A Swarming Emergent Control Method for Cluster Flight of Spacecraft

Abstract

The present invention discloses a flocking emergence control method for spacecraft cluster flight, representing the interaction topology between spacecraft monomers in the spacecraft cluster by a graph; based on the graph, establishing a mutual interaction potential function between monomers in the cluster flocking emergence to describe the interaction constraints between spacecraft monomers; according to the potential function, designing a flocking control law for cluster flight, and each spacecraft in the cluster updates its speed and tracks based on the control law to achieve and maintain the flocking flight state. Through the application of the present invention, it is possible to achieve that the movement of spacecraft cluster monomers is gentle and smooth when the spacing is very close, and the state transitions smoothly at the safe spacing holding point.

Description

Technical Field

[0001] The present invention relates to a flocking emergence control method for spacecraft cluster flight, belonging to the technical field of spacecraft cluster control. Background Technique

[0002] Flocking is a collective motion of a decentralized large number of autonomous individuals. It emerges a behavior phenomenon of aggregation and coordinated synchronization as a whole by designing local rules between individuals and making them interact with each other. A spacecraft cluster is a distributed system formed by connecting single spacecraft flying in close proximity through wireless information using a wireless network. It has autonomy, intelligence, and fault tolerance that single spacecraft do not have.

[0003] In recent years, with the implementation of the F6 program proposed by DARPA, spacecraft clusters have gradually become a research hotspot in the field of spacecraft systems. There are currently two main methods for the cooperative behavior control of spacecraft clusters, including: the spacecraft cluster behavior control based on heuristic algorithms such as particle swarm or co-evolution; the emergence cooperative behavior control based on local rules. Among them, the method for the cooperative behavior control of spacecraft clusters based on heuristic algorithms such as particle swarm or co-evolution constructs the control behavior of single spacecraft as particles or gene fragments, and uses the multi-body cooperative optimization mechanism of particle swarm or co-evolution algorithms to set relevant fitness functions to achieve the cooperative behavior control of spacecraft clusters. The existing cooperative behavior control of unmanned aerial vehicle clusters based on local rules emergence sets the interaction model relatively coarsely according to the distance between cluster single bodies, and the interaction design changes relatively linearly with the distance, which does not conform to the actual situation. It does not consider the situation that the communication gradually weakens as the distance increases, resulting in the interaction between single bodies becoming stronger first and then rapidly weakening. In addition, the traditional design control law does not consider the state switching oscillation problem of the interaction between single bodies at the safety distance holding point, which is likely to cause the flocking failure of the group. Summary of the Invention

[0004] The technical problem solved by the present invention is: overcoming the deficiencies of the prior art, a flocking emergence control method for spacecraft cluster flight is proposed, and local flocking local interaction rules of cluster single bodies with interaction strength constraint limits, communication distance constraints, and smooth interaction at the safety distance holding point are designed to achieve flocking emergence control through the interaction between spacecraft single bodies.

[0005] The technical solution of the present invention is:

[0006] A flocking emergence control method for spacecraft cluster flight, including:

[0007] Representing the interaction topology between single spacecraft in a spacecraft cluster by a graph;

[0008] Based on the said figure, establish the potential function of the interaction between swarm emergence monomers, and describe the interaction constraints between spacecraft monomers;

[0009] According to the said potential function, design a swarm flight flocking control law with constraints on the interaction strength between monomers, communication distance constraints, and smooth processing of interactions at the safe distance holding point. Each spacecraft monomer in the swarm updates its speed and tracks based on the said control law to achieve and maintain the flocking flight state.

[0010] Preferably, based on the said figure, establish the potential function of the interaction between swarm emergence monomers:

[0011]

[0012] In the formula, η i (d ij ) is the potential function corresponding to spacecraft i, which consists of a two-segment function, including the constant value stage when d ij < x A and the β A < d ij < 2c i curve when i (d ij ). d ij is the relative distance between spacecraft i and j; is the ordinate value corresponding to the maximum point of the β i (d ij ) curve, and x A is the relative distance between spacecraft i and j when the β i (d ij ) curve reaches the maximum point. c i is the safe distance holding point between spacecraft monomers;

[0013] β i (d ij ) = a i (d ij )g i (d ij )

[0014]

[0015] In the formula, k i and δ i respectively represent the proportionality coefficient and adjustable range of a(d ij ), and t i and δ′ respectively represent the adjustment intensity and adjustable range of g(d ij ).

[0016] Preferably, according to the potential function, a flocking control law for cluster flight is designed with constraints on the interaction strength between monomers, communication distance, and smooth processing of interactions at the safe distance holding point. The control law includes position feedback, velocity feedback of a spacecraft monomer and other spacecrafts within the domain of this spacecraft, and state variables for guiding the spacecraft to follow the cluster leader.

[0017] Preferably, the flocking control law for cluster flight is designed as the sum of the position feedback, velocity feedback of a spacecraft monomer and other spacecrafts within the domain of this spacecraft, and state variables for guiding the spacecraft to follow the cluster leader.

[0018] Preferably, the position feedback of a spacecraft monomer and other spacecrafts within the domain of this spacecraft is:

[0019]

[0020] φ(d ij )=η(d ij )·tanh(d ij )

[0021]

[0022] Wherein, is the position feedback of spacecraft i and other spacecrafts within the domain of this spacecraft, and N i is the adjacency set of spacecraft i; are the position vectors of spacecraft i and spacecraft j in the geocentric coordinate system, respectively.

[0023] Preferably, the velocity feedback of a spacecraft monomer and other spacecrafts within the domain of this spacecraft is:

[0024]

[0025] Wherein, is the position feedback of spacecraft i and other spacecrafts within the domain of this spacecraft, and N i is the adjacency set of the i-th spacecraft, including the set of other spacecrafts within the sphere with a radius of 2c i , and c i is the safe distance holding point between spacecraft monomers; are the velocity vectors of spacecraft i and spacecraft j, respectively;

[0026]

[0027] a ij is the adjacency relationship between spacecraft i and spacecraft j within the adjacency set, and η i (d ij ) is the potential function corresponding to spacecraft i.

[0028] Preferably, the state variables for guiding the spacecraft to follow the cluster leader are:

[0029]

[0030] where is the state variable for spacecraft i to follow the cluster leader, and c1, c2, and c3 are the coefficients of the relative displacement, relative velocity, and relative acceleration between spacecraft i and spacecraft j respectively, are the velocity vectors of spacecraft i and spacecraft j respectively.

[0031] Preferably, the interaction topology between the individual spacecraft in the spacecraft cluster is represented by a graph. In the graph, the individual spacecraft are the vertices of the graph, the interaction between the nodes is the edge of the graph, and the adjacency relationship between the individual spacecraft depends on the positional relationship between them.

[0032] Preferably, the spacecraft within the cluster update their velocities based on the control law and track, achieving and maintaining the flocking flight state, and then guiding by selecting a spacecraft as the leader to achieve the directional flocking flight of the cluster.

[0033] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. The characteristic is that when the processor executes the computer program, the above method is implemented.

[0034] The advantages of the present invention compared with the prior art are as follows:

[0035] (1) The present invention considers the situation where the interaction between the individual spacecraft gradually becomes stronger and then rapidly weakens due to the law that the communication distance between the individual spacecraft in the cluster increases and gradually weakens. The designed control law is more in line with the actual situation.

[0036] (2) The traditional emergence control law does not consider the state switching oscillation problem of the interaction between the individual spacecraft at the safety distance holding point. The present invention designs a smooth adjustment function for the interaction at the safety distance holding point, which can realize the smooth transition of the state of the individual spacecraft in the spacecraft cluster at the safety distance holding point.

[0037] (3) The present invention objectively describes the change law of the interaction between the individual spacecraft in the cluster, where the interaction with the displacement difference as the feedback gradually weakens during the process of the distance between the individual spacecraft in the cluster decreasing to zero, while highlighting the interaction with the velocity difference as the feedback. The designed control law can ensure that the individual spacecraft move smoothly and gently when the distance between them is very close. Description of the Drawings

[0038] Upon reading the following detailed description of the preferred embodiments, various other advantages and benefits will become apparent to those of ordinary skill in the art. The drawings are only for the purpose of illustrating the preferred embodiments and are not considered as a limitation of the present invention. Moreover, throughout the drawings, the same reference numerals are used to represent the same components. In the drawings:

[0039] Figure 1 This is the exponential function β corresponding to the embodiment of the present invention i (d ij ) curve graph;

[0040] Figure 2 This is the exponential function a(d ij ) curve graph corresponding to the embodiment of the present invention;

[0041] Figure 3 This is the exponential function g(d ij ) curve graph corresponding to the embodiment of the present invention;

[0042] Figure 4 This is the η i (d ij ) function variation curve graph corresponding to the embodiment of the present invention;

[0043] Figure 5 This is the flowchart of the swarming emergence flight process of the spacecraft cluster corresponding to the embodiment of the present invention;

[0044] Figure 6 This is the schematic diagram of the reference orbital coordinate system oxyz corresponding to the embodiment of the present invention. Detailed implementation manners

[0045] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the drawings and in combination with the embodiments.

[0046] Considering the situation that the interaction between monomers gradually becomes stronger and then rapidly weakens due to the increasing communication distance between cluster monomers and the decreasing law, and the traditional emergence control law does not consider the state switching oscillation problem of monomer interaction at the safe distance maintaining point, which is likely to cause the flocking failure of the group. In these two cases, a flocking emergence control method for spacecraft cluster flight is proposed. A local flocking local interaction rule for cluster monomers with constraints on the interaction strength limit, communication distance, and smooth interaction at the safe distance maintaining point is designed, and the flocking emergence control is realized through the interaction between spacecraft monomers.

[0047] This method is as Figure 5 shown, including:

[0048] 1) Describing the flocking interaction of spacecraft clusters with the help of graph theory

[0049] In the design of the local rules for the flocking emergence of spacecraft clusters, graph theory is the main analysis tool. A graph consists of vertices and edges, denoted as G=(V, E), where the vertex set V={ν1, ν2,..., ν n}; the edge set represents the adjacency relationship between vertices. The adjacency matrix A=[a ij corresponding to the adjacency graph G is a weighted adjacency matrix. In the graph, it is assumed that a node has no connectivity with itself, that is, a ij ∈[0, 1], a ii =0. The adjacency set N i of node i is defined as the set of points that satisfy {j∈V: a ij ≠0 and (i, j)∈E}.

[0050] During the flight of spacecraft clusters, considering a spacecraft as a vertex in graph theory and the interaction between nodes as the edges in the graph, the interaction topology between cluster monomers can be represented by a graph. The adjacency relationship between spacecraft monomers is:

[0051] A=[a ij , a ij ∈[0, 1] (1)

[0052] The neighbor set N i of each spacecraft monomer i is defined as the set of other spacecraft within a sphere with a certain distance as the radius.

[0053] 2) Design of the interaction potential function between monomers in the flocking emergence of spacecraft clusters

[0054] In the study of flocking emergence, maintaining a stable distance between individual agents in the cluster is one of the important goals, and a potential function is commonly used to achieve this. In the emergence control of spacecraft cluster flight, the potential function mainly plays a role in controlling and guiding the separation and aggregation of individual agents in the cluster. The present invention designs a new potential function to objectively describe the interaction constraints between individual agents in the cluster.

[0055] Suppose there are n spacecraft. To achieve the flocking state of cluster flight, the relative distance d between any two spacecraft i and j ij needs to be able to maintain a stable value within a communication range. The traditional control law lacks consideration of the dynamic boundaries of individual spacecraft, the maximum communication range limit, and the smooth transition of the state of the safety spacing holding point of individual agents, which affects the stability of the cluster flocking state. Therefore, a new potential function for the interaction between individual agents in the cluster is proposed, fully considering the maneuverability, the variation law of communication distance, and the smooth switching of the state of individual agents in the spacecraft cluster at the safety spacing holding point. The potential function is shown in Equation (2), corresponding to η i (d ij ) The function change curve is Figure 4 .

[0056]

[0057] Among them, η i (d ij ) consists of a two-segment piecewise function, including the constant value stage when d ij <x A and the β A <d ij <2c part of the β i (d ij ) curve ( Figure 1 ). is the ordinate value corresponding to the maximum point of the β i (d ij ) curve, indicating that in the stage where individual agents in the cluster approach each other, their interaction will reach the maximum value at A, and then remain constant because the interaction intensity cannot continue to increase due to the limitation of the maneuverability of individual agents in the cluster. And between x A and 2c i , it is the variation law of the interaction between individual agents as the spacing increases, specifically manifested as the part of β i (d ij ) when x A <d ij <2c i .

[0058] β i (d ij ) = a i (d ij ) g i (d ij)(3)

[0059]

[0060] Among them, β i (d ij ) is obtained by multiplying two exponential functions a(d ij ) and g(d ij ). The function a(d ij ) is as shown in Figure 2 , and its main function is: the c i point is the safety distance holding point of the cluster monomer spacing (represented by the origin in the figure). When the distance is less than this point, they repel each other, and when it is greater than this point, they attract each other. Further increasing the spacing, this attraction weakens from strong to zero. These two repulsive and attractive effects enable the monomers to form a swarm with a stable safety spacing. The function g(d ij ) is the smooth adjustment function of the cluster safety spacing holding point state, as shown in Figure 3 . As an adjustment function, it is mainly used to smoothly process the a(d ij ) curve at the safety distance holding point c i segment. Adjusting the slope of the a(d ij ) curve at the safety point c i is too large, which easily leads to strong interaction between cluster monomers at this point and causes state oscillation, reducing the impact on maintaining the swarm state, enabling the cluster to achieve smooth state switching at the safety distance point, and being conducive to maintaining the swarm state of the cluster. k i and δ i respectively represent the proportional coefficient and adjustable range of a(d ij ). t i and δ′ respectively represent the adjustment intensity and adjustment range of g(d ij ).

[0061] 3) Design of the flocking emergence flight control law for spacecraft clusters

[0062] To achieve directional flocking flight of the cluster, first ensure that the relative distance d ij between any spacecraft i and j can be maintained at a stable value within a communication range. Select the monomer interaction potential function proposed above (shown in Figure 4 ) for the design of the spacecraft flocking control law:

[0063]

[0064] Among them, is the control input for the $i$-th spacecraft. The first and second terms are the position and velocity feedbacks between the $i$-th spacecraft and the $j$-th spacecraft in its domain, respectively, which are used to achieve the flocking behavior during cluster flight. The third term is used to guide the state of spacecraft $i$ to follow the leader, making the cluster movement directional. During the cluster flight of spacecraft, the leader can select one or several of them as leaders according to the mission or construct a group virtual center as the leader. The $\varphi$ expression is shown in Equation (7), objectively describing the changing law of the interaction between cluster monomers with the feedback of the velocity difference becoming prominent while the interaction with the displacement difference as the feedback gradually weakens during the process of the distance between cluster monomers decreasing to zero. This function can make the movement of monomers slow down when the distance is very close. The vector is expressed as shown in Equation (8). The leader guidance mechanism $f$ i γ is shown in Equation (9). $N$ i is shown in Equation (10). The element $a$ of the adjacency matrix ij is shown in Equation (11). Among them, as Figure 6 shown, the reference orbital coordinate system $oxyz$ is defined, with the coordinate origin at the mass point of the reference star, the $x$-axis pointing in the direction of the geocentric radius vector of the reference star, the $z$-axis pointing in the direction of the normal of the reference point orbital plane, the $y$-axis perpendicular to the $x$-axis in the reference orbital plane and $o - xyz$ forming a right-handed rectangular coordinate system, respectively represent the position vector, velocity vector, and acceleration vector of spacecraft i in the spacecraft cluster.

[0065] $\varphi(d$ ij ) = $\eta(d$ ij )·tanh(d$ ij ) (7)

[0066] Among them,

[0067]

[0068] where $c1 \gt 0$, $c2 \gt 0$,

[0069] $c3 \gt 0$ (9)

[0070] Assume that the adjacency relationship between spacecraft depends on the relative position relationship. Let $2c$ i be the communication upper bound between spacecraft, that is, the perception range. Other spacecraft within the sphere with a radius of $2c$ i constitute the neighbor set that can transmit information to spacecraft $i$ at time $t$:

[0071] $N$ i = {i,j∈V:d ij <2ci} (10)

[0072] A = [a ij is the adjacency matrix of the internal information network diagram of the spacecraft cluster, and the definitions of each element are as follows:

[0073]

[0074] where a ij is determined by the potential function between individual spacecraft in the cluster. When the relative distance between spacecraft continuously changes, the element a of the adjacency matrix ij continuously changes in the interval [0, 1], and the neighbor set N of spacecraft i i also changes dynamically. Therefore, the topological structure between spacecraft is a dynamically changing switching topology.

[0075] 4) Swarm emergence control of spacecraft cluster

[0076] Suppose there are n spacecraft, and a certain altitude orbit is designed, such as Figure 6 , to achieve coordinated swarm flight of the cluster. By enabling each individual spacecraft in the cluster to continuously update its speed and track based on the control law (Formula 6), a good swarm flight state can be achieved and maintained. Further, by selecting a leader among them for guidance, directional swarm flight of the cluster can be achieved.

[0077] The above-described embodiments are only relatively preferred specific embodiments of the present invention. Ordinary changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included in the protection scope of the present invention.

Claims

1. A flocking emergence control method for spacecraft cluster flight, characterized in that, Including: Represent the interaction topology among spacecraft monomers in a spacecraft cluster by a graph; Based on the graph, establish a swarm emergence interaction potential function among monomers to describe the interaction constraints among spacecraft monomers; According to the potential function, design a swarm flight control law with constraints on the interaction intensity between monomers, communication distance constraints, and smooth processing of interactions at the safe distance holding point. Each spacecraft monomer in the cluster updates its velocity and tracks based on the control law to achieve and maintain the swarm flight state; Based on the graph, establish a swarm emergence interaction potential function among monomers: where η i (d ij ) is the potential function corresponding to spacecraft i, which consists of a piecewise function at both ends, including the constant value stage when d ij < x A , and the β i ij (d ij ) curve when x A < d ij < 2c i ; d ij is the relative distance between spacecraft i and j; is the ordinate value corresponding to the maximum point of the β i (d ij ) curve, x A is the relative distance between spacecraft i and j at the maximum point of the β i (d ij ) curve, and c i is the safety distance holding point between spacecraft monomers; β i (d ij ) = a i (d ij )g i (d ij ) where k i and δ i respectively represent the proportionality coefficient and the adjustable range of a(d ij ), t i and δ′ respectively represent the adjustment intensity and the adjustment range of g(d ij ).

2. The flocking emergence control method for the collective flight of spacecraft clusters according to claim 1, wherein, According to the potential function, design a swarm flight control law with constraints on interaction intensity, communication distance constraints, and smooth processing of interactions at the safe distance holding point. The control law includes position feedback, velocity feedback of a spacecraft monomer and other spacecrafts within the domain of this spacecraft, and state variables for guiding the spacecraft to follow the cluster leader.

3. A flocking emergence control method for spacecraft cluster flight according to claim 2, characterized in that, Design the swarm control law for cluster flight as the sum of the position feedback, velocity feedback of a spacecraft monomer and other spacecrafts within the domain of this spacecraft, and state variables for guiding the spacecraft to follow the cluster leader.

4. A flocking emergence control method for spacecraft cluster flight according to claim 3, characterized in that, The position feedback of a spacecraft monomer and other spacecrafts within the domain of this spacecraft is: φ(d ij ) = η(d ij )·tanh(d ij ) In the formula, is the position feedback of spacecraft i and other spacecrafts in the field of this spacecraft, and N i is the adjacency set of spacecraft i; are the position vectors of spacecraft i and spacecraft j in the geocentric coordinate system respectively.

5. The flocking emergence control method for the collective flight of spacecraft clusters according to claim 3, characterized in that The velocity feedback of a spacecraft monomer and other spacecrafts within the domain of this spacecraft is: In the formula, is the position feedback of spacecraft i and other spacecrafts in the field of this spacecraft, and N i is the adjacency set of spacecraft i, including other spacecraft sets within the sphere with a radius of 2c i where c i is the safety distance maintaining point between spacecraft monomers; are the velocity vectors of spacecraft i and spacecraft j respectively; a ij is the adjacency relationship between spacecraft i and spacecraft j in the adjacent set, η i (d ij ) is the potential function corresponding to spacecraft i.

6. The flocking emergence control method for the clustered flight of spacecraft according to claim 3, characterized in that The state variable for guiding the spacecraft to follow the cluster leader is: wherein, is the state quantity of spacecraft i following the cluster leader, and c1, c2, and c3 are the coefficients of the relative displacement, relative velocity, and relative acceleration of spacecraft i and spacecraft j respectively, are the velocity vectors of spacecraft i and spacecraft j respectively.

7. A flocking emergence control method for spacecraft cluster flight according to claim 1, characterized in that Represent the interaction topology among spacecraft monomers in a spacecraft cluster by a graph. In the graph, the spacecraft monomers are the vertices of the graph, the interactions between nodes are the edges of the graph, and the adjacency relationship between spacecraft monomers depends on the relative position relationship.

8. A flocking emergence control method for the collective flight of spacecraft clusters according to claim 1, characterized in that The spacecrafts in the cluster update their velocities and track based on the control law to achieve and maintain the swarm flight state, and then guide by selecting a spacecraft as the leader to achieve the directional swarm flight of the cluster.

9. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method according to any one of claims 1 to 8.

Images