A leader-unknown time-varying heterogeneous formation tracking method and related device

Abstract

The application discloses a leader-unknown time-varying heterogeneous formation tracking method and a related device, relates to the field of cluster formation tracking control, and comprises the following steps: determining all adjacent followers corresponding to a target follower according to a communication topology relationship diagram of a time-varying heterogeneous formation, and acquiring a leader state information estimation value and a leader output information estimation value of each adjacent follower; then estimating the leader state information of the target follower at the next moment by using a leader state information and a system matrix distributed observer, and then estimating the leader output information of the target follower at the current moment by using a leader output information and an output matrix distributed observer; finally, a distributed formation tracking controller is used for calculation to obtain a control input vector of the target follower at the current moment. The application can track and control the leader-unknown time-varying heterogeneous formation without a persistent excitation condition.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of cluster formation tracking control, in particular to a time-varying heterogeneous formation tracking method with unknown leader and related device. BACKGROUND

[0002] In recent decades, the distributed cooperative control of multi-agent formation has been a hot topic in the field of control, and has been widely applied in scientific research and engineering fields. Among them, how to perform time-varying formation control and construct an effective controller is a key problem widely studied and discussed in the field of multi-agent system cooperative control.

[0003] However, most of the existing researches on multi-agent formation tracking control all assume that all follower agents (followers) know the dynamic information of the leader system (leader), such as the system matrix in the case of linear dynamics. Although this assumption is also common in the study of leader-follower consensus problems, this requirement means that there is direct communication between each follower agent and the leader agent, which contradicts the distributed nature of multi-agent formation. In many practical application scenarios, the target trajectory tracked by the follower agent is generated by a non-cooperative target, that is, no follower agent can fully understand the dynamic information of the tracking target. For example, in a certain unmanned aerial vehicle-unmanned vehicle formation tracking application scenario, the tracking unmanned aerial vehicle cannot directly obtain the dynamic model of the target unmanned vehicle, as well as the speed and acceleration information of the unmanned vehicle. Therefore, the problem of multi-agent formation tracking control with unknown leader has become an important and challenging problem that has received more and more attention in recent years; before designing a formation tracking controller for such a system, a corresponding parameter observer needs to be designed to estimate the dynamic information of the leader.

[0004] However, many existing parameter observer designs require a persistent excitation (PE) condition, which requires that the amount of signals from the leader state be sufficient, but it may be difficult to ensure and verify the PE condition in advance when dealing with uncertain parameter estimation problems. Some researches have successfully relaxed the requirement for the traditional persistent excitation condition, but they are mainly used for estimating the dynamic information in a single adaptive formation or a homogeneous multi-agent formation, and it is difficult to extend these techniques to a heterogeneous multi-agent formation with an uncertain leader, because it is not feasible to ensure that all followers can directly obtain the leader information (such as input or state) in a heterogeneous multi-agent formation. Therefore, how to design a formation controller without the persistent excitation (PE) condition in a heterogeneous cluster formation with an uncertain leader is a challenging problem at present. SUMMARY

[0005] The application aims to provide a leader-unknown time-varying heterogeneous formation tracking method and related device, which can track and control the leader-unknown time-varying heterogeneous formation without persistent excitation (PE) condition.

[0006] To achieve the above-mentioned purpose, the application provides the following solutions.

[0007] In a first aspect, the application provides a leader-unknown time-varying heterogeneous formation tracking method, comprising:

[0008] According to a communication topology graph of the time-varying heterogeneous formation, all adjacent followers corresponding to a target follower are determined; the communication topology graph comprises nodes and edges; the nodes represent followers or leaders in the time-varying heterogeneous formation; the edges represent communication relationships between followers and leaders or between followers in the time-varying heterogeneous formation; the adjacent followers are followers in the time-varying heterogeneous formation that have communication relationships with the target follower; the target follower is a follower that does not have a communication relationship with a leader in the time-varying heterogeneous formation; the adjacent followers are followers that have a communication relationship with the leader or followers that do not have a communication relationship with the leader.

[0009] Leader state information estimation values and leader output information estimation values of each adjacent follower at a current time are obtained; when the adjacent follower is a follower that has a communication relationship with the leader, the leader state information estimation value and the leader output information estimation value of the adjacent follower are obtained directly from the leader; when the adjacent follower is a follower that does not have a communication relationship with the leader, the leader state information estimation value and the leader output information estimation value of the adjacent follower are values obtained by estimating the leader state information and the leader output information of the leader by the adjacent follower.

[0010] According to the leader state information estimation value of each adjacent follower at the current time, the leader state information estimation value of the target follower at the current time, and the leader system matrix estimation value, a leader state information and system matrix distributed observer is used to estimate the first-order derivative of the leader state information and the leader system matrix of the target follower, and the leader state information estimation value and the leader system matrix estimation value of the target follower at the next time are calculated.

[0011] According to the leader output information estimation value of each adjacent follower at the current moment, the leader output matrix estimation value of the target follower at the current moment and the leader state information estimation value of the target follower at the next moment, the leader output information and the leader output matrix first derivative of the target follower are estimated by using the leader output information and output matrix distributed observer, the leader output information estimation value of the target follower at the current moment and the leader output matrix first derivative estimation value are obtained, and the leader output matrix estimation value of the target follower at the next moment is calculated.

[0012] According to the leader output information estimation value of the target follower at the current moment and the time-varying formation vector of the target follower at the current moment, the control input vector of the target follower at the current moment is obtained by using the distributed formation tracking controller.

[0013] In a second aspect, the present application provides a computer device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor executes the computer program to realize the leader-unknown time-varying heterogeneous formation tracking method in the first aspect.

[0014] In a third aspect, the present application provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the leader-unknown time-varying heterogeneous formation tracking method in the first aspect.

[0015] In a fourth aspect, the present application provides a computer program product, which comprises a computer program, and the computer program is executed by a processor to realize the leader-unknown time-varying heterogeneous formation tracking method in the first aspect.

[0016] According to the specific embodiments provided by the present application, the present application has the following technical effects:

[0017] The application provides a leader-unknown time-varying heterogeneous formation tracking method and a related device. According to a communication topology relationship diagram of a time-varying heterogeneous formation, all adjacent followers corresponding to a target follower are determined. Leader state information estimation values and leader output information estimation values of each adjacent follower at a current time are obtained. According to the leader state information estimation values of each adjacent follower at the current time, a leader state information estimation value of the target follower and a leader system matrix estimation value, first-order derivatives of leader state information and a leader system matrix of the target follower are estimated by using a leader state information and system matrix distributed observer, and the leader state information estimation value of the target follower at the next time and the leader system matrix estimation value are calculated. Then, according to the leader output information estimation values of each adjacent follower at the current time, a leader output matrix estimation value of the target follower at the current time and the leader state information estimation value of the target follower at the next time, first-order derivatives of leader output information and a leader output matrix of the target follower are estimated by using a leader output information and output matrix distributed observer, the leader output information estimation value of the target follower at the current time and the first-order derivative estimation value of the leader output matrix are obtained, and the leader output matrix estimation value of the target follower at the next time is calculated. Finally, according to the leader output information estimation value of the target follower at the current time and a time-varying formation vector of the target follower at the current time, a control input vector of the target follower at the current time is obtained by using a distributed formation tracking controller. The leader state information and system matrix distributed observer and the leader output information and output matrix distributed observer are used to realize tracking control of the leader-unknown time-varying heterogeneous formation without persistent excitation (PE), reduce the amount of obtained leader information, save communication resources and improve tracking control efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative effort.

[0019] Figure 1 A flowchart of a leader-unknown time-varying heterogeneous formation tracking method provided by an embodiment of the present application is shown in the figure.

[0020] Figure 2 A flowchart of a leader-unknown time-varying heterogeneous formation tracking method provided by another embodiment of the present application is shown in the figure.

[0021] Figure 3A functional module schematic diagram of a time-varying heterogeneous formation tracking device with unknown leader provided by an embodiment of the present application;

[0022] Figure 4 A communication topology relationship schematic diagram of a time-varying heterogeneous formation provided by an embodiment of the present application;

[0023] Figure 5 A leader state vector estimation error change curve of a follower provided by an embodiment of the present application; Figure 5 (a) of FIG. 6 shows a leader state vector estimation error change curve of a follower corresponding to a numerical simulation; Figure 5 (b) of FIG. 6 shows a leader state vector estimation error change curve of a follower corresponding to a physical experiment;

[0024] Figure 6 A leader system matrix E estimation error change curve of a follower provided by an embodiment of the present application; Figure 6 (a) of FIG. 7 shows a leader system matrix E estimation error change curve of a follower corresponding to a numerical simulation; Figure 6 (b) of FIG. 7 shows a leader system matrix E estimation error change curve of a follower corresponding to a physical experiment;

[0025] Figure 7 A formation tracking error change curve of a follower provided by an embodiment of the present application; Figure 7 (a) of FIG. 8 shows a formation tracking error change curve of a follower corresponding to a numerical simulation; Figure 7 (b) of FIG. 8 shows a formation tracking error change curve of a follower corresponding to a physical experiment;

[0026] Figure 8 A position diagram of a follower and a leader at different time provided by an embodiment of the present application; Figure 8 (a) of FIG. 9 shows a position diagram of a follower and a leader at different time corresponding to a numerical simulation; Figure 8 (b) of FIG. 9 shows a position diagram of a follower and a leader at different time corresponding to a physical experiment;

[0027] Figure 9 A structural schematic diagram of a computer device provided by an embodiment of the present application. DETAILED DESCRIPTION

[0028] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0029] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0030] In one exemplary embodiment, such as Figure 1 As shown, this application provides a time-varying structural grouping tracking method with an unknown leader, including steps 101 to 105. Wherein:

[0031] Step 101: Based on the communication topology graph of the time-varying structural formation, determine all adjacent followers corresponding to the target follower; the communication topology graph includes nodes and edges; the nodes represent followers or leaders in the time-varying structural formation; the edges represent the communication relationship between followers and leaders or between followers in the time-varying structural formation; the adjacent followers are followers in the time-varying structural formation that have a communication relationship with the target follower; the target follower is a follower that does not have a communication relationship with the leader in the time-varying structural formation; the adjacent followers are followers that have a communication relationship with the leader or followers that do not have a communication relationship with the leader.

[0032] In this application, the communication topology in the time-varying structural array cluster is abstracted into an undirected graph, and the corresponding Laplace matrix L and other related quantization variables are calculated.

[0033] The time-varying structural formation includes multiple followers and one leader. The leader's system matrix E and output matrix F are unknown to all followers. Some followers can directly obtain the leader's state information (also known as state vector information), while the remaining followers cannot directly obtain the leader's state information.

[0034] Let the follower cluster consisting of N followers of the time-varying structure be denoted as The topology of communication between followers can be described as a graph. Where ν = {ν1,ν2,…,ν} N} represents a set of nodes. It is an edge set. It has a nonnegative element a ij The symmetric adjacency matrix. For followers i and j, You can use ν in ν i and ν j To refer to. If from ν i To ν j If there exists an edge between follower i and follower j, meaning there is a communication relationship between them, then a ij =1; conversely, a ij =0. Let a ii=0, i∈{1,2,…,N}. To describe the neighbor relationships in a heterogeneous cluster system, a graph is defined. Laplace matrix in It is the in-degree matrix.

[0035] In the heterogeneous formation, there is also a leader, and the topology of communication between the entire heterogeneous formation is described as a graph. The leader is node 0. If node 0 (the leader) and ν i If there is an edge between (follower i), then a 0i =1, conversely, a 0i =0. Hypothetical diagram Let L be the corresponding Laplace matrix. Then, assume that L has the following form: Where submatrix

[0036] Step 102: Obtain the estimated leader state information and estimated leader output information of each adjacent follower at the current time; when the adjacent follower is a follower with a communication relationship with the leader, the estimated leader state information and estimated leader output information of the adjacent follower are obtained directly from the leader; when the adjacent follower is a follower without a communication relationship with the leader, the estimated leader state information and estimated leader output information of the adjacent follower are respectively values ​​obtained by the adjacent follower from estimating the leader state information and the leader output information.

[0037] Step 103: Based on the estimated leader state information of each adjacent follower at the current time, the estimated leader state information of the target follower at the current time, and the estimated leader system matrix, the first derivative of the leader state information and the leader system matrix of the target follower is estimated using the distributed observer of leader state information and system matrix, and the estimated leader state information and the estimated leader system matrix of the target follower at the next time time are calculated.

[0038] Specifically, using the leader's state information and the distributed observer of the system matrix, the first derivative estimates of the leader's state information and the first derivative estimates of the leader's system matrix of the target follower are obtained (at the current time). Then, the estimated values ​​of the leader's state information and the leader's system matrix of the target follower at the next time step are calculated. Of course, the estimated values ​​of the leader's state information and the leader's system matrix of the target follower at the current time step are determined based on the first derivative estimates of the leader's state information and the leader's system matrix of the target follower at the previous time step.

[0039] For the initial time, the leader state information estimation value and the leader system matrix estimation value of the target follower and each neighboring follower can be arbitrarily assigned.

[0040] Step 104: according to the leader output information estimation value of each neighboring follower at the current time, the leader output matrix estimation value of the target follower at the current time and the leader state information estimation value of the target follower at the next time, the first order derivatives of the leader output information and the leader output matrix of the target follower are estimated by using the leader output information and output matrix distributed observer, the leader output information estimation value of the target follower at the current time and the first order derivative estimation value of the leader output matrix are obtained, and the leader output matrix estimation value of the target follower at the next time is calculated.

[0041] The leader output matrix estimation value of the target follower at the current time is determined according to the first order derivative of the leader output matrix of the target follower at the last time.

[0042] For the initial time, the leader output information estimation value and the leader output matrix estimation value of the target follower and each neighboring follower can be arbitrarily assigned, such as being assigned as 0.

[0043] Step 105: according to the leader output information estimation value of the target follower at the current time and the time-varying formation vector of the target follower at the current time, the control input vector of the target follower at the current time is calculated by using the distributed formation tracking controller.

[0044] As an optional implementation, the mathematical model of the leader state information and system matrix distributed observer is represented as:

[0045]

[0046] Wherein, θ i (t) represents the estimation value of θ of the follower i at t time, θ is the vector form of the leader system matrix E, The vec(·) operation is defined as: for any matrix Then The col(·) operation is defined as: for any matrix represents the estimation value of the leader state vector v0(t) of the follower i at t time, ξ i1 (t), ξ i2 (t),..., ξ in (t) are n components of the estimation value of the leader state vector v o (t) respectively; and are θ i(t) and ξ i (t) is the first order differential of time t; I m denotes a unit matrix of dimension m x m, denotes the tensor product operation; μ1>0 is a constant in the observer; N represents the number of followers in the time-varying formation; and are state variables of the second group of filters, respectively.

[0047] a ij denotes whether follower i and follower j have a communication relationship, when follower i and follower j have a communication relationship, a ij = 1, when follower i and follower j do not have a communication relationship, a ij = 0; a i0 denotes whether follower i and leader 0 have a communication relationship, when follower i and leader 0 have a communication relationship, a i0 = 1, when follower i and leader 0 do not have a communication relationship, a i0 = 0. That is, a ij , a i0 respectively, the communication topology graph corresponding to the submatrix of the Laplacian matrix L in the item, In this application, it is considered that the cluster communication topology graph is undirected, that is, a ij = a ji .

[0048] η i (t) is defined as:

[0049] ξ j (t) represents the estimation value of follower j to the leader state vector v0(t) at time t.

[0050] It should be noted that in this application, the leader state information, the leader output information, the leader system matrix and the leader output matrix satisfy the following relationship:

[0051]

[0052] wherein, is a bounded vector, representing the leader state vector (i.e. the leader state information); represents the leader output vector (i.e. the leader output information), is the leader system matrix, is the leader output matrix. The equation set is the dynamic model established by the present application for the leader.

[0053] As an optional implementation, the mathematical model of the second set of filters is expressed as follows:

[0054]

[0055] in, and These are the first-order differentials of D(t) and P(t), respectively; and These are the state variables of the first group of filters.

[0056] The mathematical model of the first set of filters is expressed as follows:

[0057]

[0058] in, k > 0 is a scalar gain used to ensure filter stability; Let v0(t) be the derivative. and These are the first-order differentials of G(t) and p(t), respectively; due to the derivative information of the leader's state vector. Unknown, p(t) is determined by p(t) = v0(t) - e -kt v0(0)-kf(t) is used for calculation, where

[0059] As an optional implementation, the mathematical model of the leader output information and output matrix distributed observer is expressed as follows:

[0060]

[0061] in, Let z0(t) be the estimate of the leader's output information z0(t) by follower i at time t. This represents the estimate of the leader's output matrix F by follower i at time t; for The first differential; a ik Indicates whether follower i and follower k have a communication relationship (a ik ,a i0 These are the communication topology diagrams. The Laplace matrix L neutron matrix (Items in the middle) Let z0(t) be the estimate of the leader's output information z0(t) by follower k at time t; z0(t) and F satisfy... It is the first-order differential of z0(t).

[0062] As an optional implementation, the mathematical model of the distributed formation tracking controller is expressed as follows:

[0063]

[0064] in, Ψ represents the control input vector of follower i at time t; i (·) represents the regression matrix. and Let i represent the position and velocity of follower i at time t, respectively. for The first derivative with respect to time t, Let h represent the estimate of the leader's output information z0(t) by follower i at time t. i (t) represents the time-varying formation vector of follower i at time t. for h i (t) is the first derivative of (t) with respect to time t; for The first derivative with respect to time t; For the parameter vector; k s Normal value; s i (t) is the sliding vector.

[0065] In this embodiment, the time-varying formation vector h(t) = col(h1(t),h2(t),…,h N (t) is used to represent the desired time-varying formation, h i (t) is the i-th variable in h(t).

[0066] In another exemplary embodiment of this application, the leader-unknown time-varying structural formation tracking method further includes:

[0067] Step 106: Calculate the motion state of the target follower at the next moment based on the control input vector of the target follower at the current moment, the motion state of the target follower at the current moment, and the follower dynamics model.

[0068] Specifically, based on the current time, control the input vector u i (t) and the position and velocity (i.e., motion state) of the target follower are used to obtain the acceleration variable at the current moment, and then the position and velocity at the next moment are calculated, i.e., the motion state at the next moment. This process is repeated.

[0069] As an optional implementation, the mathematical model of the follower dynamics model is expressed as follows:

[0070]

[0071] in, This represents the control input vector of follower i at time t; and denote the position, velocity and acceleration of the follower i at time t, respectively; and G i (x i (t)) are the inertia, Coriolis and centrifugal and gravitational matrices of the ith follower, respectively.

[0072] The follower dynamics model has the following characteristics: for the regression matrix where and is a parameter vector, the follower dynamics model satisfies the following equation:

[0073] M i (x i (t))y(t)+C i (x i (t),

[0074] In this application, the observer is distributed, for example, each follower only needs to calculate the state of the leader information and the system matrix distributed observer at each time , and then get the next time estimate, that is, θ i (t+Δt), ξ(t+Δt). In practical applications, the control command must be a discrete signal with a certain frequency, so the next time estimate is written as θ i (t+Δt), ξ(t+Δt), where Δt represents the control step in practical applications.

[0075] The effectiveness of the observer has a premise assumption: the communication topology graph corresponding to the formation cluster is connected. If there is a pair of isolated followers, each only has a communication relationship with the other, the observer cannot converge in this case, but the communication topology graph in this case is not connected, which does not meet the assumption conditions in this application.

[0076] The leader unknown time-varying heterogeneous formation tracking method is described from the perspective of scheme design below, referring to Figure 2 .

[0077] Step 201: Obtain the communication topology relationship of the heterogeneous formation. Abstract the communication topology relationship in the time-varying heterogeneous formation cluster as an undirected graph, and calculate to obtain the corresponding Laplacian matrix L and other related quantitative variables, providing a basis for the design of the observer and the controller in subsequent steps 203-205.

[0078] Step 202: establish the Euler-Lagrange dynamic model of the follower and the dynamic model of the leader. Obtain the corresponding characteristic equations, which provide the basis for the design of the observer and the controller in subsequent steps 203-205. Among them, the Euler-Lagrange dynamic model of the follower refers to the mathematical model of the dynamic model of the follower.

[0079] Step 203: construct the leader state information and system matrix distributed observer for the follower cluster. Among them, first construct two groups of filters, namely the first group of filters and the second group of filters, and then construct the distributed adaptive observer (i.e. the leader state information and system matrix distributed observer).

[0080] Step 204: construct the leader output information and output matrix distributed observer for the follower cluster.

[0081] Step 205: construct the distributed time-varying formation tracking controller. That is, on the basis of the two groups of distributed observers constructed in steps 203 and 204, construct the distributed time-varying formation tracking controller. Specifically, first define the sliding vector, and then construct the distributed time-varying formation tracking controller.

[0082] Step 206: according to the distributed time-varying formation tracking controller, obtain the control input vector of the follower, and control the time-varying formation of the follower cluster. According to the Euler-Lagrange dynamic model in step 202, the motion state of the follower cluster under the control of the controller can be obtained.

[0083] The two groups of distributed observers and controllers designed in the present application can realize the time-varying heterogeneous formation motion of the leader unknown heterogeneous Euler-Lagrange system.

[0084] Based on the same inventive concept, the embodiments of the present application also provide a leader unknown time-varying heterogeneous formation tracking device for implementing the leader unknown time-varying heterogeneous formation tracking method described above. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme described in the above method, so the specific limitations in one or more leader unknown time-varying heterogeneous formation tracking device embodiments provided below can refer to the limitations of the leader unknown time-varying heterogeneous formation tracking method in the above text, which will not be repeated here.

[0085] In an exemplary embodiment, as shown in Figure 3 A leader unknown time-varying heterogeneous formation tracking device is provided, which includes:

[0086] A modeling module M1 is configured to establish the Euler-Lagrange dynamic model of the follower and the dynamic model of the leader.

[0087] The first observer construction module M2 is configured to construct a leader state information and system matrix distributed observer for the follower cluster.

[0088] The second observer construction module M3 is configured to construct a leader output information and output matrix distributed observer for the follower cluster.

[0089] The controller construction module M4 is configured to construct a distributed time-varying formation tracking controller for the follower cluster on the basis of the observer.

[0090] The control module M5 is configured to control the time-varying formation of the follower cluster through the distributed time-varying formation tracking controller.

[0091] In the present application, the initial excitation condition refers to initial excitation, that is, only the signal satisfying the initial excitation condition has a value at the initial time, corresponding to the persistent excitation condition (PE). The initial excitation condition proposed in the present application refers to the provision of a signal for a certain period of time. What is described herein is that a signal (referring to a filtered signal D(t)) satisfies the initial excitation condition, and it does not mean that there is a specific "excitation" or a specific object of action. The signal satisfying the initial excitation condition means that the signal itself has a value at the initial time, rather than the requirement of continuous value in the persistent excitation condition.

[0092] Specifically, the present application requires that, in the second group of filters in the form of the filtered signal D(t) satisfies the initial excitation condition, which is mathematically expressed as:

[0093]

[0094] where t0 represents a certain finite time; δ1 represents a certain constant greater than zero; represents an m 2 dimensional unit matrix.

[0095] If G(t) satisfies the following lemma is established:

[0096] For the variable D(t) defined in the filter, a normal number δ'1 can be found, such that

[0097]

[0098] where represents the Laplacian matrix corresponding to the communication relationship of the follower cluster (not including the leader); represents an Nm 2 dimensional unit matrix.

[0099] A Lyapunov function is constructed based on the observer:

[0100]

[0101] wherein, and denote the estimation error of the leader system matrix and the leader state information of the follower i, respectively.

[0102] Then we can get:

[0103]

[0104] wherein, η(t)=col(η1(t),η2(t),…,η N (t)).

[0105] Further, by the lemma condition obtained by the initial excitation condition When t≥t0, we can further prove:

[0106]

[0107] Further, we can get Thus, the convergence of the observer is proved.

[0108] That is, as long as the initial excitation condition is met, the observer can converge. That is, the two groups of distributed observers designed in the present application can achieve convergence based on the initial excitation condition which is relatively easy to achieve, which is one of the advantages of the two groups of distributed observers designed in the present application.

[0109] The present application overcomes the problem of observer design for parameter estimation of heterogeneous multi-agent formation when the leader system matrix and the output matrix are unknown, and can ensure that the relevant adaptive parameters (leader system matrix, output matrix, state information and output information) can converge to their true values under the initial excitation (IE) condition, rather than being limited to the traditional persistent excitation (PE) condition.

[0110] The effectiveness of the method proposed in the present application is verified by a specific physical experiment of time-varying formation control of a heterogeneous cluster system. The specific implementation steps of the present example are as follows:

[0111] (1) Heterogeneous cluster composition and communication topology setting

[0112] Referring to Figure 4 , a cluster composed of 5 agents is considered, which includes 1 unmanned aerial vehicle and 4 unmanned vehicles. Among them, the unmanned aerial vehicle is the leader, and the unmanned vehicles are all followers. Among them, unmanned vehicles 1, 3, 2, 4, and 3, 4 can communicate bidirectionally, and unmanned vehicle 1 and unmanned vehicle 2 can communicate with the unmanned aerial vehicle (leader).

[0113] Figure 4 In this paper, UAV represents unmanned aerial vehicle, and UGV represents unmanned ground vehicle.

[0114] (2) The follower Euler-Lagrange dynamics model and the leader dynamics model are established

[0115] In two-dimensional dimensions, the follower Euler-Lagrange dynamics model is set as follows:

[0116]

[0117] where x i (t) = col(x 1i (t), x 2i (t)), M i (x i (t)) = m i I2, G i (x i (t)) = [m i ; m i ]; x 1i (t), x 2i (t) are two components of x i , m i represents the mass of the i-th follower, and I2 represents a 2x2 unit matrix.

[0118] For the 4 followers in , let their masses be m1 = 0.5, m2 = 0.6, m3 = 1.0, and m4 = 1.5, respectively.

[0119] In two-dimensional dimensions, the leader dynamics model is set as follows:

[0120]

[0121] where E = [0, 1, 2; -1, 0, 3; -2, -3, 0], and F = [1, 0, 0; 0, 1, 0].

[0122] (3) Desired time-varying formation setting

[0123] Here, the desired time-varying formation is set as a circular rotating formation, and for the follower i (i = 1, 2, 3, 4), the formation vector h i (t) is set as follows:

[0124]

[0125] (4) Leader state information and system matrix distributed observer setting

[0126] The first group of filters is constructed as follows:

[0127]

[0128] where the constant k = 0.5.

[0129] The second group of filters is constructed as follows:

[0130]

[0131] The distributed adaptive observer is constructed as follows:

[0132]

[0133] where the constant μ1= 0.5.

[0134] (5) Leader output information and output matrix distributed observer setting

[0135] The distributed adaptive observer is constructed as follows:

[0136]

[0137] (6) Distributed time-varying formation tracking controller setting

[0138] First, define the sliding vector as follows:

[0139]

[0140] The distributed formation tracking controller is constructed as follows:

[0141]

[0142] where the constant k s = 0.5.

[0143] (7) Simulation condition setting and results

[0144] For the intelligent agents (drones and unmanned vehicles) in the heterogeneous cluster, experiments are carried out in a two-dimensional plane, and the initial positions are set as follows: z0(0) = [1.45, -0.13] T , x1(0) = [9.41, 0.01] T , x2(0) = [3.26, 0.24] T , x3(0) = [3.26, 0.24] T , x4(0) = [3.26, 0.24] T .

[0145] Figure 5 and Figure 6 respectively represent the estimation error curves of the 2 followers and the 4 followers on the leader state vector v0(t) and the system matrix E, Figure 7The formation tracking error variation curves of the four followers, Figure 8 The figures (a) respectively show the positions of the four followers and the leader at different times. Figures 5 to 8 In the figures, (a) respectively show the numerical simulation results, and (b) respectively show the physical experiment results.

[0146] Through Figure 5 and Figure 6 It can be seen that the distributed observer provided in the application can effectively converge to the real values of the leader state information and the system matrix; through Figure 7 and Figure 8 It can be seen that, on the basis of the observer converging to the real values, the distributed formation controller provided in the application can also make the formation error converge to 0, effectively controlling the followers to achieve the expected circular rotating formation. The example verifies the effectiveness of the method proposed in the application.

[0147] Compared with the prior art, the distributed adaptive observer and controller designed in the application can realize the tracking control of the multi-agent formation with unknown leader. The main advantages are as follows:

[0148] 1) The application solves the observer design problem for parameter estimation of the heterogeneous multi-agent formation when the leader is unknown, and can ensure that the related adaptive parameters converge to their real values under the initial excitation (IE) condition, rather than being limited to the traditional persistent excitation (PE) condition.

[0149] 2) The application proposes a distributed adaptive observer and a time-varying formation tracking controller for each follower, i.e., without knowing the system matrix E, the output matrix F or the state derivative information of the leader and ensures that the heterogeneous formation system can achieve the desired time-varying formation and track the state trajectory generated by the unknown leader under the condition of unknown entire cluster information.

[0150] 3) For the observer and the time-varying formation tracking controller proposed in the application, in order to verify their effectiveness, a practical physical experiment of a heterogeneous air-ground cluster system with four unmanned vehicles and one unmanned aerial vehicle is also carried out, realizing the time-varying heterogeneous formation tracking of the unknown leader (unmanned aerial vehicle).

[0151] The application also provides an application scenario of the time-varying heterogeneous formation tracking method with unknown leader. Specifically, the time-varying heterogeneous formation tracking method with unknown leader provided in the embodiment can be applied in the time-varying heterogeneous formation tracking scene with unknown leader.

[0152] In an exemplary embodiment, a computer device, which can be a server or a terminal, is provided, and the internal structure diagram thereof can be as shown in Figure 9As shown in the figure. The computer device includes a processor, a memory, an input / output interface (I / O for short) and a communication interface. Among them, the processor, the memory and the input / output interface are connected through the system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capability. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store the platoon related data. The input / output interface of the computer device is used to exchange information between the processor and the external device. The communication interface of the computer device is used to communicate with the terminal outside through the network connection. The computer program is executed by the processor to realize a leader-unknown time-varying heterogeneous platoon tracking method.

[0153] Those skilled in the art can understand that, Figure 9 The structure shown in the figure is only a block diagram of part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. The specific computer device can include more or fewer components than those shown in the figure, or combine certain components, or have a different component arrangement. In an exemplary embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, and the processor executing the computer program to realize the steps in each of the above method embodiments.

[0154] In an exemplary embodiment, a computer readable storage medium is provided, storing a computer program, which is executed by a processor to realize the steps in each of the above method embodiments.

[0155] In an exemplary embodiment, a computer program product is provided, including a computer program, which is executed by a processor to realize the steps in each of the above method embodiments.

[0156] It should be noted that the user information (including but not limited to user equipment information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or authorized by all parties, and the collection, use and processing of related data need to comply with relevant regulations.

[0157] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer readable storage medium, and when the computer program is executed, the processes of the above-mentioned embodiments of the methods can be included. Any reference to memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical storage, high-density embedded non-volatile memory, resistive memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration but not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0158] The database involved in the embodiments provided in the present application can include at least one of a relational database and a non-relational database. The non-relational database can include a distributed database based on a blockchain, etc., without being limited thereto. The processor involved in the embodiments provided in the present application can be a general-purpose processor, a central processing unit, a graphics processing unit, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., without being limited thereto.

[0159] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combinations of the technical features do not exist contradictory, they should be considered as the scope of the present application.

[0160] The principles and implementation modes of the present application are described by using specific examples in the present application. The above-mentioned embodiments are only used to help understand the method and its core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed. In conclusion, the content of the present application should not be understood as a limitation.

Claims

1. A time-varying structural grouping tracking method with an unknown leader, characterized in that, The time-varying swarm tracking method with an unknown leader includes: Based on the communication topology graph of the time-varying structural formation, all adjacent followers corresponding to the target follower are determined. The communication topology graph includes nodes and edges. The nodes represent followers or leaders in the time-varying structural formation. The edges represent the communication relationships between followers and leaders or between followers in the time-varying structural formation. Adjacent followers are those followers in the time-varying structural formation that have a communication relationship with the target follower. The target follower is a follower that does not have a communication relationship with the leader in the time-varying structural formation. Adjacent followers are either followers that have a communication relationship with the leader or followers that do not have a communication relationship with the leader. Obtain the estimated leader state information and estimated leader output information of each adjacent follower at the current time; when the adjacent follower is a follower with a communication relationship with the leader, the estimated leader state information and estimated leader output information of the adjacent follower are directly obtained from the leader; when the adjacent follower is a follower without a communication relationship with the leader, the estimated leader state information and estimated leader output information of the adjacent follower are respectively values ​​obtained by the adjacent follower from estimating the leader state information and the leader output information. Based on the estimated leader state information of each adjacent follower at the current time, the estimated leader state information of the target follower at the current time, and the estimated leader system matrix, the first derivative of the leader state information and the leader system matrix of the target follower are estimated using a distributed observer of leader state information and system matrix, and the estimated leader state information and the estimated leader system matrix of the target follower at the next time time are calculated. Based on the estimated leader output information of each adjacent follower at the current time, the estimated leader output matrix of the target follower at the current time, and the estimated leader state information of the target follower at the next time, the leader output information and the first derivative of the leader output matrix of the target follower are estimated using a distributed observer of the leader output information and output matrix. This yields the estimated leader output information and the first derivative of the leader output matrix of the target follower at the current time, and the estimated leader output matrix of the target follower at the next time is calculated. Based on the estimated leader output information of the target follower at the current moment and the time-varying formation vector of the target follower at the current moment, the control input vector of the target follower at the current moment is calculated using a distributed formation tracking controller.

2. The time-varying structural grouping tracking method for leader-unknown situations according to claim 1, characterized in that, The mathematical model representing the leader's state information and the system matrix distributed observer is as follows: Where, θ i (t) represents the estimate of θ by follower i at time t, where θ is the vector form of the leader system matrix E. The vec(·) operation is defined as: for any matrix but The operation col(·) is defined as: for any matrix Let ξ represent the estimate of the leader's state vector v0(t) by follower i at time t. i1 (t), ξ i2 (t), ..., ξ in (t) represents the leader's state vector v o The estimated value of (t) has n components; and θ i (t) and ξ i (t) is the first derivative of (t) with respect to time t; I m This represents an m×m identity matrix. This represents the tensor product operation; μ1 > 0, which is a constant; a ij This indicates whether follower i and follower j have a communication relationship. When follower i and follower j have a communication relationship, a ij =1, when follower i and follower j do not have a communication relationship, a ij =0; a i0 This indicates whether follower i and leader 0 have a communication relationship. When follower i and leader 0 have a communication relationship, a i0 =1, when follower i and leader 0 do not have a communication relationship, a i0 =0; N represents the number of followers in the time-varying structural formation; and These are the state variables of the second group of filters; ξ j (t) represents the estimate of the leader's state vector v0(t) by follower j at time t.

3. The time-varying structural grouping tracking method for leader-unknown situations according to claim 2, characterized in that, The mathematical model of the second set of filters is expressed as follows: in, and These are the first-order differentials of D(t) and P(t), respectively; and These are the state variables of the first group of filters; The mathematical model of the first set of filters is expressed as follows: in, k > 0 represents a scalar gain. Let v0(t) be the derivative. and These are the first-order differentials of G(t) and p(t), respectively; p(t) is derived from p(t) = v0(t) - e -kt Calculate using v0(0)-kf(t). f(0) = 0.

4. The time-varying structural grouping tracking method for leader-unknown situations according to claim 2, characterized in that, The mathematical model of the leader's output information and output matrix distributed observer is expressed as follows: in, Let z0(t) be the estimate of the leader's output information z0(t) by follower i at time t. This represents the estimate of the leader's output matrix F by follower i at time t; for The first differential; a ik This indicates whether follower i and follower k have a communication relationship. Let z0(t) be the estimate of the leader's output information z0(t) by follower k at time t; z0(t) and F satisfy... It is the first-order differential of z0(t).

5. The time-varying structural grouping tracking method for leader-unknown situations according to claim 1, characterized in that, The mathematical model of the distributed formation tracking controller is expressed as follows: in, Ψ represents the control input vector of follower i at time t; i (·) represents the regression matrix. and Let i represent the position and velocity of follower i at time t, respectively. for The first derivative with respect to time t, Let h represent the estimate of the leader's output information z0(t) by follower i at time t. i (t) represents the time-varying formation vector of follower i at time t. for h i (t) is the first derivative of (t) with respect to time t; for The first derivative with respect to time t; For the parameter vector; k s Normal value; s i (t) is the sliding vector.

6. The time-varying structural grouping tracking method for leader-unknown conditions according to claim 1, characterized in that, The time-varying swarm tracking method with an unknown leader also includes: Based on the control input vector of the target follower at the current moment, the motion state of the target follower at the current moment, and the follower dynamics model, the motion state of the target follower at the next moment is calculated.

7. The time-varying structural grouping tracking method for leader-unknown cases according to claim 6, characterized in that, The mathematical model of the follower dynamics model is expressed as follows: in, This represents the control input vector of follower i at time t; and Let i represent the position, velocity, and acceleration of follower i at time t, respectively. and G i (x i (t) represents the inertia matrix, Coriolis and centrifugal matrix, and gravity matrix of the i-th follower, respectively.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the time-varying, undefined leader formation tracking method as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the time-varying, structured grouping tracking method for an unknown leader as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the time-varying, structured grouping tracking method for an unknown leader as described in any one of claims 1-7.

Images