A distributed cooperative tracking control method for UAV formation based on directed topology and packet loss compensation mechanism

Abstract

A distributed cooperative tracking control method for UAV formations based on directed topology and a packet loss compensation mechanism is proposed. This method incorporates graph theory into the cooperative control of UAV formations. A tracking error equation and cooperative control model with packet loss compensation are established under transmission packet loss, and a distributed control strategy is proposed. Furthermore, a stability condition is derived by combining model predictive control technology and theory. This stability condition is then used to solve a control sequence that achieves stable UAV formations, enabling the formation to achieve both packet loss compensation and consistent stability.

Description

Technical Field

[0001] The present application relates to the field of unmanned control, and in particular to a distributed collaborative tracking control method for a UAV formation based on directed topology and data packet loss compensation mechanism. Background Art

[0002] With the advancement of automatic control system technology, the research and application of drone formations are experiencing rapid growth. A drone formation is a computing system consisting of multiple drones operating in a single environment. Unlike a single quadcopter, a drone formation can more efficiently accomplish complex missions. Formation coordination is a key technology, requiring drones to form and maintain a pre-defined formation. In practical applications, the formation must also be able to cope with unexpected situations.

[0003] However, some existing UAV formation control technologies, such as the collaborative tracking control method for multi-UAV time-varying formations under uncertainty disclosed in CN115357048A and the collaborative adaptive tracking control method for flight formations based on a virtual leader disclosed in CN113220021A, fail to account for the limitations of the formation network. For example, packet loss can affect the performance of the UAV formation. Therefore, cooperative UAV formation tracking control under packet loss conditions is of great research significance. Summary of the Invention

[0004] In order to achieve cooperative tracking control of UAV formations under composite network constraints, this application provides a distributed cooperative tracking control method for UAV formations based on directed topology and packet loss compensation mechanism. The technical solution is as follows:

[0005] A distributed cooperative tracking control method for a UAV formation based on directed topology and packet loss compensation mechanism includes the following steps:

[0006] Step 1: All drones in the drone formation are divided into leaders and followers, and a directed topological network is used to maintain an interactive relationship between followers and leaders;

[0007] Step 2: Set the state equations of the leader and followers and the formation vector of the UAVs, and combine them with the adjacency matrix of the directed topological network to obtain the tracking error equation between the leader and followers;

[0008] Step 3: Establish a data packet loss compensation mechanism based on the packet loss situation in the UAV formation;

[0009] Step 4: Combined with the packet loss compensation mechanism, the control input equation of the follower UAV is established, and the tracking error equation with packet loss compensation is obtained;

[0010] Step 5: Use the improved model predictive control algorithm to compensate the UAV in the packet loss state;

[0011] Step 6: Establishing the state error system equation of the leader and follower in the UAV formation and constructing the cost function;

[0012] Step 7: Analyze the tracking error of each UAV to obtain the state space equation;

[0013] Step 8: Find the minimum value of the cost function. When the cost function approaches the minimum value, the UAV formation achieves consistent stability.

[0014] The beneficial effects achieved by the present invention are:

[0015] (1) Using a directed topological network to transform the UAV formation into a leader and followers and describe the interaction relationship between them, it is intuitive and accurate;

[0016] (2) Establish a packet loss compensation mechanism to compensate and improve the tracking error model, thereby improving the stability and consistency of UAV formation collaboration;

[0017] (3) In practical applications, by establishing the state error system equation and the corresponding cost function, intuitive and convenient parameter adjustments can be made, so that the formation can cope with some real-time and sudden unexpected situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of the flow of steps of the distributed collaborative tracking control method for a UAV formation described in an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0020] This embodiment provides a distributed cooperative tracking control method for UAV formation based on directed topology and data packet loss compensation mechanism. Figure 1 The specific steps are as follows:

[0021] All distributed drones in a drone formation are divided into leader drones and follower drones, and the information interaction relationship between distributed drones is generated using a directed topological network.

[0022] Optionally, establish separate system models for the UAV formation leader and N followers:

[0023] The leader system model is:

[0024] x0(k+1)=Ax0(k)+Br0(k)

[0025] y0(k)=Cx0(k)

[0026] The follower system model is:

[0027] x i (k+1)=Ax i (k)+Bu i (k)

[0028] y i (k) = Cx i (k)(i=1,2,...,N)

[0029] The formation vector of the i-th drone is:

[0030] f i (k+1)=Af i (k)+Br fi (k)

[0031] χ i (k+1)=Cf i (k)(i=1,2,...,N)

[0032] Among them, x0(k), r0(k), y0(k) are the state, external input, and output of the leader at time k respectively; x i (k),u i (k), y i (k) are the state, control input, and output of the i-th follower at time k; f i (k) χ i (k) are the formation vector, external input, and output of the i-th UAV at time k; A, B, and C are all dimensionally appropriate system matrices, and C =

[10] .

[0033] Optionally, an adjacency matrix can be used to express information interaction relationships. Specifically, all the distributed drones are set as nodes in a directed topological network using graph theory knowledge; the adjacency matrix D of the directed topological network is generated as follows: ij}∈R N×N (i,j=1,2,...,N), where i and j are adjacent drones. Element a ij =1 means that there is information interaction between the i-th UAV and the j-th UAV, and element a ij =0 means that there is no information interaction between the i-th UAV and the j-th UAV.

[0034] In an embodiment, for example, a 12= 0, it means that there is no information interaction between the first distributed UAV and the second distributed UAV. In addition, we can define a ii = 0, which means that the information interaction weight of each distributed UAV with itself is 0. It is worth mentioning that in this embodiment, the leader UAV is set to the 0th distributed UAV by default. ij It can be the information interaction weight between follower drones.

[0035] According to the state equations and information interaction relationship of the preset leader and follower drones, the control input equation u of each distributed drone is constructed i (k).

[0036] In implementation, considering that the UAV formation is to tend towards the desired stable state, when setting the control input of each distributed UAV controller, it is necessary to fully consider the relationship between the distributed UAV and other distributed UAVs. Therefore, after generating the information interaction relationship between the distributed UAVs in the UAV formation, the model of the preset leader UAV can be obtained. The model of this UAV is the consistency standard for tracking error that needs to be achieved in the UAV formation. Afterwards, for the i-th distributed UAV, the control input equation u of the i-th distributed UAV can be constructed by combining the information interaction relationship between the i-th distributed UAV and other distributed UAVs in the formation system (including the leader UAV and the follower UAV), as well as the internal state of the distributed UAV. i (k).

[0037] Optionally, based on the adjacency matrix D = {a ij}∈R N×N , the state equation of each leader and follower, constructing the tracking error equation e between the leader and follower i (k) = x i (k)-x0(k)-f i (k).

[0038] In order to deal with the packet loss problem in the formation, the Bernoulli process is introduced to describe the packet loss in the UAV formation. Specifically, θ(k) = 1 indicates successful transmission, while θ(k) = 0 indicates packet loss during the communication process. Therefore, a data packet loss compensation mechanism is established to obtain the packet loss compensation auxiliary vector Can be described as

[0039] Based on the tracking error equations of each of the leader and follower UAVs with packet loss compensation, the control input equations of each follower UAV are constructed:

[0040]

[0041] where u d(k) is the control input adjustment term, K1, K2, and K3 are all control gain matrices, K1 is time-varying, K2=I, K3=I, and I represents the unit matrix.

[0042] Based on the control input equation of the follower UAV, the simplified tracking error equation with packet loss compensation is obtained:

[0043]

[0044] and expand upon it The state error system equation of the leader and follower in the UAV formation is obtained:

[0045]

[0046] Among them, I N is the N-dimensional identity matrix, represents the Kronecker product,

[0047] The state error system equations of the leader and follower between the UAV formations are established and the cost function is constructed:

[0048]

[0049] Where E{g} represents the mathematical expectation, e(k+θ|k) represents the tracking error state with packet loss compensation predicted at time k+θ, and u d (k+θ|k) represents the control input adjustment term predicted at time k+θ. V and Y are positive definite weight matrices, and V=I 2N×2N , Y=I N×N If n approaches infinity, the cost function J(k) will tend to be uniformly stable.

[0050] According to the tracking error prediction vector with packet loss compensation, it is analyzed as follows:

[0051]

[0052]

[0053] …

[0054]

[0055] Define the augmentation vector Then the augmented vector It can be written as in, diag{g} represents a diagonal matrix,

[0056] Solve for the minimum value of the cost function, that is The constraints are in are the upper and lower bounds of the tracking error vector with packet loss compensation, and are the upper and lower bounds of the control input adjustment term, and The dimensionally positive definite weighted matrices are Represents a quadratic form consisting of the matrix X, such as And transform it into a quadratic programming problem, The constraints are Where Q = 2(G T VG+Y)、 If the cost function J(k) approaches a minimum value, the system satisfies the Lyapunov stability theory, which further indicates that the UAV formation can achieve consistent stability.

[0057] In implementation, a cost function can be introduced for each distributed UAV And solve its minimum value so that the motion state of each distributed UAV in the UAV formation remains stable under the constraints of the composite network, thereby ensuring the stability of the motion state of the UAV formation and meeting the stability performance requirements of the UAV formation.

[0058] Those skilled in the art will understand that all or part of the steps to implement the above embodiments may be accomplished by hardware, or by a program to instruct the relevant hardware, and the program may be stored in a computer-readable storage medium, which may be a read-only memory, a disk, or an optical disk, etc.

[0059] The above are all preferred embodiments of the present application and are not intended to limit the scope of protection of this application. Unless otherwise stated, any feature disclosed in this specification (including the abstract and drawings) may be replaced by other equivalent or similar features. In other words, unless otherwise stated, each feature is merely an example of a series of equivalent or similar features.

[0060] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed in the present invention should be included in the protection scope recorded in the claims.

Claims

1. A distributed cooperative tracking control method for UAV formations based on directed topology and packet loss compensation mechanism, characterized by: The method comprises the following steps: Step 1: All drones in the drone formation are divided into leaders and followers, and a directed topological network is used to maintain an interactive relationship between followers and leaders; Step 2: Set the state equations of the leader and followers and the formation vector of the UAVs, and combine them with the adjacency matrix of the directed topological network to obtain the tracking error equation between the leader and followers; Step 3: Establish a data packet loss compensation mechanism based on the packet loss situation in the UAV formation; Step 4: Combined with the packet loss compensation mechanism, the control input equation of the follower UAV is established, and the tracking error equation with packet loss compensation is obtained; Step 5: Use the improved model predictive control algorithm to compensate the UAV in the packet loss state; In step 5, the tracking error equation with packet loss compensation is obtained: Based on the state x0(k) of each leader, the follower state x i (k) Construct the tracking error equation e between the leader and the follower i (k), and expand upon it The state error system equation of the leader and follower in the UAV formation is obtained: Among them, I N is the N-dimensional identity matrix, represents the Kronecker product, Step 6: Establishing the state error system equation of the leader and follower in the UAV formation and constructing the cost function; In step 6, the state error system equation of the leader and follower between the UAV formation is established and the cost function is constructed: Among them, E{·} represents the mathematical expectation, Indicates the prediction at time k The tracking error state with packet loss compensation is always included. Indicates the prediction at time k The control input adjustment term at time; V and Y are positive definite weight matrices, and V = I 2N×2N , Y=I N×N ; If n tends to infinity, the cost function J(k) will tend to be uniformly stable; Step 7: Analyze the tracking error of each UAV to obtain the state space equation; In step 7, the tracking error prediction vector with packet loss compensation is analyzed as follows: … Define the augmentation vector: Then the augmented vector Written as follows: in, diag{·} represents a diagonal matrix, Step 8: Find the minimum value of the cost function. When the cost function approaches the minimum value, the UAV formation achieves consistent stability.

2. The distributed cooperative tracking control method for a UAV formation based on directed topology and packet loss compensation mechanism according to claim 1, characterized in that: In step 1, the UAV formation is defined as a directed topological network using graph theory knowledge, and the leader and followers exchange information through the directed topological network. Suppose there are N UAVs in the formation, and each UAV in the UAV formation is regarded as a node, and the adjacency matrix D of the directed topological network is generated. ij }∈R N×N (i,j=1,2,...,N), where i and j are adjacent drones, element a ij =1 means that there is information interaction between the i-th UAV and the j-th UAV, and element a ij =0 means that there is no information interaction between the i-th UAV and the j-th UAV.

3. The distributed cooperative tracking control method for a UAV formation based on directed topology and packet loss compensation mechanism according to claim 1, characterized in that: In step 2, the leader system model is: x0(k+1)=Ax0(k)+Br0(k) y0(k)=Cx0(k) The follower system model is: x i (k+1)=Ax i (k)+Bu i (k) y i (k)=Cx i (k)(i=1,2,...,N) The formation vector of the i-th drone is: χ i (k+1)=Cf i (k)(i=1,2,...,N) Among them, x0(k), r0(k), y0(k) are the state, external input, and output of the leader at time k respectively; x i (k),u i (k), y i (k) are the state, control input, and output of the i-th follower at time k; f i (k) χ i (k) are the formation vector, external input, and output of the i-th UAV at time k; A, B, and C are all dimensionally appropriate system matrices, and C = [1 0]; Based on the adjacency matrix D={a ij }∈R N×N , the state equations of each leader and follower and the formation vector, construct the tracking error equation e between the leader and the follower i (k) = x i (k0-x0(k)-f i (k).

4. The distributed cooperative tracking control method for a UAV formation based on directed topology and packet loss compensation mechanism according to claim 1, characterized in that: In step 3, in order to deal with the packet loss problem in the formation, the Bernoulli process is introduced to describe the packet loss in the UAV formation; θ(k) = 1 indicates successful transmission, while θ(k) = 0 indicates packet loss during the communication process; a data packet loss compensation mechanism is established to obtain the packet loss compensation auxiliary vector Described as 5. The distributed cooperative tracking control method for a UAV formation based on directed topology and packet loss compensation mechanism according to claim 1, characterized in that: In step 4, based on the tracking error equations of each leader and follower UAV, the control input equation of each follower UAV is constructed: where u d (k) is the control input adjustment term, K1, K2, and K3 are all control gain matrices, K1 is time-varying, K2=I, and K3=I.

6. The distributed cooperative tracking control method for a UAV formation based on directed topology and packet loss compensation mechanism according to claim 1, characterized in that: In step 8, the minimum value of the cost function is solved, that is: The condition is in are the upper and lower bounds of the tracking error vector with packet loss compensation, and are the upper and lower bounds of the control input adjustment term, and The dimensionally positive definite weighted matrices are Represents a quadratic form consisting of the matrix X, such as And solving the minimum value of the cost function is transformed into a quadratic programming problem, The condition is Where Q = 2(G T VG+Y)、 If the cost function J(k) approaches a minimum value, the system satisfies the Lyapunov stability theory, indicating that the UAV formation can achieve consistent stability.

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