An Autonomous Obstacle Avoidance Control and Topology Optimization Method for Large-Scale Constellation Transition

Abstract

The present invention discloses an autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions, including: centering on the leader satellite, dividing its communication area, establishing a cluster communication topology including a virtual leader satellite and other follower satellites, performing obstacle processing on the failed members in the cluster, determining the motion state and completing the initialization of the cluster communication topology; designing an improved artificial potential field with smooth transition within the communication area of the leader satellite, designing a preset time controller for satellites with special configuration requirements, realizing autonomous collision avoidance among members within the cluster and autonomous obstacle avoidance for spatial obstacles such as failed satellites; designing a dynamic topology optimization method during the overall transition of the satellite constellation to achieve real-time topology optimization during the large-scale satellite constellation transition process. This task design method can ensure the safe and stable operation of the large-scale satellite constellation during the transition process, and has the characteristics of small communication burden and fast response.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular, to an autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions. Background Art

[0002] With the development of space technology, multiple small satellites can form a satellite constellation to share information and perform space missions. Although the functions of small satellites are relatively simple, through networked flight, not only can some complex functions of traditional large satellites be achieved, but also the launch cost and operation risk can be significantly reduced, and the flexibility and robustness of the system can be remarkably enhanced. The main challenges of satellite constellations come from the dynamic coupling between satellites and the environment, as well as environmental disturbances such as J2 perturbation, air resistance, and solar radiation pressure. Long-term natural evolution will lead to an increase in the distance between member satellites, resulting in the interruption of the inter-satellite communication topology and making it difficult to maintain the safe and stable operation of the satellite constellation.

[0003] The artificial potential field method was initially used for mobile robot control. The basic idea is to design the movement of the robot in the surrounding environment as a movement in an abstract artificial gravitational field. The target point generates an "attractive force" on the mobile robot, and the obstacle generates a "repulsive force" on the mobile robot. Finally, the movement of the mobile robot is controlled by finding the resultant force. Since the artificial potential field method can artificially set the "forbidden area" of movement and is simple in mathematical description, it is very suitable for the control of large-scale satellite constellations with relatively low control requirements.

[0004] In the process of large-scale satellite constellation control, not only the safe and stable operation of the satellite constellation needs to be maintained, but also the communication topology and collision avoidance between member satellites need to be considered. The collision avoidance strategy of the artificial potential field method based solely on relative position cannot meet the task requirements under certain special conditions. At the same time, when some members in the cluster fail, it is necessary to process the failed part in a timely manner to ensure the normal operation of other members of the cluster, and at the same time, construct and optimize the topology of the satellite constellation members to achieve stable and efficient task performance. To solve this problem, it is necessary to propose an autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions. Summary of the Invention

[0005] In view of the above deficiencies in the prior art, the present invention provides an autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions, which solves the problems of weak dynamics and real-time performance of satellite cluster topology optimization, discontinuous output and output saturation of the traditional artificial potential field method, and can realize various task requirements such as cluster configuration maintenance, member collision avoidance, autonomous obstacle avoidance, and real-time topology.

[0006] To achieve the above invention objective, the technical solution adopted by the present invention is: an autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions, including the following steps:

[0007] S1. Establish an LVLH coordinate system centered on the virtual leading satellite in a large-scale satellite constellation. Divide the space around it into four regions according to the constellation scale and the communication range of the leading satellite, and determine the motion states of other follower satellites relative to the leading satellite within the communication range of the virtual leading satellite;

[0008] S2. Determine the overall communication topology of the constellation including the virtual leading satellite and all follower satellites based on graph theory;

[0009] S3. When some member satellites fail, regard them as obstacles, determine their motion states relative to other satellites, and complete the initialization of the cluster communication topology;

[0010] S4. According to the specific task requirements in the constellation transition, design a preset time controller to enable some follower satellites to reach the desired configuration required by the task within the preset time;

[0011] S5. Through the initial relative motion states of the follower satellites, regard both the follower satellites that require special configurations and the failed satellites as space obstacles, and design an improved artificial potential field method with smooth transition characteristics to achieve autonomous obstacle avoidance / collision avoidance control for the overall transition of the constellation;

[0012] S6. According to the motion states in the overall transition process of the constellation, design a dynamic topology optimization method to achieve real-time topology optimization during the transition of the large-scale constellation.

[0013] The beneficial effects of the present invention are as follows: By establishing a relative motion model of the virtual leading satellite and follower satellites in the LVLH coordinate system, establishing the overall communication topology of the constellation members, introducing a state error and comprehensive disturbance estimator, conducting real-time observation and feedback compensation of orbital relative position, velocity, and disturbance information, based on the artificial potential field method, by designing the property of smooth transition of the control force interval, achieving configuration maintenance and collision avoidance between constellation members, as well as autonomous obstacle avoidance for some failed member satellites, timely optimizing the overall topology structure of the constellation, designing and establishing the overall dynamic topology optimization of the constellation, achieving real-time topology optimization during the constellation transition, and ensuring the stability of the communication topology between member satellites and the high efficiency of task execution during the transition process.

[0014] Furthermore, the expression of the relative motion equation of the satellite in the LVLH coordinate system in step S1 is as follows:

[0015]

[0016] Where x, y, z represent the components of the position vector of the follower satellite, μ represents the gravitational coefficient, m represents the mass of the follower satellite, n represents the orbital angular velocity of the virtual leading satellite, u x , u y , u zDenote the components of the control force in the three coordinate axes, d x , d y , d z Denote the disturbance differences between the leading satellite and the following satellites in the three coordinate axes. The disturbance terms involve J2 perturbation, atmospheric drag, solar radiation pressure, etc.

[0017] When the satellite operates in a low Earth orbit, the J2 perturbation is the main disturbance factor causing satellite drift. Here, the equation of the J2 perturbation force on the satellite in the LVLH coordinate system is expressed as

[0018]

[0019] Here, J 2 = 0.0010826 is the second-order zonal harmonic coefficient.

[0020] In addition to the J2 perturbation, the atmospheric drag perturbation is another important perturbation factor affecting the operation of low Earth orbit satellites, which can be expressed as

[0021]

[0022] Among them, m represents the mass of the satellite, C D represents the drag coefficient, A represents the force-bearing area, ρ represents the atmospheric density, v rel represents the velocity vector of the spacecraft relative to the atmosphere, which can be expressed as

[0023]

[0024] Among them, R represents the satellite position vector, ω represents the angular velocity of the Earth's rotation, and its direction is along the z-axis direction.

[0025] The beneficial effects of the above further scheme are as follows: Under the consideration of the influence of J2 perturbation, atmospheric drag perturbation, etc. in the low Earth orbit, a relative motion dynamics model between the leading satellite and the following satellites in the satellite cluster is established, laying a foundation for the high-precision in-orbit operation of the satellite cluster.

[0026] Furthermore, in an embodiment of the present invention, for the overall communication topology established among the satellite cluster members based on the graph theory idea in step S2, for a large-scale satellite cluster, with the virtual leading satellite as the center, determine the communication distance of the virtual leading satellite, so that as many following satellites as possible form a communication topology with the virtual leading satellite, evenly distribute the following satellites with special spatial configurations around the virtual leading satellite, ensure the communication topology between the configured satellites and the virtual leading satellite, as well as the network connectivity of other following satellites during the space flight process, calculate the number of satellites and the communication volume within the communication distance of the following satellites, select the following satellites with less communication volume to form a communication topology, ensure that the following satellites maintain a complete topological connection, and use it as the basis for subsequent dynamic topology planning.

[0027] The beneficial effects of the above further solution are as follows: By establishing the overall communication topology of the satellite cluster based on graph theory, the complexity of the topological connections between the satellite cluster members and the communication volume of some following satellites can be effectively reduced. Considering the balance and connectivity of the network, the following satellites can selectively form communication topologies with other following satellites within their communication ranges, which can greatly reduce the computational amount of the processes related to a single satellite and improve the overall operation efficiency of the satellite cluster.

[0028] Furthermore, the step S4 includes the following steps:

[0029] S401. Taking the virtual leading satellite as the center, design an improved artificial potential field with smooth transition properties in the repulsion zone and the attraction zone of the region divided in the step S1;

[0030] S402. According to the mission requirements, design a preset time controller to form a specific configuration of some satellites in the satellite cluster within a preset time and maintain the configuration.

[0031] The beneficial effects of the above further solution are as follows: According to the four regions divided in the space within the communication distance around the virtual leading satellite, through the smooth transition design, the control forces in the attraction zone and the repulsion zone change continuously with the change of the distance between the target and the virtual leading satellite, realizing the smooth transition of the control forces between the regions. Regarding the satellites with special configurations and the failed satellites as obstacles, it can not only meet the configuration maintenance required by the mission within the satellite cluster, but also achieve the autonomous collision avoidance between the member satellites and the autonomous obstacle avoidance control for the space obstacles, ensuring the reliability and safety of the overall operation of the satellite cluster.

[0032] Furthermore, the expression of the improved artificial potential field method with smooth transition properties designed with the virtual leading satellite as the center in the step S401 is as follows:

[0033]

[0034] where p i = [x i , y i , z i T is the position of the i-th following satellite relative to the virtual leading satellite in the LVLH coordinate system with the virtual leading satellite as the center, ||p i || 2 represents the distance of the following satellite from the virtual leading satellite within the communication area of the virtual leading satellite, u i1 is the repulsion function, E i1 is the field strength of the repulsion zone, η i1 is the repulsion gain, d is the outer radius of the safety distance of the virtual leading satellite, r 1 is the inner radius of the repulsion zone, r2 is the outer radius of the repulsive force region, u i2 is the gravitational potential function, η i2 is the gravitational gain, H is the outer radius of the free flight region, a 1 is the inner radius of the gravitational region, a 2 is the outer radius of the gravitational region, ξ i1 , ξ i2 is the control gain, λ is the simulated charge density, ε 0 is the simulated dielectric constant, r e and a e are the position representation quantities in the potential field. According to the satellite motion state, calculate the included angle between the relative motion position vector and the velocity vector of the satellite, and judge the relative motion trend of the satellite. For the away motion in the repulsive force region and the approaching motion in the gravitational region, no additional artificial potential field forces are applied.

[0035] The beneficial effect of the above further solution is: The present invention realizes the maintenance control of the overall configuration of a large-scale satellite swarm through the above formula.

[0036] Furthermore, in step S402, a preset time control strategy is performed on some follower satellites according to mission requirements, and its expression is as follows:

[0037]

[0038]

[0039] Among them, is the system dynamics model, is the observed value of the uncertain disturbance term, k ip , k in is the control gain coefficient, δ i is a constant that satisfies the condition , s ip is the timed sliding mode function, s in is the positive linear sliding mode function, is a time-varying function, η is a positive constant, t 0 , t f are the start time and the preset time respectively, e i1 , e i2 are the relative position error and the relative velocity error between the virtual leader satellite and the follower satellite respectively, b > 0, c ≥ 0, γ i > 0.

[0040] The beneficial effect of the above further solution is: The present invention realizes the preset time control of forming a special configuration for some members inside the satellite swarm through the above formula.

[0041] Furthermore, in step S5, the special configuration satellites and partially failed satellites in the cluster are regarded as space obstacles, and an autonomous obstacle avoidance control strategy based on an improved artificial potential field method with smooth transition properties is designed for other following satellites in the cluster. The expression is as follows:

[0042]

[0043]

[0044]

[0045] where u i3 is the repulsive force function commonly used in the artificial potential field method, η i3 is the repulsive force gain, E i is the field strength in the artificial potential field of the i-th following satellite, p i =[x i ,y i ,z i T is the position of the i-th following satellite relative to the virtual leader satellite in the LVLH coordinate system centered on the virtual leader satellite, p j =[x j ,y j ,z j T is the position vector of the j-th reconstructed / failed satellite relative to the virtual leader satellite in the LVLH coordinate system centered on the virtual leader satellite, d i is the outer radius of the safety distance of the i-th satellite, D i is the action radius of the artificial potential field of the i-th following satellite, u i4 is a dynamic artificial potential field controller based on the relative velocity between following satellites, ξ i3 ,ξ i4 are control gains, η i4 is the repulsive force gain, is the velocity vector of the i-th following satellite relative to the virtual leader satellite in the LVLH coordinate system, is the velocity vector of the j-th reconstructed / failed satellite relative to the virtual leader satellite in the LVLH coordinate system. According to the satellite motion state, calculate the included angle between the relative motion position vector and the velocity vector of the satellite, judge the relative motion trend of the satellite, and no additional artificial potential field force is applied to the away motion in the repulsive force area and the approaching motion in the gravitational force area.

[0046] The beneficial effect of the above further scheme is that the present invention realizes the autonomous obstacle avoidance control of some special configuration satellites and failed satellites in the satellite cluster through the above formula.

[0047] ​​Furthermore, in step S6, a large-scale satellite constellation dynamic topology optimization method is designed, and the distance matrix between the follower satellites in the satellite constellation is defined as:

[0048]

[0049] where l ij represents the distance between the i-th follower satellite and the j-th follower satellite in the satellite constellation, and the main diagonal represents that the distance between each follower satellite and itself is 0.

[0050] The adjacency matrix corresponding to the distance matrix A between the follower satellites is defined as:

[0051]

[0052] where n ij is the element in the adjacency matrix B corresponding to l ij in the distance matrix A. Conditional constraints on the distance l ij between any two follower satellites in the distance matrix A can directly affect the values of the corresponding elements in the B matrix.

[0053] The communication distance of any one follower satellite in the satellite constellation is defined as l f . If the distance l ij between two follower satellites in the satellite constellation is ≤ l f , then the corresponding element n ij in the B matrix is 1; otherwise, n ij is 0. The main diagonal value represents a single follower satellite itself, and the element value is always 0. Thus, the communication topology of the follower satellites in the satellite constellation can be judged according to the element distribution in the matrix B.

[0054] Through the element distribution in the adjacency matrix B, the balance and connectivity of the satellite communication topology are balanced. The elements in the adjacency matrix B are operated and permuted, and the distances between a single satellite and other satellites in the matrix A are compared and calculated. Under the condition of meeting the communication distance, it is connected to the i satellites with the closest relative distance, satisfying i ≤ i m , where i m is the maximum number of connections of the communication topology of a single member satellite. And the corresponding elements in the adjacency matrix B are set to 1. Even if other satellites meet the communication distance constraints, they will no longer be connected and the adjacency matrix elements will not be permuted. By using this indirect connection method, while reducing the satellite communication load, the communication topology of the whole cluster is ensured.

[0055] For the above-mentioned topological constraint conditions, a topological optimization method in which the optimization objective function is processed in the form of a penalty function is proposed. For each member satellite, at most i mRegarding the constraint conditions for m satellites to maintain communication, at any moment during the constellation transition process, it is introduced into the objective function in the form of a penalty function term. When the degree d(v) of a certain vertex in the network is greater than i m , that is, when the number of edges connected to this vertex is greater than i

[0056]

[0057] where α is a positive real number set artificially, called the penalty factor; is the average path length. By minimizing it, the reduction of network communication delay can be achieved. is the natural connectivity. Among them, the larger the natural connectivity, the stronger the robustness of the network can be achieved. is the difference between the average side length of the network and the maximum communication distance, called the zero-order stability of the network. Making it as large as possible can enhance the stability of the network. ω 1 , ω 2 , ω 3 are the weight coefficients of the average path length, natural connectivity, and zero-order average stability respectively. Through the optimal design of the three indicators by the objective function, the purpose of reducing network delay, enhancing network robustness and stability, and improving network communication performance is achieved.

[0058] During the large-scale constellation transition process, the follower satellites with special configurations are evenly distributed in the surrounding space of the virtual leader satellite, and it is ensured that the configuration satellites all maintain a communication topology with the virtual leader satellite. Other follower satellites fly in their surrounding space. Calculate the distance between any two follower satellites, record all the distance data in the same matrix A, and determine the communication range constraint l of the follower satellites f . For those that meet the communication range, set the elements in the corresponding adjacency matrix B of the distance matrix to 1, otherwise set them to 0. Determine the communication topology between the follower satellites through the element distribution in the adjacency matrix. By calculating, determine the number of connections of each follower satellite with other follower satellites at the current moment. Weigh the connectivity and the balance of the network, so that the follower satellites can choose other follower satellites within the communication range and with less traffic for communication topology. As the constellation transition process progresses, calculate in real time the satellites that enter the communication range and the satellites that leave the communication range, and continuously update the changes in the adjacency matrix elements. Deal with it in the form of a penalty function in the optimization objective function of the optimization problem of the satellite connection number constraint. Execute this optimization method at any moment during the constellation transition process to further optimize the satellite communication topology. Continuously update the real-time communication topology of the entire constellation according to the above method, and perform dynamic topology optimization on the constellation transition process.

[0059] The beneficial effects of the above further solution are as follows: Using a network-optimized genetic algorithm to design the dynamic topology construction and optimization during the large-scale satellite constellation transition can, to a certain extent, reduce the search space, improve the search efficiency, minimize the network delay as much as possible, and enhance the robustness and reliability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flowchart of the method of the present invention;

[0061] Figure 2 It is a schematic diagram of the hierarchical structure of the artificial potential field method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0063] As Figure 1 shown, the method includes the following steps:

[0064] In step S1, an LVLH coordinate system is established with the virtual leader satellite as the center, and the space around the virtual leader satellite is divided into four regions according to the communication distance of the virtual leader satellite. Further, as Figure 2 shown, the four regions in step S1 are respectively a no-fly safety zone, a repulsive force zone, a free flight zone, and an attractive force zone. At the same time, variable field strengths are set within the repulsive force zone and the attractive force zone to determine the relative motion states of all follower satellites within the current communication area of the virtual leader satellite in the LVLH coordinate system.

[0065] For example, through GPS, the positions and velocities of the main satellite and the slave satellites in the constellation in the inertial system can be obtained in real time, and then the positions and velocities of the slave satellites in the LVLH coordinate system centered on the main satellite can be calculated in real time through coordinate transformation.

[0066] In step S2, the overall communication topology of the satellite constellation including the virtual leader satellite and all follower satellites is determined based on the graph theory idea.

[0067] Specifically, in the cluster, as long as the distance between any two satellites is within the communication range, it is considered that there is inter-satellite communication. By weighing the balance and connectivity of the network, a selective communication topology is carried out, and then the overall communication topology of all satellites in the cluster can be obtained, which can be used as the main basis for subsequent dynamic topology optimization.

[0068] In step S3, when some member satellites fail, they are regarded as obstacles, their motion states relative to other satellites are determined, and the initialization of the cluster communication topology is completed.

[0069] Specifically, when some member satellites in the cluster fail, the failed satellites will directly interrupt the communication topology with other member satellites around them, and may even cause other satellites at a distance to lose the communication topology with the cluster. The failed satellites can no longer establish communication with the members in the cluster and can be regarded as space obstacles. On this basis, the initial state of the communication topology of other satellites within the current satellite group is determined.

[0070] In step S4, according to the specific task requirements in the satellite group transition, a preset time controller is designed to enable some follower satellites to reach the desired configuration required by the task within a preset time. The implementation method is as follows:

[0071] S401. Centering on the virtual leader satellite, an improved artificial potential field with a smooth transition property is designed in the repulsive zone and the gravitational zone of the area divided in step S1.

[0072] S402. According to the task requirements, a preset time controller is designed to form a specific configuration of some satellites in the satellite group within a preset time and maintain the configuration.

[0073] In this embodiment, the expression of the improved artificial potential field method with a smooth transition property designed centering on the virtual leader satellite is as follows:

[0074]

[0075]

[0076] where p i = [x i , y i , z i T is the position of the i-th follower satellite relative to the virtual leader satellite in the LVLH coordinate system centered on the virtual leader satellite, ||p i || 2 represents the distance of the follower satellite from the virtual leader satellite within the communication area of the virtual leader satellite, u i1 is the repulsive force function, E i1 is the field strength of the repulsive zone, η i1 is the repulsive gain, d is the outer radius of the safety distance of the virtual leader satellite, r 1 is the inner radius of the repulsive zone, r 2 is the outer radius of the repulsive zone, u i2 is the gravitational potential function, η i2 is the gravitational gain, H is the outer radius of the free flight zone, a 1is the inner radius of the gravitational region, a 2 is the outer radius of the gravitational region, ξ i1 , ξ i2 is the control gain, λ is the simulated charge density, ε 0 is the simulated permittivity, r e and a e are the position representation quantities in the potential field. According to the satellite motion state, calculate the angle between the relative motion position vector and the velocity vector of the satellite, and judge the relative motion trend of the satellite. For the away motion in the repulsive force region and the approaching motion in the gravitational region, no additional artificial potential field forces are applied.

[0077] According to the mission requirements, the expression of the preset time controller designed for some following satellites is as follows:

[0078]

[0079]

[0080] Among them, is the system dynamics model, is the observed value of the uncertain disturbance term, k ip , k in is the control gain coefficient, δ i is a constant that satisfies the condition s ip is the timed sliding mode function, s in is the positive linear sliding mode function, is a time-varying function, η is a positive constant, t 0 , t f are the start time and the preset time respectively, e i1 , e i2 are the relative position error and relative velocity error between the virtual leader satellite and the following satellite respectively, b > 0, c ≥ 0, γ i > 0.

[0081] In step S5, regard the configuration satellites and some failed satellites in the cluster as space obstacles, and the expression of the autonomous obstacle avoidance control based on the improved artificial potential field method with smooth transition properties designed for other following satellites is as follows:

[0082]

[0083]

[0084]

[0085] Among them, u i3 is the repulsive force function commonly used in the artificial potential field method, η i3 is the repulsive force gain, E iis the field strength in the artificial potential field of the $i$-th follower satellite, $p$ i = [x i , y i , z i T is the position of the $i$-th follower satellite relative to the virtual leader satellite in the LVLH coordinate system centered on the virtual leader satellite, $p$ j = [x j , y j , z j T is the position vector of the $j$-th reconstructed / failed satellite relative to the virtual leader satellite in the LVLH coordinate system centered on the virtual leader satellite, $d$ i is the outer radius of the safety distance of the $i$-th satellite, $D$ i is the action radius of the artificial potential field of the $i$-th follower satellite, $u$ i4 is the dynamic artificial potential field controller based on the relative velocity between follower satellites, $\xi$ i3 , $\xi$ i4 is the control gain, $\eta$ i4 is the repulsive force gain, is the velocity vector of the $i$-th follower satellite relative to the virtual leader satellite in the LVLH coordinate system, is the velocity vector of the $j$-th reconstructed / failed satellite relative to the virtual leader satellite in the LVLH coordinate system. According to the satellite motion state, calculate the included angle between the relative motion position vector and the velocity vector of the satellite, judge the relative motion trend of the satellite, and no additional artificial potential field force is applied to the away motion in the repulsive force area and the approaching motion in the gravitational force area.

[0086] In step S6, design a large-scale satellite swarm dynamic topology optimization method, and define the distance matrix between each follower satellite in the satellite swarm as:

[0087]

[0088] where, $l$ ij represents the distance between the $i$-th follower satellite and the $j$-th follower satellite in the satellite swarm. The main diagonal represents that the distance between each follower satellite and itself is 0.

[0089] Define the adjacency matrix corresponding to the distance matrix $A$ between follower satellites as:

[0090]

[0091] where, $n$ ij is the element in the adjacency matrix $B$ corresponding to $l$ ij in the distance matrix $A$. Conditional constraints on the distance $l$ ij between any two follower satellites in the distance matrix $A$ can directly affect the value of the corresponding element in the $B$ matrix.​​

[0092] Define the communication distance of any follower satellite in the satellite cluster as \(l\). f , if the distance \(l\) between two follower satellites in the satellite cluster ij ≤ \(l\) f , then the corresponding element \(n\) in matrix \(B\) ij = 1, otherwise \(n\) ij = 0. The values on the main diagonal represent a single follower satellite itself, and the element values are always 0. Thus, the communication topology of the follower satellites in the satellite cluster can be judged according to the element distribution in matrix \(B\).

[0093] Through the element distribution in the adjacency matrix \(B\), balance the balance and connectivity of the satellite communication topology, operate and permute the elements in the adjacency matrix \(B\), compare and calculate the distances between a single satellite and other satellites in matrix \(A\), and connect with the \(i\) satellites with the closest relative distance when the communication distance is satisfied, where \(i\leq i\) m , where \(i\) m is the maximum connection number of the communication topology of a single member satellite, and set the corresponding element to 1 in the adjacency matrix \(B\). Even if other satellites meet the communication distance constraints, they will no longer be connected and the adjacency matrix elements will not be permuted. By using this indirect connection method, while reducing the satellite communication load, ensure the communication topology of the overall cluster.

[0094] For the above-mentioned topological constraint conditions, a topological optimization method is proposed to process the optimization objective function in the form of a penalty function. For the constraint condition that each member satellite communicates with at most \(i\) m satellites at the same time, at any moment during the satellite cluster transition, introduce it into the objective function in the form of a penalty function term. When the degree \(d(v)\) of a certain vertex in the network is greater than \(i\) m , that is, when the number of edges connected to this vertex is greater than \(i\) m , punish it, and design the objective function as

[0095]

[0096] where \(\alpha\) is a positive real number set by humans, called the penalty factor; is the average path length, and minimizing it can reduce the network communication delay, is the natural connectivity, where maximizing the natural connectivity as much as possible can enhance the robustness of the network, is the difference between the average side length of the network and the maximum communication distance, called the zero-order stability of the network, and making it as large as possible can enhance the network stability, \(\omega\) 1 , \(\omega\) 2 , \(\omega\) 3The weight coefficients of the average path length, natural connectivity, and zero-order average stability, respectively. Through the optimization design of the three indicators by the objective function, the purpose of reducing the network delay, enhancing the network robustness and stability, and improving the network communication performance is achieved.

[0097] During the large-scale satellite swarm transition process, the follower satellites with special configurations are evenly distributed in the surrounding space of the virtual leader satellite, and it is ensured that the configuration satellites all maintain a communication topology with the virtual leader satellite. Other follower satellites fly in their surrounding space. Calculate the distance between any two follower satellites, record all the distance data in the same matrix A, and determine the communication range constraint l of the follower satellites. f , for those that meet the communication range, set the elements in the corresponding adjacency matrix B of the distance matrix to 1, otherwise set them to 0. Determine the communication topology between the follower satellites through the element distribution in the adjacency matrix. Calculate the connection quantity of each follower satellite with other follower satellites at the current moment, weigh the connectivity and the balance of the network, so that the follower satellites can select other follower satellites within the communication range and with less traffic for communication topology. As the satellite swarm transition process progresses, calculate in real time the satellites that enter the communication range and the satellites that leave the communication range, and continuously update the change of the adjacency matrix elements. Handle it in the form of a penalty function in the optimization objective function of the optimization problem of the satellite connection quantity constraint. Execute this optimization method at any moment during the satellite swarm transition process to further optimize the satellite communication topology. Continuously update the real-time communication topology of the entire satellite swarm according to the above method, and perform dynamic topology optimization on the satellite swarm transition process.

[0098] The autonomous obstacle avoidance control and topology optimization method for large-scale satellite swarm transition proposed in the embodiment of the present invention divides the communication area centered on the virtual leader satellite, and adopts different artificial potential fields in different areas to maintain the configuration stability of the entire satellite swarm; based on the motion states of the members in the satellite swarm, determine the overall communication topology of the satellite swarm based on the graph theory idea, design a preset time controller for some member satellites in the cluster according to the task requirements, and regard the satellites forming special configurations and some failed satellites as obstacles to ensure that other member satellites in the cluster do not collide during the task, and design a dynamic topology optimization method for the overall topology optimization problem of the satellite swarm to achieve real-time topology optimization during the satellite swarm transition process. This method is applicable to the configuration maintenance, collision avoidance, topology optimization, etc. of satellite clusters under space perturbation conditions.

[0099] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these changes and modifications.

Claims

1. An autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions, characterized in that, it includes the following steps: S1. Establish an LVLH coordinate system with the virtual leader satellite in the large-scale satellite constellation as the center. Divide the space around it into four regions according to the constellation scale and the communication range of the leader satellite, namely the no-fly safety zone, the repulsion zone, the free flight zone, and the gravitational zone, and determine the motion states of other follower satellites relative to the leader satellite within the communication range of the virtual leader satellite; S2. Determine the overall communication topology of the satellite constellation including the virtual leader satellite and all follower satellites based on graph theory; S3. When some member satellites fail, regard them as obstacles, determine their motion states relative to other satellites, and complete the initialization of the cluster communication topology; S4. According to the specific task requirements in the satellite constellation transition, design a preset time controller to enable some follower satellites to reach the desired configuration required by the task within a preset time, including the following steps: S401. With the virtual leader satellite as the center, design an improved artificial potential field with smooth transition properties in the repulsion zone and the gravitational zone. The specific expression is: where p i = [x i , y i , z i Τ is the position of the i-th follower satellite relative to the virtual leader satellite in the LVLH coordinate system centered on the virtual leader satellite, ||p i || 2 represents the distance of the follower satellite from the virtual leader satellite within the communication area of the virtual leader satellite, u i1 is the repulsive force function, E i1 is the field strength of the repulsive force area, η i1 is the repulsive force gain, d is the outer radius of the safety distance of the virtual leader satellite, r 1 is the inner radius of the repulsive force area, r 2 is the outer radius of the repulsive force area, u i2 is the gravitational potential function, η i2 is the gravitational gain, H is the outer radius of the free flight area, a 1 is the inner radius of the gravitational force area, a 2 is the outer radius of the gravitational force area, ξ i1 , ξ i2 is the control gain, λ is the simulated charge density, ε 0 is the simulated dielectric constant, r e and a e are the position representation quantities in the potential field. According to the satellite motion state, calculate the included angle between the relative motion position vector and the velocity vector of the satellite, and judge the relative motion trend of the satellite. For the away motion in the repulsive force area and the approaching motion in the gravitational force area, no additional artificial potential field forces are applied;​ S402. According to the task requirements, design a preset time controller to form a specific configuration of some satellites in the satellite constellation within a preset time and maintain the configuration; S5. Through the initial relative motion states of the follower satellites, regard the follower satellites that require special configurations and the failed satellites as space obstacles, and design an improved artificial potential field method with smooth transition characteristics to achieve autonomous obstacle avoidance / collision avoidance control for the overall transition of the satellite constellation; S6. According to the motion states during the overall transition process of the satellite constellation, design a dynamic topology optimization method to achieve real-time topology optimization during the large-scale satellite constellation transition process.

2. The autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions according to claim 1, characterized in that, in step S1, the space around the virtual leader satellite is divided into four regions, namely the no-fly safety zone, the repulsion zone, the free flight zone, and the gravitational zone. The relative motion expression of the follower satellite relative to the leader satellite is: where x, y, z represent the components of the follower satellite position vector, μ represents the gravitational coefficient, m represents the mass of the follower satellite, n represents the orbital angular velocity of the virtual leader satellite, u x , u y , u z represents the components of the control force in the three coordinate axis directions, d x , d y , d z represents the disturbance differences in the three coordinate axis directions between the leader satellite and the follower satellite. The disturbance terms involve J2 perturbation, atmospheric drag, solar radiation pressure, etc.

3. The autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions according to claim 1, characterized in that, in step S402, when designing the preset time controller, the control force expression is: Among them, is the system dynamics model, is the observed value of the uncertain disturbance term, k ip , k in are the control gain coefficients, δ i is a constant that satisfies the condition , s ip is the timed sliding mode function, s in is the positive linear sliding mode function, is a time-varying function, η is a positive constant, t 0 , t f are the starting time and the preset time respectively, e i1 , e i2 are the relative position error and the relative velocity error between the virtual leader satellite and the follower satellite respectively, b > 0, c ≥ 0, γ i > 0.

4. The autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions according to claim 1, characterized in that, in step S5, the satellites that require configurations and some failed satellites are regarded as obstacles, and autonomous obstacle avoidance control based on an improved artificial potential field method with smooth transition properties is designed for other follower satellites. The expression is: where u i3 is the repulsive force function commonly used in the artificial potential field method, η i3 is the repulsive force gain, E i is the field strength in the artificial potential field of the i-th follower satellite, p i = [x i , y i , z i Τ is the position of the i-th follower satellite relative to the virtual leader satellite in the LVLH coordinate system centered on the virtual leader satellite, p j = [x j , y j , z j Τ is the position vector of the j-th reconstructed / failed satellite relative to the virtual leader satellite in the LVLH coordinate system centered on the virtual leader satellite, d i is the outer radius of the safety distance of the i-th satellite, D i is the action radius of the artificial potential field of the i-th follower satellite, u i4 is the dynamic artificial potential field controller based on the relative velocity between follower satellites, ξ i3 , ξ i4 are the control gains, η i4 is the repulsive force gain, is the velocity vector of the i-th follower satellite relative to the virtual leader satellite in the LVLH coordinate system, is the velocity vector of the j-th reconstructed / failed satellite relative to the virtual leader satellite in the LVLH coordinate system;​​ According to the motion state of the satellite, calculate the included angle between the relative motion position vector and the velocity vector of the satellite, judge the relative motion trend of the satellite, and no additional artificial potential field force is applied to the away motion in the repulsion zone and the approaching motion in the gravitational zone.

5. The autonomous obstacle avoidance control and topology optimization method for large-scale satellite constellation transitions according to claim 1, characterized in that, in step S6, when designing the large-scale satellite constellation dynamic topology optimization method, based on the network optimization genetic algorithm, define the distance matrix between each follower satellite in the satellite constellation as: where l ij represents the distance between the i-th and j-th follower satellites in the satellite cluster, and the main diagonal indicates that the distance between each follower satellite and itself is 0; Define the adjacency matrix corresponding to the distance matrix A between the defined and following satellites as: where n ij is the element in the adjacency matrix B corresponding to l in the distance matrix A ij For the distance l between any two following satellites in the distance matrix A, ij performing conditional constraints can directly affect the value of the corresponding element in the B matrix; Define the communication distance of any one of the follower satellites in the satellite constellation as l f , if the distance l between two follower satellites in the satellite constellation ij ≤l f , then the corresponding element n in the B matrix ij = 1, otherwise n ij = 0. The values on the main diagonal represent a single follower satellite itself, and the element values are always 0. Thus, the communication topology of the follower satellites in the satellite constellation can be judged according to the element distribution in the matrix B; By means of the element distribution in the adjacency matrix B, the balance and connectivity of the satellite communication topology are balanced. The elements in the adjacency matrix B are operated and permuted, and the distances between a single satellite and other satellites in the matrix A are compared and calculated. When the communication distance is satisfied, the satellite is connected to the i satellites with the closest relative distance, where i ≤ i m , where i m is the maximum connection number of the communication topology of a single member satellite, and the corresponding element in the adjacency matrix B is set to 1. Even if other satellites satisfy the communication distance constraint, they will no longer be connected and the adjacency matrix elements will not be permuted. By adopting this indirect connection method, while reducing the satellite communication load, the communication topology of the overall cluster is ensured; For the above-mentioned topological constraint conditions, a topological optimization method is proposed in which the optimization objective function is processed in the form of a penalty function. For the constraint condition that each member satellite can communicate with at most i m satellites simultaneously, at any moment during the satellite constellation transition process, it is introduced into the objective function in the form of a penalty function term. When the degree d(v) of a certain vertex in the network is greater than i m , that is, when the number of edges connected to this vertex is greater than i m , it is penalized, and the designed objective function is Among them, α is an artificially set positive real number, called the penalty factor; is the average path length. By minimizing it, the network communication delay can be reduced. is the natural connectivity, where The natural connectivity can be as large as possible to enhance the robustness of the network. is the difference between the average side length of the network and the maximum communication distance, which is called the zero-order stability of the network. Making it as large as possible can enhance the stability of the network. 1 ,ω 2 ,ω 3 They are the weight coefficients of average path length, natural connectivity and zero-order average stability. Through the optimization design of the three indicators of the objective function, the purpose of reducing network delay, enhancing network robustness and stability, and improving network communication performance is achieved; During the large-scale satellite constellation transition process, the follower satellites with special configurations are evenly distributed in the surrounding space of the virtual leader satellite, and it is ensured that all the configured satellites maintain communication topology with the virtual leader satellite. Other follower satellites fly in their surrounding space. Calculate the distance between any two follower satellites, record all the distance data in the same matrix A, and determine the communication range constraint l of the follower satellites. f , set the element in the corresponding adjacency matrix B of the distance matrix to 1 if it meets the communication range, otherwise set it to 0. Determine the communication topology between the follower satellites through the element distribution in the adjacency matrix. Calculate the connection number of each follower satellite with other follower satellites at the current moment, weigh the connectivity and the balance of the network, so that the follower satellites can select other follower satellites within the communication range and with less communication volume for communication topology. As the satellite constellation transition process progresses, calculate in real time the satellites that enter the communication range and the satellites that leave the communication range, and continuously update the change of the adjacency matrix elements. Deal with it in the form of a penalty function in the optimization objective function of the optimization problem of the satellite connection number constraint. Execute this optimization method at any moment during the satellite constellation transition process to further optimize the satellite communication topology. Continuously update the real-time communication topology of the entire satellite constellation according to the above method, and perform dynamic topology optimization on the satellite constellation transition process.

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