electrostatic levitation mechanism has the characteristic of a large measurement range; while in the high-resolution mode, the characteristics of the electrostatic levitation force are changed, the noise situation is different, and the measurement range of the electrostatic levitation mechanism is reduced to meet the requirements of high-resolution measurement.

[0119] In one specific embodiment, the control equations for this mode are the same as those for the test mass release and capture mode. The difference lies in the relatively large electrostatic levitation force and the resulting noise in the test mass release and capture mode. Additionally, the electrostatic levitation mechanism also measures the displacement of the test mass. In the test mass release and capture mode, its range is... Its range in high-resolution mode is The schematic diagram of this model is as follows: Figure 6 As shown.

[0120] The drag-free control mode includes the following: This mode follows the control equation framework of the "inspection mass release and capture mode." Unlike the inspection mass release and capture mode, which applies electrostatic levitation force to all axes of the inspection mass, the drag-free control mode only applies to the x and y axes of inspection mass 1 and the x-axis of inspection mass 2. During the control process, the displacement of the inspection mass in the cavity coordinate system needs to be transformed to the satellite body coordinate system as error. Using the satellite's micro-thrusters as actuators, the forces acting on the satellite in the body coordinate system are calculated through PID control. Combined with other relevant equations, a dynamic model of the satellite in the "drag-free mode" is finally constructed, achieving precise control of the satellite's motion.

[0121] In one specific embodiment, this mode still follows the control equations of the "inspection mass release and capture mode". However, unlike the inspection mass release and capture mode where electrostatic levitation force is applied to all axes of the inspection mass, the drag-free control mode uses the x and y axes of inspection mass 1 and the x axis of inspection mass 2 as the error, and the satellite's micro-thruster as the actuator for PID control. It should be noted that the error must be based on the satellite's body coordinate system; that is, the displacements of inspection mass 1 along the x and y axes in cavity coordinate system 1 and the displacement of inspection mass 2 along the x axis in cavity coordinate system 2 need to be transformed to the satellite's body coordinate system. The specific expression is as follows:

[0122] ;

[0123] ;

[0124] in, These represent the displacements of inspection mass 1 and inspection mass 2 in the satellite body coordinate system, respectively. This represents the displacement of inspection mass 1 along the x-axis in its cavity coordinate system. This represents the displacement of inspection mass 1 along the z-axis in its cavity coordinate system. and By using the satellite's micro-thrusters as actuators and applying PID control to the error and satellite's micro-thrusters, the forces acting on the satellite in its body coordinate system can be obtained. Then, by applying the equations described in the "test mass release capture mode" to electrostatically levitate the remaining axes, a dynamic model of the satellite in "drag-free mode" can be constructed. A schematic diagram of this mode is shown below. Figure 7 As shown.

[0125] In one specific embodiment, a full-process dynamic model of the three-satellite system for gravitational wave detection is constructed collaboratively for each mode of each satellite. The trigger time of each working mode of each satellite is extracted as an independent input parameter interface, specifically: the release time of test mass 1 in satellite 1. The release time of test mass 2 in satellite 1 The time when high-resolution mode control begins to be implemented in satellite 1 (in inspection quality 1). The time when high-resolution mode control begins to be implemented in satellite 1 (inspection quality 2). Time when Satellite 1 enters drag-free control mode The release time of test mass 1 in satellite 2 The release time of test mass 2 in satellite 2 The time when high-resolution mode control begins to be implemented in Satellite 2 (Test Quality 1). The time when high-resolution mode control begins to be implemented in satellite 2 (in inspection quality 2). Time when Satellite 2 enters drag-free control mode The release time of test mass 1 in satellite 3 The release time of the test mass 2 in satellite 3 The time when high-resolution mode control begins to be implemented in satellite 3 for quality inspection 1. The time when high-resolution mode control begins to be implemented in satellite 3 (in inspection quality 2). The time when satellite 3 enters drag-free control mode .

[0126] Each satellite's system is treated as a separate class, containing attributes and methods related to that satellite. For example, the satellite's attitude dynamics system includes attributes such as moment of inertia, angular velocity, and quaternions, as well as methods for calculating satellite acceleration and updating its state. The satellite's electrostatic levitation system includes attributes such as the mass, forces, and state of the satellite and the test mass, as well as methods for updating the test mass's state and rotation matrix. The Samsung system can be constructed by calling instances of these classes.

[0127] The dynamic modeling includes: describing the relationship between angular acceleration, moment of inertia and control torque using attitude dynamics equations; quantifying attitude using quaternion differential equations; and constructing an attitude adjustment control system using attitude error calculation formulas and PID controller equations.

[0128] The motion state of the inspection mass in the cavity coordinate system is characterized by the dynamic equation. Based on the interference force generated by the electrostatic levitation force on the satellite, the motion of the inspection mass is regulated by the PID control strategy.

[0129] The input parameter interface includes the release and capture time of each inspection mass in each satellite, the start time of high-resolution mode control for each inspection mass, and the start time of drag-free mode control for each satellite, comprising 15 input parameter interfaces.

[0130] In one specific embodiment, the trigger time of each satellite's operating mode is used as the design variable, and the constraint is as follows:

[0131] (1) Pattern triggering sequence logic:

[0132]

[0133] (2) Pattern triggering time logic:

[0134]

[0135] The fitness function includes: the time to enter the scientific measurement mode, which is defined as the satellite being in drag-free control mode and the sensitive axis displacement always being less than 1. The displacement of the non-sensitive axis is always less than The times for the three satellites to enter scientific measurement are set as follows: , , The fitness function is set to The final optimization objective of task planning is to minimize this fitness function.

[0136] In the task planning problem, the ER-PSO algorithm is used for solution. ER-PSO is an improved algorithm based on particle swarm optimization. Its specific principle is as follows: Initialize the velocity, quantity, and position of particles. The velocity of a particle during its movement is calculated based on its fitness; particles with better fitness have lower velocities, and vice versa. The particle's direction consists of the globally optimal direction, any particle direction from the experience pool, and a random direction. An attenuation factor is set initially to reduce the velocity and random direction of the particles. An experience pool is constructed; all particles are recorded in the experience pool during movement. When the experience pool is full, new particles are added while the particle with the worst fitness is removed to ensure the experience pool is constantly updated and maintained. Based on the above principles, the task planning problem can be solved relatively quickly.

[0137] The specific steps are as follows: initialize the maximum particle velocity. The initial exploration rate of the particle is 100. The particle decay rate is 0.9. The value is 0.99, and the experience pool capacity is... The initial number of particles is 15, and the number of algorithm iterations is 80.

[0138] Initially, 15 random particles are generated, and the experience pool and global optimum are initialized. The experience pool is not filled during this process. During optimization, the maximum velocity of each generation of particles is determined by... Determined; in each generation, the exploration rate of each particle is determined by... Determined; the velocity of each particle is determined by Confirmed, among which The fitness of this particle, This represents the minimum fitness value of particles in the previous generation population. The maximum fitness value of the particle in the previous generation population; the search direction of the particle is determined by... It is confirmed that, among them, This represents the normalized direction vector pointing from the current particle's position to the optimal particle's position. This represents the normalized direction vector pointing from the current particle's position to the position of any particle in the experience pool. This represents the initial exploration rate of the particle. This represents a normalized random direction vector, which is processed according to the following rules before the experience pool is filled: Figure 8 The principle illustrated here is to fill the experience pool by updating the particle positions according to the particle velocity and direction update method described above, and directly adding new particles to the experience pool; when the experience pool is full, the particle positions are updated again according to the same particle velocity and direction update method, and new particles are directly added to the experience pool, while the worst particle in the current experience pool is deleted. For example... Figure 9As shown, the results of the ER-PSO algorithm and the PSO algorithm are compared. In the PSO algorithm, the inertia weight is 0.7, the individual learning factor is 1.4, the social learning factor is 1.4, the number of particles is 15, and the maximum number of iterations is 80. The simulation time for each satellite in both algorithms was from January 1, 2024 to February 10, 2024, totaling 960 hours. The optimization results are as follows. Figure 10 As shown.

[0139] In one specific embodiment, during the optimization process of the ER-PSO algorithm, the independent variables of the particles, particle fitness, and the time when each satellite in each particle enters the science verification mode are recorded in real time. The fitness function of the top three particles is reconstructed and re-substituted into the algorithm. The optimal solution is obtained by solving the fitness function, and the optimal solution for the task planning problem is reconstructed to obtain a solution that is more in line with the purpose of task planning. The optimal solution reconstruction of the ER-PSO algorithm and the PSO algorithm is shown in Table 1 and Table 2. The mission planning results obtained based on the ER-PSO algorithm are as follows: Satellite 1's inspection quality 1 is released for capture at 248, Satellite 1's inspection quality 1 is controlled in high-resolution mode at 325, Satellite 1's inspection quality 2 is released for capture at 240, Satellite 1's inspection quality 2 is controlled in high-resolution mode at 301, and Satellite 1 is controlled without drag at 410; Satellite 2's inspection quality 1 is released for capture at 294, Satellite 2's inspection quality 1 is controlled in high-resolution mode at 359, Satellite 2's inspection quality 2 is released for capture at 267, Satellite 2's inspection quality 2 is controlled in high-resolution mode at 345, and Satellite 2 is controlled without drag at 479; Satellite 3's inspection quality 1 is released for capture at 229, Satellite 3's inspection quality 1 is controlled in high-resolution mode at 351, Satellite 3's inspection quality 2 is released for capture at 290, Satellite 3's inspection quality 2 is controlled in high-resolution mode at 331, and Satellite 3 is controlled without drag at 430.

[0140] Table 1 Optimal Solution Reconstruction of ER-PSO Algorithm

[0141]

[0142] Table 2 Reconstruction of the Optimal Solution by the PSO Algorithm

[0143]

[0144] This invention also provides a drag-free satellite end-to-end mission planning system based on the ER-PSO algorithm, the system comprising:

[0145] The dynamics model construction module is used to establish a full-process dynamics model of the Samsung system, which is used to detect gravitational waves on dragless satellites.

[0146] The planning model construction module is used to set design variables, constraints and fitness functions based on the full-process dynamic model of the Samsung system to obtain a drag-free satellite full-process mission planning model.

[0147] The preliminary optimization module is used to solve the mission planning problem based on the ER-PSO algorithm for the entire process mission planning model of the towless satellite, and obtain preliminary optimization results.

[0148] The mission planning module is used to reconstruct the fitness function of the top three particles in fitness ranking during the ER-PSO algorithm solution process based on the preliminary optimization results, so as to obtain the shortest time for the three satellites to enter the scientific measurement mode simultaneously and the time for the three satellites to enter each mode of the three-satellite system in the whole process, and complete the mission planning.

[0149] Specifically, this embodiment presents a dragless satellite mission planning system based on the ER-PSO algorithm, which achieves systematic and automated processing of dragless satellite mission planning through modular design. The system's dynamic model construction module establishes a dynamic model covering the entire process, including attitude adjustment, mass release and capture verification, high resolution, and dragless control. The planning model construction module sets up a design variable system with 15 input parameter interfaces and complete constraints. The preliminary optimization module uses an ER-PSO algorithm enhanced by an experience pool replay mechanism, significantly improving global search capability and convergence performance. The mission planning module further optimizes the three-satellite synchronization performance through fitness function reconstruction technology. Compared with traditional manual experience planning or simple optimization methods, this system can automatically handle complex multi-constraint optimization problems, greatly improving the accuracy, efficiency, and reliability of mission planning. It provides a complete mission planning solution for high-precision space science experiments such as gravitational wave detection, and has good engineering application value and promising prospects for widespread application.

[0150] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A drag-free satellite end-to-end mission planning method based on the ER-PSO algorithm, characterized in that, Includes the following steps: A full-process dynamic model of the Samsung system is established, which is used for gravitational wave detection of dragless satellites. Based on the Samsung system full-process dynamics model, design variables, constraints and fitness functions are set to obtain the drag-free satellite full-process mission planning model. For the aforementioned dragless satellite full-process mission planning model, the mission planning problem is solved based on the ER-PSO algorithm, and preliminary optimization results are obtained; The aforementioned mission planning model for the dragless satellite full-process process is used to solve the mission planning problem based on the ER-PSO algorithm, yielding preliminary optimization results, including: Initialize the particle swarm, perform iterative optimization according to the basic process of the particle swarm optimization algorithm, and obtain the fitness value of each particle by updating the particle velocity and position. The particle swarm optimization process is improved based on the experience pool replay mechanism. The global search capability and convergence performance of the particle swarm optimization algorithm are enhanced by the real-time update and maintenance mechanism of the experience pool, and preliminary optimization results are obtained. Based on the preliminary optimization results, the fitness functions of the top three particles in terms of fitness during the ER-PSO algorithm solution process are reconstructed to obtain the shortest time for the three satellites to enter the scientific measurement mode simultaneously and the time for the three satellites to enter each mode of the entire three-satellite system process, thus completing the mission planning.

2. The drag-free satellite full-process mission planning method based on the ER-PSO algorithm as described in claim 1, characterized in that, The establishment of the full-process dynamic model of the Samsung system includes: The Samsung system's entire process is designed with various modes, including attitude adjustment mode, quality release capture mode, high resolution mode, and drag-free control mode. Dynamic models were performed for each mode of the entire process of the Samsung system to construct a dynamic model involved in the entire mission planning of the gravitational wave detection satellite. A full-process dynamic model of the three-satellite system for gravitational wave detection was constructed based on the collaborative operation of each satellite and its mode, and the triggering time of each working mode of each satellite was extracted as an independent input parameter interface.

3. The drag-free satellite full-process mission planning method based on the ER-PSO algorithm as described in claim 2, characterized in that, The attitude adjustment mode includes: initializing the orbital six elements and attitude Euler angles of the three satellites, determining the construction method of the initial body coordinate system of each satellite, and setting a specific target coordinate system for each satellite during the attitude adjustment process to achieve mutual tracking and attitude alignment between the satellites.

4. The drag-free satellite full-process mission planning method based on the ER-PSO algorithm as described in claim 2, characterized in that, The dynamic modeling includes: describing the relationship between angular acceleration, moment of inertia and control torque using attitude dynamics equations, quantifying attitude using quaternion differential equations, and constructing an attitude adjustment control system using attitude error calculation formulas and PID controller equations. The motion state of the inspection mass in the cavity coordinate system is characterized by the dynamic equation. Based on the interference force generated by the electrostatic levitation force on the satellite, the motion of the inspection mass is regulated by the PID control strategy. The input parameter interface includes the release and capture time of each inspection mass in each satellite, the start time of high-resolution mode control for each inspection mass, and the start time of drag-free mode control for each satellite, comprising 15 input parameter interfaces.

5. The drag-free satellite full-process mission planning method based on the ER-PSO algorithm as described in claim 1, characterized in that, The establishment of a drag-free satellite full-process mission planning model based on the Samsung system's full-process dynamics model includes setting design variables, constraints, and fitness functions, including: The trigger times of each satellite's operating mode extracted from the full-process dynamic model of the Samsung system are used as design variables; Setting constraints includes the logic for the mode triggering sequence and the logic for the mode triggering time; The fitness function is set as the sum of the times when each satellite enters the scientific measurement mode, resulting in a drag-free satellite full-process mission planning model. The scientific measurement mode is defined as the satellite being in drag-free control mode and the sensitive axis displacement being less than [a certain value]. and non-sensitive axis displacement less than .

6. The drag-free satellite end-to-end mission planning method based on the ER-PSO algorithm as described in claim 5, characterized in that, The design variables include the release capture time of each inspection mass in each satellite, the start time of each inspection mass in each satellite to start high-resolution mode control, and the start time of drag-free mode control in each satellite, including 15 input parameter interfaces. The mode triggering sequence logic is as follows: the release capture time of each inspection quality is less than the time of each inspection quality performing high-resolution mode control, and the time of each inspection quality performing high-resolution mode control is less than the time of each satellite starting to perform drag-free mode control. The mode triggering time logic is as follows: the release time of each inspection quality is greater than the simulation start time, and the time for each satellite to perform drag-free mode control is less than the simulation end time.

7. The drag-free satellite full-process mission planning method based on the ER-PSO algorithm as described in claim 1, characterized in that, The particle swarm initialization includes: setting the particle swarm size, maximum number of iterations, inertia weight, and learning factor, and randomly initializing the position and velocity of each particle within the constraints of the design variables; The iterative optimization process includes: calculating the new position and new velocity of each particle according to the particle velocity update formula and the position update formula; calculating the fitness value corresponding to the position of each particle based on the drag-free satellite full-process mission planning model; updating the individual optimal position and the global optimal position; and repeating the iteration until the convergence condition is met. The experience pool replay mechanism includes: establishing an experience pool to store historical excellent solutions, setting the experience pool capacity and update strategy; during particle swarm optimization, adding excellent particles that meet the conditions to the experience pool; when a particle gets stuck in a local optimum, selecting historical excellent solutions from the experience pool to guide the search direction of the current particle. The real-time update and maintenance mechanism of the experience pool includes: sorting the solutions in the experience pool according to their fitness values, and removing poor solutions when the experience pool is full using an elimination strategy.

8. The drag-free satellite full-process mission planning method based on the ER-PSO algorithm as described in claim 7, characterized in that, Based on the preliminary optimization results, the fitness functions of the top three particles in the ER-PSO algorithm solution process are reconstructed to obtain the shortest time for the three satellites to simultaneously enter the scientific measurement mode and the corresponding time for each satellite to enter each mode, thus completing the mission planning, including: The fitness values ​​of all particles during the ER-PSO algorithm iteration are statistically analyzed and sorted in ascending order. The three particles with the smallest fitness values ​​are selected as candidate optimal solutions. The selected particles are verified to meet the constraints. If they do not meet the constraints, the next particle with a smaller fitness value is selected to replace them, so as to ensure that the three selected particles are all feasible solutions. Based on the position information of the three candidate particles, the evaluation weights and evaluation indicators of the fitness function are reset, and the evaluation weight of the three-star synchronization performance is increased to obtain the reconstructed fitness function. The reconstructed fitness function is substituted into the full-process dynamic model of the three-satellite system for simulation calculation. The reconstruction fitness values ​​of the three candidate solutions are compared, and the solution with the smallest reconstruction fitness value is selected as the final mission planning scheme. The corresponding optimal time series for each satellite to enter each mode is output.

9. A dragless satellite end-to-end mission planning system based on the ER-PSO algorithm, used to execute the dragless satellite end-to-end mission planning method based on the ER-PSO algorithm as described in any one of claims 1-8, characterized in that, The system includes: The dynamics model construction module is used to establish a full-process dynamics model of the Samsung system, which is used to detect gravitational waves on dragless satellites. The planning model construction module is used to set design variables, constraints and fitness functions based on the full-process dynamic model of the Samsung system to obtain a drag-free satellite full-process mission planning model. The preliminary optimization module is used to solve the mission planning problem based on the ER-PSO algorithm for the entire process mission planning model of the towless satellite, and obtain preliminary optimization results. The mission planning module is used to reconstruct the fitness function of the top three particles in fitness ranking during the ER-PSO algorithm solution process based on the preliminary optimization results, so as to obtain the shortest time for the three satellites to enter the scientific measurement mode simultaneously and the time for the three satellites to enter each mode of the three-satellite system in the whole process, and complete the mission planning.

Images