An unmanned aerial vehicle swarm control method based on a fixed-time cluster algorithm

Abstract

The application discloses a kind of unmanned aerial vehicle group control method based on fixed time cluster algorithm.The method is first based on second-order multi-agent system theory, establishes the dynamics model of second-order unmanned aerial vehicle group.Then, to reduce the communication times between unmanned aerial vehicle group, introduce dynamic threshold variable, design suitable dynamic event trigger mechanism for each unmanned aerial vehicle.Then, based on dynamic event trigger mechanism, design a novel fixed time control protocol for single unmanned aerial vehicle.Finally, with the aid of Lyapunov stability analysis, the sufficient condition that unmanned aerial vehicle group can cluster is obtained, and Zeno behavior is excluded.

Description

Technical Field

[0001] This invention relates to a fixed-time control method, specifically to a novel cluster algorithm based on a drone swarm system. Background Technology

[0002] With the rapid development of unmanned aerial vehicle (UAV) technology, UAV swarm control has become a research hotspot in modern intelligent systems and automation. UAV swarms, through the collaborative efforts of multiple UAVs, can achieve more complex and efficient mission execution in various fields such as military, environmental monitoring, and logistics delivery. However, due to the large scale of UAV swarms and limited communication between individuals, achieving efficient collaborative control faces many challenges. Traditional swarm control methods typically rely on centralized control strategies or self-organizing mechanisms, but these methods may not meet the requirements of real-time performance and robustness in dynamic environments. Especially when mission time is limited, how to complete swarm control tasks within a fixed time becomes a critical issue. Therefore, UAV swarm control methods based on fixed-time swarm algorithms have emerged, aiming to improve the collaborative efficiency and response speed of UAV swarms under complex tasks.

[0003] In UAV swarm control, traditional swarm algorithms, such as consensus-based control methods and game-theoretic distributed control methods, can address the coordination problem among UAVs to some extent. However, these algorithms typically assume ideal communication conditions and environmental stability, making them ill-equipped to handle real-world issues like communication delays, individual malfunctions, and environmental changes. Particularly in large-scale UAV swarms, the time complexity and computational resource requirements of the algorithms increase significantly, impacting the system's real-time performance and stability. Fixed-time swarm algorithms, by introducing a fixed-time convergence mechanism, ensure that all UAVs reach the desired swarm state within a predetermined time, regardless of initial state changes. This approach not only effectively reduces algorithm complexity but also enhances the system's robustness and adaptability in complex environments.

[0004] Fixed-time convergence control strategies offer significant advantages in UAV swarm control. This method, by designing appropriate control laws, ensures system convergence within a pre-defined finite time, overcoming the limitation of traditional control methods where convergence time depends on initial conditions. Specifically, fixed-time control algorithms can achieve rapid consensus, formation control, and obstacle avoidance for UAV swarms without being affected by initial states. Furthermore, fixed-time swarm algorithms exhibit strong robustness, capable of handling challenges such as communication delays, node failures, and environmental uncertainties that UAVs may encounter during mission execution. Therefore, UAV swarm control methods based on fixed-time swarm algorithms have 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 swarming.

[0006] The specific technical solution of this invention is as follows: A method for controlling unmanned aerial vehicle (UAV) swarms based on a fixed-time clustering algorithm, comprising the following steps:

[0007] Based on the theory of second-order multi-agent systems, a dynamic model of a 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 drone swarm with N followers and one leader. The dynamics model of the i-th drone is shown in the following steps:

[0010]

[0011] Where, x i (t), v i (t) represents the position and velocity of the i-th drone, respectively. i (t) is the control input for 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:

[0012]

[0013] In the formula, x0(t) and v0(t) represent the leader's position and velocity, respectively. u0(t) is the leader's control input, and f0 is a nonlinear function.

[0014] Furthermore, to reduce the number of communications between drone swarms, a dynamic threshold variable is introduced, and a suitable dynamic event triggering mechanism is designed for each drone. The specific steps are as follows:

[0015] For the i-th agent, the discrete time step is... Determined by the following dynamic event triggering conditions

[0016]

[0017] In the formula, ε vi (t)=v i (t)-v0(t),

[0018]

[0019] θ is a positive constant, η i(t) is an auxiliary variable, described as follows:

[0020]

[0021] In the formula, η i (0)>0, a, b, v>0 and 0<δ≤1.

[0022] Furthermore, based on a dynamic event triggering mechanism, a novel fixed-time control protocol is designed for a single UAV. The specific steps are as follows:

[0023] To study fixed-time leader-follower swarms in multi-agent systems, we designed a fixed-time distributed controller for each UAV based on dynamic event triggering, with the following expression:

[0024]

[0025] In the formula, To conserve communication resources and avoid continuous communication between drone swarms, the i-th drone only communicates at discrete times. To communicate. α, β, and κ > 0; p and q are the ratio of two positive odd numbers, and p > 1, 0. <q<1。

[0026] Next, using Lyapunov stability analysis, the necessary conditions for the drone swarm to swarm and the exclusion of Zeno behavior are derived. The specific steps are as follows:

[0027] C001: Construct the following Lyapunov candidate functions:

[0028] W(t) = V1(t) + V2(t)

[0029] In the formula

[0030] C002: We can obtain

[0031]

[0032] C003: Further details are available.

[0033]

[0034] In the formula, All of them are measurable parts.

[0035] C004: Next, we can obtain...

[0036]

[0037] C005: There exists a positive definite matrix H satisfying H = R T R, further...

[0038]

[0039] C006: We have

[0040]

[0041] C007: Then

[0042]

[0043] C008: Further details

[0044]

[0045] C009: Finally, it can be deduced that...

[0046]

[0047] C010: Similarly, we can deduce

[0048]

[0049] C011: We can conclude that...

[0050]

[0051] C012: The above formula can be further written as

[0052]

[0053] C013: We can easily obtain

[0054]

[0055] C014: Next

[0056]

[0057] C015: Then, there is

[0058]

[0059] C016: In the formula

[0060]

[0061]

[0062] C017: Finally, it can be deduced that ∈ i (t) can achieve fixed-time consistency at the equilibrium point, and the upper bound of the fixed time is .

[0063]

[0064] C018: Based on the above analysis, we can conclude that when Next, we can deduce

[0065]

[0066] C019: According to The definition can be known Because the number of particles is finite and their trajectories are continuous, when t < T pre At a specific point in time, we can find certain particles that satisfy... therefore, It is bounded. That is to say... In the formula, μ>0. Then we can derive...

[0067]

[0068] C020: That means because

[0069]

[0070] C021: and

[0071]

[0072] C022: To complete the analysis, we assume Therefore, thereafter Furthermore, if we can find certain agents that satisfy certain conditions at certain specific points in time... Therefore, the above assumption holds true. Next, when t < T pre ,right Points can be obtained

[0073]

[0074] C023: When t≥T pre hour,

[0075]

[0076] C024: Based on previous analysis We can further conclude

[0077]

[0078] C025: A conclusion can be drawn.

[0079]

[0080] C026: Based on the above analysis, in order to exclude Zeno behavior, we first need to consider ||∈ i Taking the derivative of (t)||, we get

[0081]

[0082] C027: Next

[0083]

[0084] C028: In the formula

[0085]

[0086]

[0087]

[0088] C029: Due to We can conclude

[0089]

[0090] C030: Then there is

[0091]

[0092] C031: In the formula

[0093]

[0094]

[0095] C032: Then

[0096]

[0097] C033: Therefore, in the triggering mechanism, the time interval between two consecutive triggering moments is... Zeno behavior has been ruled out. This demonstrates that our designed dynamic time-triggered mechanism is reasonable, and the proof is complete. Attached Figure Description

[0098] Figure 1 A topology diagram of an unmanned aerial vehicle (UAV) swarm system;

[0099] Figure 2 A three-dimensional position trajectory diagram of a swarm of drones;

[0100] Figure 3-4 The trajectory of the drone swarm's position status on a two-dimensional plane;

[0101] Figure 5-6 The trajectory of the drone swarm's velocity state in a two-dimensional plane;

[0102] Figure 7-8 The trajectory of the speed error of the drone swarm in a two-dimensional plane;

[0103] Figure 9 The convergence trajectory diagram for the dynamic threshold;

[0104] Figure 10 A timeline of event triggers for each agent;

[0105] Figure 11 Figures are attached to the abstract; Detailed Implementation

[0106] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0107] A method for controlling unmanned aerial vehicle (UAV) swarms based on a fixed-time clustering algorithm includes the following steps:

[0108] Step 1: Set the various system parameters;

[0109] Step 2: Set up the topology for drone swarm communication;

[0110] Step 3: Set up the event triggering mechanism;

[0111] Step 4: Set up a distributed control protocol based on an event-triggered mechanism;

[0112] Step 5: Set the initial position and speed of a single drone;

[0113] Step 6: Set the system's external inputs and nonlinear terms;

[0114] Step 7: Set up the leader's control inputs;

[0115] An embodiment of the present invention is described below:

[0116] Consider a second-order drone swarm with N followers and one leader. The dynamics model of the i-th drone is shown in the following steps:

[0117]

[0118] Where, x i (t), v i (t) represents the position and velocity of the i-th drone, respectively. The initial state is x1(0) = [8, 18]. Tx3(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 .

[0119] u i (t) represents the control input for each UAV:

[0120]

[0121] In the formula, α=6, β=2.8, β=4.6, p=7 / 5, q=3 / 5.

[0122] ζ i (t) is an unknown external disturbance and f(·) is a nonlinear function, expressed as:

[0123] ζ i (t)=1.55sin(v i (t))

[0124] f(x i (t), v i (t), t) = 0.5cos(1.5v) i (t))-0.5sign(v i (t)), i=0, 1, 2,…,N

[0125] The dynamic model of the leader is as follows:

[0126]

[0127] In the formula, x o x0(t) and v0(t) represent the leader's position and velocity, respectively, and x0(0) = [15, 15]. T v0 = [0.7, 0.8] T .

[0128] u0(t) is the leader's control input, expressed as:

[0129] u0(t)=0.5sin(5v0(t)))

[0130] For the i-th agent, the discrete time step is... Determined by the following dynamic event triggering conditions

[0131]

[0132]

[0133] In the formula, a=3, b=2, θ=0.8, ω=1, δ=0.3.

[0134] The topology diagram of the unmanned aerial vehicle system is as follows: 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 This is a trajectory diagram of the drone swarm's position and status on a two-dimensional plane. Figure 5-6 The image shows the trajectory of the drone swarm's velocity state in a two-dimensional plane. Figure 7-8 The image shows the trajectory of the drone swarm's velocity error in a two-dimensional plane. Figure 9 This is a convergence trajectory diagram for the dynamic threshold. Figure 10 A timeline for event triggering for each agent.

[0135] References

[0136] [1] Xu Z, Liu H, Liu Y. Fixed-time leader-following flocking for nonlinear second-order multi-agent systems[J]. IEEE access, 2020, 8: 86262-86271.

Claims

1. A method for controlling unmanned aerial vehicle (UAV) swarms based on a fixed-time clustering algorithm, characterized in that, Includes the following steps: Step 1: Based on the theory of second-order multi-agent systems, establish a dynamic model of a second-order UAV swarm, as follows: Consider a second-order drone swarm with N followers and one leader. The dynamics model of the i-th drone is as follows: Where, x i (t), v i (t) represents the position and velocity of the i-th drone, respectively, u i (t) is the control input for each UAV, ζ i Given that (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 leader's position and velocity, respectively, u0(t) is the leader's control input, and f(·) is a nonlinear function; Step 2: To reduce the number of communications between drone swarms, a dynamic threshold variable is introduced, and a suitable dynamic event triggering mechanism is designed for each drone, as follows: For the i-th agent, the discrete time step is... Determined by the following dynamic event triggering conditions Where, ε vi (t)=v i (t)-v0(t), θ is a positive constant, η i (t) is an auxiliary variable, described as follows: Where, η i (0) > 0, a, b, v > 0 and 0 < δ ≤ 1; Step 3: Based on the dynamic event triggering mechanism, design a novel fixed-time control protocol for a single UAV, as follows: in, To conserve communication resources and avoid continuous communication between drone swarms, the i-th drone only communicates at discrete times. For communication, α, β, and κ > 0; p and q are the ratio of two positive odd numbers, and p > 1, 0 < q < 1.

Images