Formation control method of heterogeneous multi-agent system under joint connected topology

Abstract

The invention discloses a formation control method of a heterogeneous multi-agent system under joint connected topology, and relates to the technical field of unmanned aerial vehicle cluster control. The invention designs a control algorithm for the formation control problem of the heterogeneous multi-agent system under the joint communication topology, and solves the formation control problem under the condition of communication topology joint communication by calculating the control rate of the formation pattern of the agents, so that the heterogeneous agents can move towards expected positions, and the formation control efficiency is improved. The position is the position corresponding to the expected formation configuration, so that the expected formation configuration is realized, and the formation adaptability of the heterogeneous multi-agent system is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle cluster control, and in particular relates to a formation control method for a heterogeneous multi-agent system under a joint connected topology. Background Art

[0002] Cluster systems and related issues have received extensive attention from industry and academia. Compared with a single individual, cluster systems can achieve cooperation between homogeneous / heterogeneous individuals through collaborative control, thereby achieving the effect of 1+1>2. Information interaction between individuals is the prerequisite for collaborative control of cluster systems. Whether it is a centralized or distributed control method, individuals are required to be able to communicate quickly and efficiently. However, in actual applications, cluster systems are easily affected by many factors such as complex electromagnetic environments, geographical environments, and meteorological conditions, resulting in the inability of the cluster system's topological network to connect in real time, and even causing security issues such as link interruption and node damage.

[0003] Faced with complex and ever-changing mission environments, cluster systems are often affected by factors such as the geographical environment and electromagnetic interference, making it difficult to ensure real-time connectivity of the communication topology, resulting in interruptions and disconnections of the communication link at certain moments in continuous time, but the union of the communication topology graphs within the time set is connected, that is, the communication topology is jointly connected. Existing research mainly focuses on the stability of the formation. As the size of the cluster system formation increases, the complexity of the communication topology is also increasing. In addition, due to environmental constraints during the execution of tasks, it is difficult for the cluster system to be globally connected in real time, which poses a great challenge to the control problem of the multi-agent system. Therefore, the formation control problem under the condition of joint topological connectivity needs to be studied urgently. Summary of the invention

[0004] The present invention provides a formation control method for a heterogeneous multi-agent system under a joint connected topology. The present invention designs a control algorithm for the formation control problem of a heterogeneous multi-agent system under a joint connected topology, solves the formation control problem under the condition of joint connectivity of communication topologies, enables heterogeneous agents to move toward a desired position, i.e., a position corresponding to a desired formation configuration, thereby realizing a desired formation shape and improving the formation adaptability of the heterogeneous multi-agent system.

[0005] In view of this, according to one aspect of an embodiment of the present invention, a formation control method for a heterogeneous multi-agent system under a joint connected topology is provided, comprising:

[0006] Step S01: Obtaining the formation where i∈{1, 2, ..., N}, N is the number of heterogeneous multi-agent systems, and for each agent

[0007]

[0008] y i (tt) = C i x i (t)

[0009] For the agent v i status, For the agent v i The control input, y i (t)∈R p For the agent v i The control output, They represent the system matrix, input matrix, and output matrix of the multi-agents respectively, and the formation represents the expected position of each agent;

[0010] Step S02: Design matrix X i and U i , i∈{1, 2, ..., N} satisfies the following equation

[0011] X i S r =A i X i +B i U i

[0012] 0=C i X i -F

[0013] Among them, (F, S r ) is detectable, S r and F are constant matrices;

[0014] Step S03: Determine the formula

[0015] Is it established? If yes, proceed to step S04;

[0016] Step S04: Design matrix K 1i , so that A i +B i K 1i Satisfies Hurwitz theorem;

[0017] Step S05: Let K 2i =U i -K 1i X i ;

[0018] Step S06: Determine a constant α, so that α satisfies 0<α<2min{Re(λ(EM i ))}, where λ(EM i) is EM i , i=1,2,..,the smallest non-zero eigenvalue of N,

[0019] M satisfies the equation L k =ME;

[0020] Step S07: Let K r =PF T , where the matrix P is the Riccati equation Symmetric positive definite solution of , Q is a positive definite matrix;

[0021] Step S08: Let w ij (t) and the Laplacian matrix The weights in are equal, where

[0022]

[0023] Step S09: K 1i , K 2i , K r , α, w ij (t) Substitute into the control law u i (t):

[0024]

[0025] in, and i are the state and output of the observer, respectively. δ i (t)∈R q is relative to The state offset of h yi (t) = Fδ i (t), v i (t) is h y (t) compensation amount.

[0026] Optionally, in step S03, if If not, redesign the formation h y (t).

[0027] Optionally, trigonometric functions are included in the formula for the desired position.

[0028] Optionally, the multi-agent system moves under the control law, and verifies whether the agents have formed a desired formation based on the positions of the agents at multiple moments after the initial position.

[0029] Optionally, the positions of the agents at multiple moments after the initial position are determined according to the trajectory of the multi-agent system moving under the control law.

[0030] Optionally, the error between the position of each agent and the expected position is calculated, and when the error converges to 0, the corresponding control rate forms the expected formation.

[0031] Optionally, the intelligent agent is a drone.

[0032] Optionally, there is a time series [t k , t k+1 ), t0=0 and the positive constant T satisfies 0 <t k+1 -t k <T。 Yes k , t k+1 ), where And there exist τ0 and τ1 satisfying τ0≤t κ+1 -t κ ≤τ1, and They are The topology in time and its corresponding Laplacian matrix, G k yes The union of k It's G k The Laplacian matrix of is the switching signal of the topology. When the communication topology of the multi-agent system changes,

[0033] Facing the complex and changeable mission environment and the influence of factors such as the geographical environment and electromagnetic interference, the present invention ensures the real-time connectivity of the communication topology, so that the communication topology is jointly connected in a continuous time, thereby enhancing the stability of the formation. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A multi-agent topology diagram according to an embodiment of the present invention;

[0035] Figure 2 A topology switching signal diagram according to an embodiment of the present invention;

[0036] Figure 3 is a relative position diagram of an intelligent agent according to an embodiment of the present invention;

[0037] Figure 4 A motion trajectory diagram of a multi-agent formation according to an embodiment of the present invention;

[0038] Figure 5 is an output error graph of each agent according to an embodiment of the present invention; DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] The present invention is a formation control problem of heterogeneous multi-agent systems under a joint connected topology. A control algorithm is designed to solve the formation control problem under the joint connected communication topology, so that heterogeneous agents can move toward the desired position, that is, the desired formation configuration h. yi The corresponding positions are determined to achieve the desired formation and improve the formation adaptability of the heterogeneous multi-agent system.

[0041] A high-order heterogeneous multi-agent system formed by N heterogeneous agents has:

[0042]

[0043] y i (t) = C i x i (t)

[0044] Where i∈{1, 2, …, N}, y i (t)∈R p They represent the state, control input, and output of the agent respectively. They represent the system matrix, input matrix, and output matrix of the cluster respectively.

[0045] use Represents the formation of a heterogeneous multi-agent system.

[0046] The joint connectivity topology is defined as follows: There exists a time series [t k , t k+1 ) t0=0 and the positive constant T satisfies 0 <t k+1 -t k <T。 Yes k , t k+1 ), where And there exist τ0 and τ1 satisfying τ0≤t κ+1 -t κ ≤τ1, and They are The topology in time and its corresponding Laplacian matrix, Gk yes The union of k It's G k The Laplacian matrix of is the switching signal of the topology. When the communication topology of the multi-agent system changes, Corresponding to topologies G1, G3, G4, G2, Switch in order from small to large m. When the multi-agent system uses topology G1 as the communication topology, The communication topology of the multi-agent system is G1→G3.

[0047] The design method of the formation controller of the heterogeneous cluster system under the joint connectivity topology is as follows:

[0048] Step 1: Design the formation h y , i∈{1, 2, ..., N};

[0049] Step 2: Design matrix X i and U i And Ui,i∈{1,2,...,N} satisfies the following equation;

[0050] X i S r =A i X i +B i U i

[0051] 0=C i X i -F

[0052] Among them, (F, S r ) is observable or detectable;

[0053] Step 3: Detection formula Is it true? If it is true, go to the next step; if it is not true and the expected formation configuration cannot be formed, jump to step 1 and redesign h y ,i∈{1,2,..,N}

[0054] Step 4: Design matrix K 1i , so that A i +B i K 1i Satisfies Hurwitz theorem;

[0055] Step 5: Let K 2i =U i -K 1i X i ;

[0056] Step 6: Select a constant α such that α satisfies 0<α<2min{Re(λ(EM))}, where λ(EM) is the smallest non-zero eigenvalue of EM. M is the equation that satisfies L k =ME;

[0057] Step 7: Let K r =PF T , where the matrix P is the Riccati equation Symmetric positive definite solution of , Q is a positive definite matrix;

[0058] Step 8: Let w ij (t) and the Laplacian matrix The weights in are equal, where

[0059]

[0060] Step 9: Substitute the parameters K calculated from steps 1 to 8 1i , K 2i , K r ,α,w ij (t) Substitute into the control law:

[0061]

[0062] Among them, and i are the state and output of the observer, respectively. Sr and F are constant matrices, δ i (t)∈R q is relative to The state offset of h yi (t) = Fδ i (t), v i (t) is h y (t) compensation amount.

[0063] Furthermore, the formula for the expected position includes trigonometric functions, which is a way of expressing the formula for the expected position.

[0064] Furthermore, the multi-agent system moves under the control law, and verifies whether the agents have formed a desired formation based on the positions of the agents at multiple moments after the initial position.

[0065] Furthermore, the positions of the agents at multiple moments after the initial position are determined according to the trajectory of the multi-agent system moving under the control law.

[0066] Furthermore, the error between the position of each agent and the expected position is calculated. When the error converges to 0, the corresponding control rate forms the expected formation.

[0067] Example

[0068] The present invention is further described below with reference to the accompanying drawings and specific embodiments:

[0069] The heterogeneous cluster system is as follows:

[0070] Agent 1:

[0071] Agent 2:

[0072] Agent 3:

[0073] Agent 4:

[0074] The joint connectivity topology is Figure 1 As shown, L is the Laplacian matrix of the union of G1, G2, G3, and G4,

[0075] Step 1: Design the desired formation of the team, that is, the expected position of each agent in the agent formation:

[0076]

[0077] Step 2: Design To satisfy the formula but

[0078] Step 3: Let v1, v2, v3, v4 and δ i as follows:

[0079] v1=[-2cos(t);0;-2sin(t);0]

[0080] v2=[0; 2cos(t+π / 2); 2sin(t+π / 2)]

[0081] v3=[-2cos(t+π / 2);-2sin(t+π / 2)]

[0082] v4=[2cos(t);sin(t)]

[0083]

[0084] Satisfy constraints

[0085] Step 4: Design Make A i +B i K 1i It satisfies Hurwitz's theorem;

[0086] Step 5: Let K 2i =U i -K 1i X i ,but

[0087] Step 6: From L k =ME, Available Then 0<α<3, let α=1;

[0088] Step 7: Let Q be the unit matrix, and use the Riccati equation Available Let K r =PF T ,but

[0089] Step 8: Let w ij (t) and the Laplacian matrix The weights in are equal;

[0090] Step 9: Substitute the parameters K calculated from steps 1 to 8 1i , K 2i , K r ,α,w ij (t) Substitute into the control law:

[0091]

[0092] The topology switching signal of G1-G4 is as follows Figure 2 As shown, Corresponding to topologies G1, G2, G3, G4, Switch in order from small to large m. When changes occur, the topology changes accordingly.

[0093] Figure 3It represents the position relationship of the members of the heterogeneous multi-agent formation at t=0s, 10s, 25s, and 40s, where the diamond, square, triangle, and cross represent the output of the four agents respectively. The initial position of the agent is shown in (a) at t=0s. The multi-agent system moves under the designed control law to form the desired formation. From the position of the multi-agent system at t=10s, 25s, and 40s, it can be seen that the agents form the desired quadrilateral formation.

[0094] Figure 4 The motion trajectory of each node in the heterogeneous multi-agent system from 0s to 40s is shown, and the positions of the agents at t = 0s, 10s, 25s, and 40s are marked, corresponding to Figure 3 The position of the agent at different times.

[0095] The output errors of the four agents are as follows: Figure 5 As shown in the figure, the four curves represent the distance errors of the four agents from the expected position, namely norm(e i ), e i =y i -ξ i -h yi The error curves of the four agents in the multi-agent system converged to zero, forming the desired formation.

[0096] The above is only a specific embodiment of the present invention, and the present invention is described in detail. The unexplained part is a conventional technology. However, the protection scope of the present invention is not limited to this. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A formation control method for a heterogeneous multi-agent system under a joint connected topology, characterized in that: include: Step S01: Obtaining the formation where i∈{1, 2, .., N}, N is the number of heterogeneous multi-agent systems, and for each agent y i (t)=C i x i (t) For the agent v i status, For the agent v i The control input, y i (t)∈R p For the agent v i The control output, They represent the system matrix, input matrix, and output matrix of the multi-agents respectively, and the formation represents the expected position of each agent; Step S02: Design matrix X i and U i , i∈{1, 2, ..., N} satisfies the following equation X i S r =A i X i +B i U i 0=C i X i -F Among them, (F, S r ) is detectable, S r and F are constant matrices; Step S03: Determine the formula Is it established? If yes, proceed to step S04; Step S04: Design matrix K 1i , so that A i +B i K 1i Satisfies Hurwitz theorem; Step S05: Let K 2i =U i -K 1i X i ; Step S06: Determine a constant α, so that α satisfies 0<α<2min{Re(λ(EM i ))}, where λ(EM i ) is EM i , the smallest non-zero eigenvalue of i = 1, 2, ..., N, M satisfies the equation L k =ME; Step S07: Let K r =PF T , where the matrix P is the Riccati equation Symmetric positive definite solution of , Q is a positive definite matrix; Step S08: Let w ij (t) and the Laplacian matrix The weights in are equal, where Step S09: K 1i , K 2i , K r , α, w ij (t) Substitute into the control law u i (t): in, and i are the state and output of the observer, respectively. δ i (t)∈R q is relative to The state offset of h yi (t) = Fδ i (t), v i (t) is h y (t) compensation amount.

2. The method according to claim 1, characterized in that In step S03, if If not, redesign the formation h y (t).

3. The method according to claim 1, characterized in that The formula for the desired position includes trigonometric functions.

4. The method according to claim 1, characterized in that: The multi-agent system moves under the control law, and verifies whether the agents have formed a desired formation based on the positions of the agents at multiple moments after the initial position.

5. The method according to claim 4, characterized in that The positions of the agents at multiple moments after the initial position are determined according to the trajectory of the multi-agent system moving under the control law.

6. The method according to claim 1, characterized in that The error between the position of each agent and the expected position is calculated. When the error converges to 0, the corresponding control rate forms the expected formation.

7. The method according to claim 1, characterized in that The intelligent agent is a drone.

8. The method according to claim 1, characterized in that There is a time series t0=0 and the positive constant T satisfies 0 <t k+1 -t k <T, Yes k , t k+1 ), where And there exist τ0 and τ satisfying τ0≤t k+l -t k ≤τ, and They are The topology in time and its corresponding Laplacian matrix, G k yes The union of k It's G k The Laplacian matrix of is the switching signal of the topology. When the communication topology of the multi-agent system changes,

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