High-robustness satellite cluster formation control method and system

Abstract

The invention discloses a high-robustness satellite cluster formation control method and system, and the method comprises the following steps: S1, measuring the actual position between satellites in a satellite cluster, and solving the relative navigation of the satellite cluster through a multi-event point C-W equation based on least square optimization; s2, satellite cluster formation maintenance based on fuel equalization: calculating an ideal position between two satellites in a satellite cluster, and performing formation maintenance according to a deviation between an actual position and the ideal position; and S3, formation reconstruction trajectory planning based on an improved pseudo-spectral method, and performing trajectory planning when formation reconstruction is needed in the step. According to the method and the system, the navigation precision, the fuel balance and the measurement precision can be improved.

Description

Technical Field

[0001] The present invention relates to the field of aerospace orbit control, in particular to the technology of high-robustness satellite cluster formation control, and specifically relates to a high-robustness satellite cluster formation control method and system. Background Art

[0002] The relative orbit control of satellite cluster formation flight mainly controls the magnitude and direction of the relative velocity between satellites in the cluster. The accuracy of relative position is crucial for the formation effect of formation flight, especially for precise formation flight in a small-scale fly-around configuration. In practice, the inter-satellite communication link of the satellite cluster may be interrupted, resulting in intermittent unavailability of relative measurement and inability to output relative navigation information. For fine formation control, it is necessary to accurately predict the relative motion state between satellites for a long time to accurately determine the moment of reaching the error boundary and formulate control strategies. Therefore, high-precision relative navigation and on-board long-term relative motion state prediction in the case of intermittent unavailability of relative navigation sensors are urgent problems to be solved in engineering practice. In addition, when designing the autonomous reconstruction trajectory from the initial formation to the target formation, if the collision probability is verified throughout the process, the computational cost will be very high. If only the values at the segmentation points are verified, it is difficult to ensure that collisions can be avoided.

[0003] The technology of satellite cluster formation control has become a research hotspot in the aerospace field in recent years and is widely used in tasks such as earth observation, deep space exploration, scientific experiments, and communication enhancement. With the increase in the complexity and scale of space missions, the capabilities of single satellites are difficult to meet the requirements of high resolution, high flexibility, and high reliability. Therefore, the formation flight mode in which multiple satellites work together has become the mainstream trend. Through reasonable formation control, satellite clusters can perform high-precision measurements, achieve rapid response, and improve the redundancy of tasks. However, in practical applications, satellite formation control involves complex problems such as orbital dynamics, multi-body interactions, fuel optimal control, and collision avoidance. How to efficiently and safely manage satellite clusters has become a key challenge.

[0004] The basis of satellite formation control is orbital dynamics modeling and relative motion description. Existing methods are mainly based on the following theories: The Clohessy-Wiltshire (CW) equation is used to describe the relative motion of satellites in the case of near-circular orbits and is suitable for formation control in a short time. The CW equation has been widely used in the formation maintenance of low-orbit satellites, but its accuracy is low on long time scales or in high-eccentricity orbits. Similar to the CW equation, the Hill equation is used to describe the relative motion in the reference frame of the main satellite and can be used for short-term prediction, but it cannot accurately describe the influence of orbital perturbations.

[0005] For relative position estimation, the current implementation usually filters the relative velocity through a Kalman filter to obtain relatively accurate initial information on relative velocity, and uses a single event point to solve the analytical solution coefficients of the C-W equation, so as to use the analytical solution for relative motion state prediction under interrupted navigation data. For autonomous reconfiguration orbit design, the current solution adopts a planning method based on numerical optimization. To simplify the problem, this method usually divides the entire reconfiguration process into segments for planning.

[0006] For the formation control problem, the current formation control methods can be roughly classified into the following categories: The first is feedback control (PID), such as a feedback mechanism based on proportional-integral-derivative control, which adjusts the thrust using the measured relative position and velocity. However, PID control is difficult to handle orbital perturbations and nonlinear effects, and its performance is relatively limited. The second is sliding mode control (SMC). For the uncertainties of the system, sliding mode control uses a switching control law to enhance robustness, but it is prone to high-frequency chattering, which affects the performance of the actuator. There is also a type of adaptive control, which combines parameter estimation methods to achieve compensation for unknown perturbations and improve control accuracy. For the optimal control method, it includes the linear quadratic regulator (LQR) and dynamic programming. The linear quadratic regulator (LQR) calculates the optimal control law by optimizing fuel consumption and error minimization, and is suitable for small-scale formation keeping. Dynamic programming uses the Bellman equation to solve the optimal control problem, but the computational complexity is relatively high, making it difficult to apply to large-scale satellite clusters. Currently, convex optimization and pseudospectral methods are relatively popular, including sequential convex optimization (SCOP), which transforms non-convex constraint problems into a series of convex optimization problems for solution, improving computational efficiency and feasibility, and numerical optimization of trajectories based on pseudospectral methods, which is suitable for high-precision orbit maneuvers.

[0007] For collision avoidance strategies, the existing collision avoidance methods mainly fall into two categories. One is the collision avoidance method based on hard constraints: directly adding a minimum safety distance constraint to the optimization problem, such as quadratic programming (QP) or second-order cone programming (SOCP), to ensure that satellites do not collide, but the computational complexity is relatively high. The other is the collision avoidance method based on soft constraints: using potential functions or penalty terms to reduce the collision risk during the optimization process, but parameters need to be adjusted to balance collision avoidance and fuel consumption.

[0008] Disadvantages of calculating relative navigation based on Kalman filtering and single-event point C-W equation: First, it cannot accurately describe the relative motion spatial configuration of two satellites; second, it does not consider the analytical solution error of the C-W equation. Since the analytical solution does not consider constraints such as space perturbation, the long-term prediction accuracy is poor. When using the prediction results for guidance control law calculation, the guidance law error is large and the formation control error is large; third, the calculation amount is large, and more sampling needs to be performed on the satellite to obtain ideal results. If the navigation data is interrupted, the filtering result is poor, and even catastrophic consequences may be brought to the formation flight control. Disadvantages of the planning method based on numerical optimization: When the number of segments is large, the calculation amount will increase sharply, making it difficult to apply online.

[0009] Existing collision avoidance strategies often adopt conservative estimates during the optimization process to ensure that the safety distances of all satellites are not violated. However, overly conservative collision avoidance constraints may lead to a reduction in the feasible solution space of trajectory optimization, causing the solution result to deviate from the optimal solution, thereby increasing unnecessary fuel consumption. For example, although the traditional second-order cone programming (SOCP) method can strictly meet the collision avoidance requirements, the calculated trajectory may be far from the optimal energy path, resulting in propellant waste.

[0010] Most current formation control methods are solved based on deterministic models and are difficult to effectively handle uncertain factors such as actuator errors, communication delays, and external perturbation forces. For example, the traditional LQR method may cause the control signal to diverge when the actuator is saturated, while sliding mode control (SMC), although having good robustness, may increase actuator losses due to high-frequency switching. In addition, the optimal control based on the pseudospectral method is easily affected by environmental perturbations, resulting in trajectory deviations.

[0011] Current formation control methods, such as optimal control, convex optimization, and pseudospectral methods, have high computational complexity when solving high-dimensional nonlinear constraint optimization problems. For example, although the sequential convex optimization (SCOP) method can effectively solve non-convex constraint problems, when facing a large-scale satellite cluster, the computational resource requirements increase significantly, making it difficult to meet the requirements of real-time control. In addition, the computational amount of the dynamic programming method increases exponentially in the high-dimensional state space, making it difficult to apply to actual tasks. Summary of the Invention

[0012] Aiming at the problems existing in the prior art, the purpose of the present invention is to provide a high-robustness satellite cluster formation control method and system, which can improve navigation accuracy, fuel balance, and measurement accuracy.

[0013] To achieve the above object, the present invention provides a high-robustness satellite cluster formation control method, and the method includes the following steps: S1: Measure the actual positions between satellites in the satellite cluster, and use the multi-event point C-W equation based on least squares optimization to solve the relative navigation of the satellite cluster; S2: Satellite constellation formation maintenance based on fuel balance. In this step, the ideal positions between two satellites in the satellite constellation are calculated, and formation maintenance is performed according to the deviation between the actual position and the ideal position. S3: Formation reconfiguration trajectory planning based on the improved pseudospectral method. In this step, trajectory planning is carried out when formation reconfiguration is required.

[0014] Furthermore, after the initial conditions of the satellite formation are determined, the relative positions and velocities between every two satellites in the satellite constellation at each moment are solved according to the C-W equation.

[0015] Furthermore, step S1 includes: S1.1 Establish the target satellite orbit coordinate system; S1.2 Solve the analytical solution of the C-W equation in the satellite orbit coordinate system; S1.3 Establish and solve the least squares fitting measurement equation.

[0016] Furthermore, the specific implementation method of step S1.1 is as follows: Define any one of the two satellites as the target satellite, and its coordinate system is defined with the coordinate origin at the centroid of the target satellite, the Z-axis in the target satellite orbit plane pointing from the centroid of the target satellite to the center of the earth; the Y-axis is perpendicular to the orbit plane, pointing to the negative normal of the orbit plane, opposite to the direction of the orbit angular momentum vector ; the X-axis forms a right-handed helix with the Y and Z axes, pointing in the satellite flight direction; express the relative state of the two satellites in the target satellite orbit coordinate system, and define the relative position and velocity vectors of the two satellites in the target satellite orbit coordinate system as: 、 ; Among them, represents the relative position vector between the two satellites, 、 、 respectively represent the components of the relative position vector in the X, Y, and Z axis directions, and are abbreviated as 、 、 ; represents the velocity vector between the two satellites, 、 、 respectively represent the components of the velocity vector in the X, Y, and Z axis directions, and are abbreviated as 、 、 .

[0017] Furthermore, the specific implementation method of step S1.2 is as follows: Describe the relative motion dynamics equation of the two satellites with the C-W equation, then the C-W equation is described in the target satellite orbit coordinate system as: ; Among them, is the angular velocity of the target satellite's orbit, is the control force applied to each axis, , , are the second-order derivatives with respect to time of the components of the relative position vector in the target satellite's orbit coordinate system;

[0018] When no maneuvering control is performed on the target satellite, , it is known that the relative position of the two satellites at time , , ), and the relative velocity ( , , ). Let , , , , , , then the analytical solution of the C-W equation is expressed as: ; Among them, , ([[]] , , ) represents the relative position of the two satellites at time , ([[]] , , ) represents the relative velocity of the two satellites at time .

[0019] Furthermore, in step S1.3, taking the coefficients , , , , , as state variables, and the relative position obtained from the relative navigation sensor as the measurement quantity, then the measurement equation of the C-W fitting relative motion prediction at time ; Among them, , , respectively represent the positions of the th satellite; represents the position vector of the th satellite, is the state transition matrix of the th satellite, is the The initial state of a satellite, For the th satellite's period, represents the position matrix of the overall satellite cluster formation, is the transfer matrix of the overall cluster satellite formation, represents the transpose operation symbol of the matrix; If there are number of relative position measurement quantities at time, then the measurement equation of the total C-W fitting relative motion prediction can be expressed as: ;

[0020] Using the least squares solution method to solve the fitting C-W solution coefficients: ; After accurately solving through the above formula, the fitting C-W solution is: ;

[0021] Among them, and respectively represent the position and velocity of the th satellite.

[0022] Furthermore, in step S2, the formation maintenance method based on fuel balance is specifically as follows: First, the fuel states of each satellite in the cluster are monitored in real time, and the imbalance degree of fuel distribution is calculated; an optimized scheduling strategy is adopted to reasonably allocate orbit control tasks, so that satellites with sufficient fuel undertake more adjustment tasks, while satellites with less fuel minimize thrust consumption.

[0023] Furthermore, step S2 specifically includes: S2.1 Select the main satellite; every other orbital period, detect the current remaining fuel values of each satellite, compare them according to the current remaining fuel values of each satellite, and select the satellite with the least current remaining fuel value as the main satellite; record the state of the main satellite in the O orbital coordinate system as , , where is the position of the main satellite, is the velocity of the main satellite; S2.2 Calculate the position of the slave satellite; S2.3 Calculate the error between the actual position and the ideal position of the satellite. When it exceeds the error threshold, start the orbit correction program. The other satellites except the main satellite are slave satellites.

[0024] Further, in step S3, the constraint conditions of the cluster reconstruction trajectory optimization process include inter-satellite collision avoidance constraints, output torque constraints, and configuration optimization time constraints; the optimization objective of the cluster reconstruction is to solve the optimal trajectory of the formation reconstruction for the satellite relative motion model.

[0025] On the other hand, the present invention provides a highly robust satellite cluster formation control system for implementing the satellite cluster formation control method according to the present invention.

[0026] The beneficial effects of the present invention are as follows: (1) Improvement in navigation accuracy: The relative navigation is solved by using the multi-event point C-W equation based on least squares optimization, reducing the navigation error and being able to accurately describe the relative motion of two satellites.

[0027] (2) Improvement in fuel balance: The present invention can optimize the fuel distribution strategy while meeting the formation control requirements, avoiding individual satellites from exiting prematurely due to fuel exhaustion, thereby effectively extending the cluster mission life.

[0028] (3) Improvement in measurement accuracy: This method only measures the relative position and velocity of the satellites, avoiding the large errors caused by absolute orbit measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a flowchart of the highly robust satellite cluster formation control method according to the present invention; Figure 2 is a schematic diagram of the satellite coordinate system according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0030] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments of the present invention belong to the scope of protection of the present invention.

[0031] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. In addition, the terms "first", "second", and "third" are only used for descriptive purposes and should not be construed as indicating or implying relative importance.

[0032] In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, the terms "installation", "connection", and "coupling" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0033] The following will Figure 1 - Figure 2 describe the specific embodiments of the present invention in detail. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0034] The present invention provides a high-robustness satellite cluster formation control technology. According to the high-robustness satellite cluster formation control method of the present invention, it includes the following steps: Step S1: Measure the actual positions between satellites in the satellite cluster, and use the multi-event point C-W equation based on least-squares optimization to solve the relative navigation of the satellite cluster; the relative navigation sensor is installed on each satellite and is used to measure the relative positions with other satellites. The relative navigation sensor includes an inter-satellite rangefinder, an optical camera, and / or a laser rangefinder. Only the relative positions between satellites need to be measured, and the velocity is deduced through the analytical solution of the C-W equation. This method needs to measure the relative positions of all satellite pairs in the satellite cluster to ensure the navigation accuracy of the entire cluster. For example, a cluster with 3 satellites needs to measure the relative positions of 3 pairs of satellites.

[0035] Step S2: Satellite cluster formation maintenance based on fuel balance. This step calculates the ideal positions between two satellites in the satellite cluster and performs formation maintenance according to the deviation between the actual position and the ideal position; Step S3: Monitor whether formation reconfiguration is required (such as changes in mission requirements or configuration adjustments). If so, enter step S3; otherwise, return to step S1 to continue monitoring the relative positions. Formation reconfiguration trajectory planning based on the improved pseudospectral method. This step performs trajectory planning when formation reconfiguration is required.

[0036] The present invention can perform high-precision relative navigation in the case where the relative navigation sensor is intermittently unavailable, and can reduce the calculation amount while meeting the collision avoidance requirements during formation reconfiguration, meeting the real-time requirements of on-orbit calculation, and having high robustness. The role of the relative navigation sensor is to provide real-time relative position data between satellites for the least-squares fitting in step S1. Obtain relative position data from the relative navigation sensor, and the relative navigation sensor data is the core input of step S1.

[0037] In step S1, a relative navigation method under relative measurement interruption. Relative measurement interruption refers to a temporary data loss caused by sensor failure, communication interruption, or occlusion. At this time, it is necessary to rely on the analytical solution of the C-W equation for state prediction to ensure navigation continuity.

[0038] After the initial conditions of the satellite formation are determined (the initial conditions include the relative position and relative velocity at the initial moment, provided by the ground station or on-board sensors), it is necessary to solve the relative position and velocity between every two satellites in the satellite cluster at each moment according to the C-W equation. The present invention proposes to use the multi-event point C-W equation based on least squares optimization to solve the relative navigation of the satellite cluster.

[0039] S1.1 Establish the target satellite orbit coordinate system.

[0040] As Figure 2 shown, define any one of the two satellites as the target satellite, adopt the LVLH relative coordinate system, define the centroid of the target satellite as the coordinate origin of the LVLH relative coordinate system, and the target satellite serves as the main star of the entire formation, and the rest are secondary stars. Since the formation needs to maintain a specific configuration, it is necessary to measure the relative states between members. Therefore, it is necessary to set a reference benchmark in the entire formation, and the main star is set as the target satellite as the reference benchmark for the entire cluster formation. The relative states measured by each member are based on the reference orbit of the main star as the relative measurement benchmark. The LVLH coordinate system is defined as the coordinate origin located at the centroid of the target satellite, the Z-axis is in the target satellite orbit plane and points from the centroid of the target satellite to the geocenter; the Y-axis is perpendicular to the orbit plane, points to the negative normal of the orbit plane, and is opposite to the direction of the orbit angular momentum vector ; the X-axis forms a right-handed helix with the Y and Z axes and points in the satellite flight direction. Assume that the target satellite is in a stationary state at the coordinate origin, and calculate the coordinate position and velocity direction information of the current satellite relative to the target satellite.

[0041] Express the relative state of the two satellites in the target satellite orbit coordinate system. Define the relative position and velocity vectors of the two satellites in the target satellite orbit coordinate system as: 、 ; Relative measurement interruption refers to a temporary data loss caused by sensor failure, communication interruption, or occlusion. At this time, it is necessary to rely on the analytical solution of the C-W equation for state prediction to ensure navigation continuity. Among them, represents the relative position vector between the two satellites, 、 、 respectively represent the components of the relative position vector in the X, Y, and Z directions of the coordinate axes, and can be abbreviated as 、 、 . represents the velocity vector between the two satellites, 、 , represent the components of the velocity vector in the X, Y, and Z directions of the coordinate axes, and can be abbreviated as , , .

[0042] S1.2 Solve the analytical solution of the C-W equation in the satellite orbit coordinate system.

[0043] Using the C-W equation to describe the relative motion dynamics equation of two satellites, the C-W equation is described in the target satellite orbit coordinate system as:

[0044] where, is the orbital angular velocity of the target satellite, is the control force applied to each axis, , , are the second-order derivatives of the relative position vector components in the target satellite orbit coordinate system with respect to time; When no maneuver control is performed on the target satellite, that is , given the relative position of the two satellites at time , , ), and the relative velocity ( , , ), let , , , , , , then the analytical solution of the C-W equation is expressed as: ;

[0045] where, , , , represent the relative position of the two satellites at time, ( , , ) represents the relative velocity of the two satellites at time. n: Orbital angular velocity of the target satellite (rad / s), calculated from the semi-major axis of the orbit. u: Control force (N), provided by the propulsion system. f: Space perturbation force (such as atmospheric drag, solar radiation pressure), which needs to be modeled or measured.

[0046] S1.3 Establish and solve the least squares fitting measurement equation.

[0047] The coefficient , , , , , As a state variable, and the relative position obtained from the relative navigation sensor on the slave satellite As a measurement quantity, then The measurement equation of the C-W fitting relative motion prediction at time t is expressed as: ;

[0048] Wherein, , , respectively represent the positions of the th satellite; represents the position vector of the th satellite, is the state transition matrix of the th satellite, is the initial state of the th satellite, is the period of the th satellite, represents the position matrix of the overall satellite cluster formation, is the transition matrix of the overall cluster satellite formation, represents the transpose operation symbol of the matrix.

[0049] If there are pieces of relative position measurement quantities at time t, then the total measurement equation of the C-W fitting relative motion prediction can be expressed as:

[0050] Using the least squares solution method to solve the fitting C-W solution coefficients:

[0051] After accurately solving by the above formula, for the th satellite, the fitting C-W solution is: ;

[0052] Wherein, and respectively represent the position and velocity of the th satellite.

[0053] Step S2. Satellite cluster formation maintenance based on fuel balance. The "ideal position" in step S2 is calculated based on the navigation result of S1, and the actual position deviation is provided by the relative position data of S1.

[0054] During the formation flight of a satellite constellation, long-term orbit maintenance and adjustment can lead to uneven fuel consumption among satellites, thus affecting the overall lifespan and control performance of the formation. To extend the mission cycle of the formation and maintain the consistency of control strategies, the present invention proposes a formation maintenance method based on fuel balance.

[0055] This method first monitors the fuel status of each satellite in the constellation in real time and calculates the degree of imbalance in fuel distribution. Based on this, an optimized scheduling strategy is adopted to reasonably allocate orbit control tasks, enabling satellites with sufficient fuel to undertake more adjustment tasks, while satellites with less fuel minimize thrust consumption as much as possible. In addition, to ensure control stability, the algorithm comprehensively considers factors such as dynamic constraints, communication delays, and control accuracy, and optimizes the allocation and execution mode of propulsion pulses.

[0056] Compared with traditional formation maintenance strategies, this method can achieve fuel consumption balance while ensuring orbit accuracy, avoiding individual satellites from prematurely exiting the mission due to fuel exhaustion, thereby improving the mission sustainability and control robustness of the entire satellite constellation. Step S2 specifically includes:

[0057] S2.1 Select the master satellite. Every other orbital period, detect the current remaining fuel values of each satellite, compare them according to the current remaining fuel values of each satellite, and select the satellite with the least current remaining fuel value as the master satellite.

[0058] Assume that when the first satellite is selected as the master satellite, in order to prevent it from consuming fuel for orbit maintenance maneuvers, it is considered that its relative state in the virtual center O orbital coordinate system is ideal at this time. Denote the state of the master satellite in the O orbital coordinate system as , , where is the position of the master satellite, is the velocity of the master satellite. The state , of the master satellite is updated regularly by the ground station or indirectly deduced through inter-satellite relative measurement data (such as a coordinate system with the master satellite as the origin).

[0059] S2.2 Calculate the position of the slave satellites.

[0060] Satellites other than the master satellite are slave satellites. Taking the first satellite as the master satellite and the second satellite as the slave satellite as an example, the method for calculating the position of the slave satellite is as follows:

[0061] S2.2.1 Detect the relative state , of the slave satellite in the master satellite's orbital coordinate system, and its state in the virtual center O orbital coordinate system is , . Among them , is measured by the relative navigation sensor on the slave satellite, , is the ideal state of the current slave satellite relative to the virtual center.

[0062] S2.2.2 Calculate the state of the current slave satellite in the orbital coordinate system of the virtual center O , : According to the position and velocity of the master satellite in the equatorial inertial coordinate system , the transformation matrix from the orbital coordinate system of the virtual center O to the equatorial inertial coordinate system is , then the relative position and velocity of the master satellite can be expressed as: are the position and velocity of the virtual center O in the equatorial inertial coordinate system. In the present invention, the orbital coordinate system of the master satellite is approximately used as the virtual center coordinate system (R0≈R1, V0≈V1), avoiding iterative calculation, and the error is within an acceptable range (such as 0.1 m).

[0063] S2.2.3 From the position and velocity of the master satellite in the equatorial inertial coordinate system and the relative state of the slave satellite in the orbital coordinate system of the master satellite is , The meaning is the transformation matrix from the orbital coordinate system of the master satellite to the equatorial inertial coordinate system. The position and velocity of the slave satellite in the equatorial inertial coordinate system can be obtained as: The relative state of the slave satellite in the virtual center O can be expressed as: It can be seen from the above formula that to solve and , the transformation matrix from the orbital coordinate system of the virtual center O to the equatorial inertial coordinate system must be obtained. And this matrix is a function of the absolute position R0 and velocity V0 of the virtual center O. Since R0 and V0 are unknown, only by iterative solution can the solutions of R0 and V0 be obtained, and then be determined, which will inevitably increase the computational burden.

[0064] In fact, for a satellite formation, the distance between the primary satellite and the virtual center is very close, and the values of R1 and V1 are very close to those of R0 and V0. Then, R1 and V1 can be considered to replace R0 and V0. Mathematical simulation shows that when the formation radius is 1000m, the relative position calculation error caused by using R1 and V1 to replace R0 and V0 for calculation is less than 0.1m, and the relative velocity error is less than 1mm. Therefore, it can be assumed that . Thus, the position and velocity of the slave satellite relative to the virtual center orbital coordinate system can be expressed as: ; After the primary satellite is selected, 、 are determined, and then and can be calculated.

[0065] S2.3 Calculate the error between the actual position and the desired position of the slave satellite. When the error exceeds the error threshold, start the orbit correction program. The threshold is set according to the mission accuracy requirements. Preferably, the position error threshold is 10m, and the velocity error is 0.1m / s. Adjust the position of the slave satellite through pulse thrust.

[0066] Step S3. Formation reconfiguration trajectory planning method based on improved pseudospectral method.

[0067] After the configuration design is completed, when the mission requirements change (such as configuration adjustment, obstacle avoidance), S3 is triggered by ground instructions or on-board autonomous decision-making, and a trajectory design for autonomous reconfiguration from the initial formation to the target formation is required. During the satellite formation reconfiguration process, the changes in position and velocity must always satisfy the relative motion model. The present invention designs a swarm reconfiguration method based on the improved pseudospectral method. Considering the main satellite orbit as a circular orbit and the influence of space perturbation forces, the motion model of the th slave satellite in the satellite formation can be obtained as: ; In the formula, represents the position of the th satellite, n is the average motion angular velocity of the primary satellite, 、 、 respectively represent the components of the control acceleration on each axis, 、 、 respectively represent the components of the space perturbation force on each axis. 、 、 respectively represent the components of the acceleration of the th satellite on each axis. The The positions and velocities of the satellites.

[0068] The constraint conditions of the cluster reconstruction trajectory optimization process include inter-satellite collision avoidance constraint, output torque constraint, and configuration optimization time constraint. The three constraints are added simultaneously.

[0069] The inter-satellite collision avoidance constraint adopts a collision avoidance strategy based on the safety domain during the satellite formation flight. Considering the satellite size and formation configuration size, the safety distance is set to , preferably using a safety factor of 10 times, the safety distance is set to 10 times the satellite diameter. According to the satellite size and mission requirements, such as a satellite diameter of 5m, the safety distance can be set to = 50m. Then the collision avoidance between the main satellite and the sub-satellites and the collision avoidance constraint between the sub-satellites are: ; In the formula, ≠ j, and , j = 1, 2,..., N, x, y, z represent the relative positions in the main satellite orbital coordinate system.

[0070] The output torque constraint is due to the limited output amplitude of the thruster, requiring that the output amplitude of each thruster in the three directions does not exceed the maximum amplitude: ; ( , , ) represents the relative position of the th satellite in the main satellite orbital coordinate system, ( , , ) represents the relative position of the jth satellite in the main satellite orbital coordinate system, represents the safety distance threshold.

[0071] The optimization time constraint is due to taking the minimum fuel as the performance index. In order to make the satellite formation reconstruction optimization time not too large, it is necessary to limit the satellite formation reconstruction optimization time according to the specific situation: ; In the formula, is the termination time, is the given reconstruction optimization time.

[0072] In order to reduce the fuel consumption in the satellite formation configuration optimization process, the minimum total energy consumption of the satellite formation is taken as the optimization goal: ; In the formula, , , are the thrust accelerations of the th satellite in the x, y, z three directions respectively (i.e.: , , respectively represent the components of the control acceleration on each axis). Finally, the thrust accelerations of the th star in the x, y, and z directions can be obtained.

[0073] Therefore, the optimization objective of cluster reconstruction is to solve the optimal trajectory of formation reconstruction for the satellite relative motion model, comprehensively considering collision avoidance constraints, output torque constraints, configuration optimization time constraints, and performance indicators.

[0074] Furthermore, a numerical optimization design solution strategy is adopted. Since the pseudospectral method has the advantages of small computational volume and high computational accuracy, the Gauss pseudospectral method is used to solve the formation reconstruction problem to simplify the calculation and meet the real-time requirements. The extended form of the Gauss pseudospectral method for multi-star satellite formation is to transform the formation reconstruction problem into the following nonlinear programming problem: ; In the formula, represents the objective function of trajectory optimization, represents the relative kinematic model of satellite formation, Ψ represents the boundary value constraints of the trajectory optimization problem, and C represents the inter-satellite collision avoidance constraints, output torque constraints, and optimization time constraints during the maneuver. Finally, the thrust accelerations of the th star in the x, y, and z directions can be obtained. represents the initial state of the satellite, is the terminal state of the satellite, represents the terminal time, is the state of the satellite at time , is the control input at time , represents the Lagrange interpolation basis function constructed by the pseudospectral method, represents the dynamic equation of the satellite.

[0075] In addition, the present invention also provides a high-robustness satellite cluster formation control system, which is used to implement the above high-robustness satellite cluster formation control method.

[0076] Compared with the existing satellite cluster formation control and reconstruction methods, the present invention has significant advantages in fuel balance control and trajectory optimization, which are mainly reflected in the following aspects: (1) Improved navigation accuracy: The relative navigation is solved by using the multi-event point C-W equation based on least squares optimization, reducing the navigation error and being able to accurately describe the relative motion of two satellites.

[0077] (2)Improved fuel balance: The present invention proposes a formation maintenance method based on fuel balance, which can optimize the fuel distribution strategy while meeting the formation control requirements, avoid premature withdrawal of individual satellites due to fuel exhaustion, and thus effectively extend the mission life of the cluster.

[0078] (3)Improved measurement accuracy: This method only measures the relative position and velocity of satellites, avoiding the large errors caused by absolute orbit measurement.

[0079] Any process or method description in the flowchart of the present invention or described in other ways herein can be understood as representing a module, segment, or part of code including one or more executable instructions for implementing a specific logical function or process, which can be implemented in any computer-readable medium for an instruction execution system, apparatus, or device. The computer-readable medium can be any medium including storage, communication, propagation, or transmission of a program for use by an instruction execution system, apparatus, or device, including read-only memory, magnetic disks, or optical discs, etc.

[0080] In the description of this specification, the description referring to terms such as "embodiment", "example", etc. means that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic expressions of the above terms do not necessarily refer to the same embodiment or example. In addition, those skilled in the art can combine or combine different embodiments or examples described in this specification and the features therein without contradiction.

[0081] Although the above content has shown and described embodiments of the present invention, it can be understood that the above embodiments are exemplary and cannot be construed as limitations on the present invention. Those of ordinary skill in the art can perform update operations such as changes, modifications, substitutions, and variations on the above embodiments within the scope of the present invention.

Claims

1. A high-robustness satellite cluster formation control method, characterized in that The method includes the following steps: S1: Measure the actual positions between satellites in the satellite cluster, and solve the relative navigation of the satellite cluster using the multi-event point C-W equation based on least squares optimization; S2: Satellite cluster formation maintenance based on fuel balance, calculate the ideal positions between two satellites in the satellite cluster, and perform formation maintenance according to the deviation between the actual position and the ideal position; S3: Formation reconfiguration trajectory planning based on the improved pseudospectral method, and perform trajectory planning when formation reconfiguration is required.

2. The high-robustness satellite cluster formation control method according to claim 1, wherein, In step S1, after the initial conditions of the satellite formation are determined, the relative positions and velocities between every two satellites in the satellite cluster at each moment are solved according to the C-W equation.

3. The high-robustness satellite cluster formation control method according to claim 1, characterized in that Step S1 includes: S1.1 Establish the target satellite orbit coordinate system; S1.2 Solve the analytical solution of the C-W equation in the satellite orbit coordinate system; S1.3 Establish and solve the least squares fitting measurement equation.

4. The high-robustness satellite cluster formation control method according to claim 3, characterized in that The specific implementation method of step S1.1 is as follows: Define any one of the two satellites as the target satellite, and its coordinate system is defined with the coordinate origin located at the center of mass of the target satellite, and the Z-axis is in the target satellite orbit plane and points from the center of mass of the target satellite to the center of the earth; The Y-axis is perpendicular to the orbital plane, pointing to the negative normal of the orbital plane, opposite to the direction of the orbital angular momentum vector ; the X-axis forms a right-handed helix with the Y- and Z-axes, pointing in the direction of the satellite's flight. The relative states of the two satellites are expressed in the target satellite's orbital coordinate system. The relative position and velocity vectors of the two satellites in the target satellite's orbital coordinate system are defined as: , ; Among them, represents the relative position vector between two stars, , , respectively represent the components of the relative position vector in the X, Y, and Z directions of the coordinate axes, and are respectively abbreviated as , , ; represents the velocity vector between two stars, , , respectively represent the components of the velocity vector in the X, Y, and Z directions of the coordinate axes, and are respectively abbreviated as , , .

5. The high-robustness satellite cluster formation control method according to claim 3, wherein The specific implementation method of step S1.2 is as follows: Use the C-W equation to describe the relative motion dynamics equation of the two satellites, then the C-W equation is described in the target satellite orbit coordinate system as: ； Among them, is the angular velocity of the target satellite orbit, is the control force applied to each axis, , , are the second-order derivatives with respect to time of the components of the relative position vector in the target satellite orbit coordinate system; When the target satellite is not maneuvered, , the relative position ( , , , ) and relative velocity ( , , ) of the two satellites at a known time are known. Let , , , , . Then the analytical solution of the C-W equation is expressed as: ; Among them, , ([[]]END]] , , ) represents the relative position of the two stars at time , , ) represents the relative velocity of the two stars at time 6. The high-robustness satellite cluster formation control method according to claim 3, characterized in that In step S1.3, taking the coefficients , , , , , as state variables, and the relative position obtained from the relative navigation sensor as measurement variables, then the measurement equation for the C-W fitting relative motion prediction at time is expressed as: ; Among them, , , respectively represent the positions of the th satellite; represents the position vector of the th satellite, is the state transition matrix of the th satellite, is the initial state of the th satellite, is the period of the th satellite, represents the position matrix of the overall satellite cluster formation, is the transition matrix of the overall cluster satellite formation, represents the transpose operation symbol of the matrix; If there is a measurement of the relative position at a certain moment, the measurement equation of the overall C-W fitting relative motion prediction is expressed as: ; Use the least squares solution method to solve the fitting C-W solution coefficients: ； Solve exactly by the above formula After that, the fitted C-W solution is as follows: ; Among them, and respectively represent the position and velocity of the th satellite.

7. The high-robustness satellite cluster formation control method according to claim 1, characterized in that In step S2, the formation maintenance method based on fuel balance is specifically as follows: First, monitor the fuel status of each satellite in the cluster in real time, and calculate the imbalance degree of fuel distribution; Adopt an optimized scheduling strategy to reasonably allocate orbit control tasks, so that satellites with sufficient fuel undertake more adjustment tasks, while satellites with less fuel reduce thrust consumption.

8. The high-robustness satellite cluster formation control method according to claim 7, characterized in that Step S2 specifically includes: S2.1 Select the primary satellite; every other orbital period, detect the current remaining fuel values of each satellite, compare them according to the current remaining fuel values of each satellite, and select the satellite with the least current remaining fuel value as the primary satellite; record the state of the primary satellite in the O - orbital coordinate system as , , where is the position of the primary satellite, is the velocity of the primary satellite; S2.2 Calculate the position of the slave satellite; S2.3 Calculate the error between the actual position and the ideal position of the satellite. When it exceeds the error threshold, start the orbit correction program. The other satellites except the main satellite are slave satellites.

9. The high-robustness satellite cluster formation control method according to claim 1, characterized in that In step S3, the constraint conditions of the cluster reconfiguration trajectory optimization process include inter-satellite collision avoidance constraints, output torque constraints, and configuration optimization time constraints; The optimization goal of the cluster reconfiguration is to solve the optimal trajectory of the formation reconfiguration for the satellite relative motion model.

10. A satellite cluster formation control system with high robustness, characterized in that, The system is used to implement the high-robustness satellite cluster formation control method according to any one of claims 1-9.

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