Unmanned aerial vehicle group control method based on fixed time clustering algorithm

Abstract

The invention discloses an unmanned aerial vehicle group control method based on a fixed time clustering algorithm. The method comprises the following steps: firstly, based on a second-order multi-agent system theory, establishing a kinetic model of a second-order unmanned aerial vehicle group; then, in order to reduce the number of times of communication between the unmanned aerial vehicle groups, a dynamic threshold value variable is introduced, and a proper dynamic event triggering mechanism is designed for each unmanned aerial vehicle; then, based on a dynamic event triggering mechanism, a novel fixed time control protocol is designed for a single unmanned aerial vehicle. And finally, by means of Liapunov stability analysis, obtaining a sufficient condition that the unmanned aerial vehicle group can cluster, and eliminating a Zeno behavior.

Description

Technical Field

[0001] The invention relates to a fixed time control method, and in particular to a new cluster algorithm based on a drone swarm system. Background Art

[0002] With the rapid development of drone technology, drone swarm control has become a research hotspot in the field of modern intelligent systems and automation. UAV swarms can achieve more complex and efficient task execution in many fields such as military, environmental monitoring, and logistics distribution through the collaborative cooperation of multiple drones. However, due to the large scale of drone swarms and limited communication between individuals, there are many challenges in achieving efficient collaborative control. Traditional swarm control methods usually rely on centralized control strategies or self-organizing mechanisms, but these methods may not meet the requirements of real-time and robustness in dynamic environments. Especially when the task time is limited, how to complete the cluster control task within a fixed time becomes a key issue. Therefore, a drone swarm control method based on a fixed-time cluster algorithm has emerged, aiming to improve the collaborative efficiency and response speed of drone swarms under complex tasks.

[0003] In the control of drone swarms, traditional swarm algorithms, such as control methods based on consistency theory and distributed control methods based on game theory, can solve the coordination problem between drones to a certain extent, but these algorithms usually assume ideal communication conditions and environmental stability, and are difficult to deal with real-world problems such as communication delays, individual failures, and environmental changes. Especially in large-scale drone swarms, the time complexity of the algorithm and the demand for computing resources will increase significantly, which will affect the real-time and stability of the system. The fixed-time-based cluster algorithm can ensure that all drones reach the desired cluster state within a predetermined time by introducing a fixed-time convergence mechanism, regardless of how the initial state changes. This method can not only effectively reduce the complexity of the algorithm, but also enhance the robustness and adaptability of the system in complex environments.

[0004] The application of fixed-time convergence control strategy in the control of drone swarms has significant advantages. This method overcomes the limitation of traditional control methods that the convergence time depends on the initial conditions by designing appropriate control laws so that the system state converges within a preset finite time. Specifically, the fixed-time control algorithm can achieve tasks such as rapid consistency, formation control, and obstacle avoidance of drone swarms without being affected by the initial state. In addition, the fixed-time clustering algorithm has strong robustness and can cope with challenges such as communication delays, node failures, and environmental uncertainties that drones may encounter during mission execution. Therefore, the drone swarm control method based on the fixed-time clustering algorithm has broad potential in practical applications and can provide reliable technical support for the efficient execution of complex tasks. Summary of the invention

[0005] The purpose of this invention is to propose a UAV swarm control method based on a fixed-time clustering algorithm, which can effectively improve the speed and accuracy of UAV swarm clustering;

[0006] The specific technical solution of the present invention is as follows: A method for controlling a drone swarm based on a fixed-time cluster algorithm comprises the following steps:

[0007] Based on the second-order multi-agent system theory, a dynamic model of the second-order UAV swarm is established;

[0008] For the second-order multi-agent system in reference [1], the following UAV swarm dynamics model is established;

[0009] Consider a second-order UAV swarm with N followers and a leader. The dynamic model of the i-th UAV is as follows:

[0010] Among them, x i (t), v i (t) respectively represent the position and velocity of the ith UAV. i (t) is the control input of each UAV, ζ i (t) is an unknown external disturbance and f(·) is a nonlinear function. The leader’s dynamic model is as follows:

[0011] Where x0(t) and v0(t) represent the position and velocity of the leader, respectively. u0(t) is the control input of the leader, and f0 is a nonlinear function.

[0012] Furthermore, in order to reduce the number of communications between drone groups, dynamic threshold variables are introduced to design a suitable dynamic event trigger mechanism for each drone. The specific steps are as follows:

[0013] For the i-th agent, the discrete time instant Determined by the following dynamic event trigger conditions

[0014] In the formula, ε vi (t) = v i (t)-v0(t),

[0015]

[0016] θ is a positive constant, η i (t) is an auxiliary variable described by:

[0017] Where η i (0)>0, a, b, v>0 and 0<δ≤1.

[0018] Furthermore, based on the dynamic event triggering mechanism, a novel fixed-time control protocol is designed for a single UAV. The specific steps are as follows:

[0019] In order to study the fixed-time leader-follower clustering of multi-agent systems, we designed a fixed-time distributed controller based on dynamic event triggering for each drone, which is expressed as follows:

[0020] In the formula, In order to save communication resources and avoid continuous communication between drone groups, the i-th drone only communicates at discrete moments. α, β and κ>0; p, q are the ratios of two positive odd numbers, and p>1, 0 <q<1。

[0021] Next, with the help of Lyapunov stability analysis, we can derive the necessary conditions for the drone swarm to cluster and eliminate Zeno behavior. The specific steps are as follows:

[0022] C001: Construct the following Lyapunov candidate function: W(t)=V1(t)+V2(t)

[0023] In the formula

[0024] C002: We can get

[0025] C003: Further

[0026] In the formula, It's all measurable.

[0027] C004: Next we can get

[0028] C005: There exists a positive definite matrix H such that H = R T R, furthermore

[0029] C006: We have

[0030] C007: Then

[0031] C008: Further

[0032] C009: Finally, it can be deduced

[0033] C010: Similarly, we can deduce

[0034] C011: We can conclude

[0035] C012: The above formula can be further written as

[0036] C013: We can easily get

[0037] C014: Next

[0038] C015: Then, there is

[0039] C016:

[0040] C017: Finally, it can be inferred that ∈ i (t) Fixed-time consistency can be achieved at the equilibrium point, and the upper bound of the fixed time is

[0041] C018: Through the above analysis, we can conclude that Next, we can deduce

[0042] C019: According to The definition of Since the number of particles is limited and the velocity trajectory is continuous, when t<T pre , at a specific point in time, we can find some particles that satisfy therefore, is bounded. That is to say Where μ>0. Then we can get

[0043] C020: That means because

[0044] C021: and

[0045] C022: To complete the analysis, we assume that Therefore, then there is Furthermore, if we can find some agents that satisfy Then the above assumptions hold. Next, when t<T pre ,right Points can be obtained

[0046] C023: When t ≥ T pre hour,

[0047] C024: Based on previous analysis We can further conclude that

[0048] C025: Conclusion can be drawn

[0049] C026: According to the above analysis, in order to exclude Zeno behavior, first ||∈ i (t)|| Taking the derivative we can get

[0050] C027: Next

[0051] C028:

[0052] C029: Due to We can conclude

[0053] C030: Then there is

[0054] C031:

[0055] C032: Then

[0056] C033: It can be seen that in the trigger mechanism, the time interval between two consecutive triggering moments is Zeno behavior is ruled out. This shows that the dynamic time trigger mechanism we designed is reasonable, and the proof is complete. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is the topological structure diagram of the drone swarm system;

[0058] Figure 2 It is the position trajectory diagram of the drone group in three-dimensional space;

[0059] Figure 3-4 It is the trajectory diagram of the position status of the drone group in the two-dimensional plane;

[0060] Figure 5-6 It is the trajectory diagram of the speed state of the drone group in the two-dimensional plane;

[0061] Figure 7-8 It is the trajectory diagram of the UAV group velocity error in the two-dimensional plane;

[0062] Fig. 9 It is the convergence trajectory diagram of the dynamic threshold;

[0063] Fig.10 A graph of event triggering times for each agent;

[0064] Fig.11 A diagram for the abstract; DETAILED DESCRIPTION

[0065] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0066] A method for controlling a swarm of drones based on a fixed-time clustering algorithm comprises the following steps:

[0067] Step 1: Set various system parameters;

[0068] Step 2: Set up the topology of drone group communication;

[0069] Step 3: Set up event trigger mechanism;

[0070] Step 4: Set up a distributed control protocol based on an event trigger mechanism;

[0071] Step 5: Set the initial position and speed of a single drone;

[0072] Step 6: Set the external input and nonlinear term of the system;

[0073] Step 7: Set the leader's control input;

[0074] An embodiment of the present invention is described below:

[0075] Consider a second-order UAV swarm with N followers and a leader. The dynamic model of the i-th UAV is as follows:

[0076] Among them, x i (t), v i (t) represent the position and velocity of the ith UAV respectively. The initial state is x1(0) = [8, 18] T , x3(0) = [17, 12] T , x4(0) = [12, 12] T , x5(0) = [15, 22] T , x6(0) = [10, 24] T , v1(0) = [1.2, 0.2] T , v2(0) = [1.1, 1.6] T , v3(0) = [1.5, 0.95] T , v4(0) = [0.75, 1.2] T , v5(0) = [1.0, 1.8] T , v6(0) = [0.2, 1.0] T .

[0077] u i (t) is the control input for each UAV:

[0078] In the formula, α=6, β=2.8, β=4.6, p=7 / 5, q=3 / 5.

[0079] ζ i (t) is an unknown external disturbance and f(·) is a nonlinear function expressed as: ζ i(t)=1.55sin(v i (t)) f(x i (t), v i (t), t) = 0.5cos(1.5v i (t))-0.5sign(v i (t)), i=0, 1, 2,…,N

[0080] The leader dynamics model is as follows:

[0081] In the formula, x o (t), v0(t) represent the position and velocity of the leader respectively, x0(0) = [15, 15] T , v0 = [0.7, 0.8] T .

[0082] u0(t) is the control input of the leader, expressed as: u0(t)=0.5sin(5v0(t)))

[0083] For the i-th agent, the discrete time instant Determined by the following dynamic event trigger conditions

[0084]

[0085] In the formula, a=3, b=2, θ=0.8, ω=1, δ=0.3.

[0086] The topological structure of the UAV system is shown in the figure Figure 1 As shown, the position trajectory of the drone swarm in three-dimensional space is as follows Figure 2 As shown, Figure 3-4 is the trajectory diagram of the position state of the drone group in the two-dimensional plane, Figure 5-6 is the trajectory diagram of the UAV group speed state in the two-dimensional plane, Figure 7-8 is the trajectory diagram of the UAV group velocity error in the two-dimensional plane, Fig. 9 is the convergence trajectory diagram of the dynamic threshold, Fig.10 A graph of the event triggering moments for each agent.

[0087] References

[0088] [1]Xu Z,Liu H,Liu Y.Fixed-time leader-following flocking fornonlinear second-order multi-agent systems[J].IEEE access,2020,8:86262-86271。

Claims

1. A method for controlling a swarm of drones based on a fixed-time clustering algorithm, characterized in that: The following steps are involved: Based on the second-order multi-agent system theory, a dynamic model of the second-order UAV swarm is established; In order to reduce the number of communications between drone groups, dynamic threshold variables are introduced, and a suitable dynamic event trigger mechanism is designed for each drone; Based on the dynamic event triggering mechanism, a novel fixed-time control protocol is designed for a single UAV. With the help of Lyapunov stability analysis, sufficient conditions for drone swarms to cluster are obtained, and Zeno behavior is eliminated.

2. The method for controlling a swarm of unmanned aerial vehicles based on a fixed-time cluster algorithm according to claim 1 is characterized in that Based on the second-order multi-agent system theory, the dynamic model of the second-order UAV swarm is established. The specific steps are as follows: Consider a second-order UAV swarm with N followers and a leader. The dynamic model of the i-th UAV is as follows: In the formula, x i (t), v i (t) represents the position and velocity of the i-th UAV; u i (t) is the control input of each UAV; ζ i (t) is an unknown external disturbance and f(·) is a nonlinear function; the dynamic model of the leader is as follows: Where x0(t) and v0(t) represent the position and velocity of the leader respectively; u0(t) is the control input of the leader; and f0 is a nonlinear function.

3. According to the UAV swarm control method based on fixed time cluster algorithm in claim 2, in order to reduce the number of communications between UAV swarms, a dynamic threshold variable is introduced, and a suitable dynamic event trigger mechanism is designed for each UAV. The specific steps are as follows: For the i-th agent, the discrete time instant Determined by the following dynamic event trigger conditions In the formula, ∈ vi (t) = v i (t)-v0(t) and θ is a positive constant, η i (t) is an auxiliary variable described by: Where η i (0)>0, a, b, v>0 and 0<δ≤1.

4. According to the UAV swarm control method based on fixed-time cluster algorithm described in claim 3, a novel fixed-time control protocol is designed for a single UAV based on a dynamic event trigger mechanism, and the specific steps are as follows: In order to study the fixed-time leader-follower clustering of multi-agent systems, we designed a fixed-time distributed controller based on dynamic event triggering for each drone, which is expressed as follows: In the formula, In order to save communication resources and avoid continuous communication between drone groups, the i-th drone only communicates at discrete moments. communicate; α, β and κ>0; p, q are the ratios of two positive odd numbers, and p>1, 0 <q<1。 5. The method for controlling a swarm of unmanned aerial vehicles based on a fixed-time cluster algorithm according to claim 4 is characterized in that With the help of Lyapunov stability analysis, we can derive the necessary conditions for drone swarms to cluster and eliminate Zeno behavior. The specific steps are as follows: B001: Construct the following Lyapunov candidate function: W(t)=V1(t)+V2(t) In the formula, B002: Through analysis, we can get B003: Further In the formula, They are all measurable parts; B004: Next we can get B005: There exists a positive definite matrix H that satisfies H = R T R, furthermore B006: We have B007: Then B008: Further B009: Finally, it can be deduced B010: Similarly, we can deduce B011: We can conclude B012: The above formula can be further written as B013: We can easily get B014: Next B015: Then, there is B016: In the formula B017: Finally, we can infer that ∈ i (t) Fixed-time consistency can be achieved at the equilibrium point, and the upper bound of the fixed time is B018: Through the above analysis, we can conclude that Next, we can deduce B019: According to The definition of t≥T pre ; Due to the limited number of particles and the continuity of the velocity trajectory, when t<T pre , at a specific point in time, we can find some particles that satisfy therefore, is bounded; that is, In the formula, μ>0; then we can get B020: That means because B021: and B022: To complete the analysis, we assume that Therefore, then there is Furthermore, if we can find some agents that satisfy Next, when t<T pre ,right Points can be obtained B023: When t ≥ T pre hour, B024: Based on previous analysis We can further conclude that B025: It can be concluded B026: Based on the above analysis, in order to exclude Zeno behavior, firstly ||∈ i (t)|| Taking the derivative we can get B027: Next B028:Formula B029: Due to We can conclude B030: Then there is B031: In the formula B032: Then B033: It can be seen that in the trigger mechanism, the time interval between two consecutive trigger moments is The Zeno behavior has been ruled out, which shows that the dynamic time trigger mechanism we designed is reasonable, and the proof is complete.

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