Leader-unknown time-varying heterogeneous formation tracking method and related device

Abstract

The invention discloses a leader-unknown time-varying heterogeneous formation tracking method and a related device, and relates to the field of cluster formation tracking control, and the method comprises the steps: determining all adjacent followers corresponding to a target follower according to a communication topological relation graph of a time-varying heterogeneous formation, obtaining a leader state information estimation value and a leader output information estimation value of each adjacent follower; the leader state information of the target follower at the next moment is estimated by using the leader state information and a system matrix distributed observer, and then the leader output information of the target follower at the current moment is estimated by using the leader output information and an output matrix distributed observer; and finally, calculating by using a distributed formation tracking controller to obtain a control input vector of the target follower at the current moment. According to the method and the device, the time-varying heterogeneous formation unknown to the leader can be tracked and controlled under the condition that persistent excitation is not needed.

Description

Technical Field

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

[0002] In recent decades, distributed cooperative control of multi-agent formations has been a hot topic in the control field and has been widely used in scientific research and engineering. Among them, how to perform time-varying formation control and construct effective controllers are key issues that have been widely studied and discussed in the field of cooperative control of multi-agent systems.

[0003] However, most existing studies on multi-agent formation tracking control assume that all following agents (followers) know the dynamic information of the leading 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 consistency problems, this requirement means that each following agent has direct communication with the leader, which contradicts the distributed nature of multi-agent formations. In many practical application scenarios, the target trajectory tracked by the following agent is generated by a non-cooperative target, that is, no following agent can fully understand the dynamic information of the tracking target. For example, in a certain drone-unmanned vehicle formation tracking application scenario, the tracking drone 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 an unknown leader has become an important and challenging problem that has received increasing attention in recent years; before designing a formation tracking controller for such a system, it is necessary to design a corresponding parameter observer to estimate the dynamic information of the leader.

[0004] However, many existing parameter observer designs require continuous excitation (PE) conditions, which require that the amount of signals from the leader state is rich enough. However, it may be difficult to ensure and verify the PE conditions in advance when dealing with uncertain parameter estimation problems. Some studies have successfully relaxed the requirements of traditional continuous excitation conditions, but they are mainly used for dynamic information estimation in single adaptive formations or homogeneous multi-agent formations. It is very difficult to extend these techniques to heterogeneous multi-agent formations with uncertain leaders, because in heterogeneous multi-agent formations, it is not feasible to ensure that all followers can directly obtain leader information (e.g., input or state). Therefore, how to design a formation controller that does not require continuous excitation (PE) conditions in heterogeneous cluster formations with uncertain leaders is currently a challenging problem. Summary of the invention

[0005] The purpose of the present application is to provide a method and a related device for tracking a time-varying conformal formation with an unknown leader, which can realize tracking and control of the time-varying conformal formation with an unknown leader without the need for continuous excitation (PE).

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a method for tracking a time-varying conformational formation with an unknown leader, comprising:

[0008] According to the communication topology relationship diagram of the time-varying structural formation, all adjacent followers corresponding to the target follower are determined; the communication topology relationship diagram 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 the communication relationship 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.

[0009] Obtain the leader state information estimate and the leader output information estimate of each adjacent follower at the current moment; when the adjacent follower is a follower having a communication relationship with the leader, the leader state information estimate and the leader output information estimate of the adjacent follower are both directly obtained from the leader; when the adjacent follower is a follower not having a communication relationship with the leader, the leader state information estimate and the leader output information estimate of the adjacent follower are respectively estimated values ​​of the leader state information and the leader output information by the adjacent follower.

[0010] According to the leader state information estimate of each adjacent follower at the current moment, the leader state information estimate of the target follower at the current moment and the leader system matrix estimate, the leader state information of the target follower and the first-order derivative of the leader system matrix are estimated using the leader state information and system matrix distributed observer, and the leader state information estimate and the leader system matrix estimate of the target follower at the next moment are calculated.

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

[0012] According to the estimated value of the 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, a distributed formation tracking controller is used to calculate to obtain a control input vector of the target follower at the current moment.

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

[0014] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for tracking a time-varying heterogeneous formation with an unknown leader as described in the first aspect.

[0015] In a fourth aspect, the present application provides a computer program product, including a computer program, which, when executed by a processor, implements the leader-unknown time-varying heterogeneous formation tracking method described in the first aspect.

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

[0017] The present application provides a method and related device for tracking a time-varying heterogeneous formation with an unknown leader. According to the communication topology diagram of the time-varying heterogeneous formation, all adjacent followers corresponding to the target follower are determined; the leader state information estimate and the leader output information estimate of each adjacent follower at the current moment are obtained; according to the leader state information estimate of each adjacent follower at the current moment, the leader state information estimate of the target follower and the leader system matrix estimate, the leader state information of the target follower and the first-order derivative of the leader system matrix are estimated using the leader state information and system matrix distributed observer, and the leader state information estimate and the leader system matrix estimate of the target follower at the next moment are calculated; and then according to the leader state information estimate of each adjacent follower at the current moment, the leader state information estimate of the target follower and the leader system matrix estimate are estimated. The estimated value of the leader output information, the estimated value of the leader output matrix of the target follower at the current moment, and the estimated value of the leader state information of the target follower at the next moment are estimated by using the leader output information and the output matrix distributed observer to estimate the leader output information of the target follower and the first-order derivative of the leader output matrix, and the estimated value of the leader output matrix of the target follower at the next moment is calculated; finally, according to the estimated value of the 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 distributed formation tracking controller is used to calculate to obtain the control input vector of the target follower at the current moment. The present application realizes tracking control of a time-varying conformal formation with an unknown leader without the need for persistent excitation (PE) through the distributed observer of the leader state information and the system matrix and the distributed observer of the leader output information and the output matrix, while reducing the amount of leader information obtained, saving communication resources, and improving the tracking control efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0019] Figure 1 A flowchart of a method for tracking a time-varying heterogeneous formation with an unknown leader provided in an embodiment of the present application;

[0020] Figure 2 A schematic flow chart of a method for tracking a time-varying conformational formation with an unknown leader provided in another embodiment of the present application;

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

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

[0023] Figure 5 A curve diagram showing a change in the estimation error of a leader's state vector by a follower provided in an embodiment of the present application; Figure 5 (a) represents the estimated error curve of the leader's state vector by the follower corresponding to the numerical simulation; Figure 5 (b) represents the curve diagram of the estimated error change of the leader's state vector by the follower corresponding to the physical experiment;

[0024] Figure 6 A curve diagram showing the estimated error variation of the leader system matrix E by the follower provided in an embodiment of the present application; Figure 6 (a) represents the estimated error curve of the leader system matrix E corresponding to the numerical simulation; Figure 6 (b) represents the curve diagram of the estimated error change of the leader system matrix E by the follower corresponding to the physical experiment;

[0025] Figure 7 A curve diagram of a formation tracking error variation of a follower provided in an embodiment of the present application; Figure 7 (a) represents the curve diagram of the follower formation tracking error change corresponding to the numerical simulation; Figure 7 (b) shows the curve diagram of the tracking error variation of the followers’ formation corresponding to the physical experiment;

[0026] Figure 8 A diagram of the positions of followers and leaders at different times provided in an embodiment of the present application; Figure 8 (a) shows the position diagram of the follower and the leader at different times corresponding to the numerical simulation; Figure 8 (b) represents the position diagram of the follower and the leader at different times corresponding to the physical experiment;

[0027] Fig. 9 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0029] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0030] In an exemplary embodiment, Figure 1 As shown, the present application provides a method for tracking a time-varying heterogeneous formation with an unknown leader, comprising the following steps 101 to 105. Among them:

[0031] Step 101: Determine all adjacent followers corresponding to the target follower according to the communication topology relationship diagram of the time-varying structural formation; the communication topology relationship diagram 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 the communication relationship 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 relationship in the time-varying polymorphic formation cluster is abstracted into an undirected graph, and the corresponding Laplace matrix L and other related quantitative variables are calculated.

[0033] Among them, the time-varying conformational formation includes multiple followers and a leader. The system matrix E and output matrix F of the leader are unknown to all followers. Some followers can directly obtain the state information of the leader (also called state vector information), while the remaining followers cannot directly obtain the state information of the leader.

[0034] The follower cluster consisting of N followers in the time-varying conformational formation is denoted as The topological structure of the followers communicating with each other can be described as a graph where ν={ν1,ν2,…,ν N} represents a node set, is an edge set, is a non-negative element a ij The symmetric adjacency matrix of . For follower i and follower j, You can use the ν in ν i and ν j To refer to. If from ν i to j There is an edge between them, that is, there is a communication relationship between follower i and follower j, then a ij =1; otherwise a ij = 0. Let a ii=0,i∈{1,2,…,N}. In order to describe the neighbor relationship in the heterogeneous cluster system, we define the graph The Laplace matrix of in is the in-degree matrix.

[0035] In the heterogeneous formation, there is also a leader, and the topological structure of the communication between the entire heterogeneous formation is described as The leader is node 0. If node 0 (leader) and ν i (follower i), then a 0i =1, otherwise, a 0i = 0. Assume that The corresponding Laplace matrix is ​​L, then assume that L has the following form: The sub-matrix

[0036] Step 102: Obtain the leader state information estimate and the leader output information estimate of each adjacent follower at the current moment; when the adjacent follower is a follower having a communication relationship with the leader, the leader state information estimate and the leader output information estimate of the adjacent follower are both directly obtained from the leader; when the adjacent follower is a follower not having a communication relationship with the leader, the leader state information estimate and the leader output information estimate of the adjacent follower are the values ​​estimated by the adjacent follower for the leader state information and the leader output information, respectively.

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

[0038] That is, the leader state information and the system matrix distributed observer are used to obtain the first-order derivative estimate of the leader state information and the first-order derivative estimate of the leader system matrix of the target follower (at the current moment), and then the leader state information estimate and the leader system matrix estimate of the target follower at the next moment are calculated. Of course, the leader state information estimate and the leader system matrix estimate of the target follower at the current moment are determined based on the first-order derivative estimate of the leader state information and the first-order derivative estimate of the leader system matrix of the target follower at the previous moment.

[0039] For the initial moment, the leader state information estimation value and the leader system matrix estimation value of the target follower and each adjacent follower can be specified arbitrarily.

[0040] Step 104: Based on the leader output information estimate of each adjacent follower at the current moment, the leader output matrix estimate of the target follower at the current moment, and the leader state information estimate of the target follower at the next moment, the leader output information and output matrix distributed observer are used to estimate the leader output information and the first-order derivative of the leader output matrix of the target follower at the current moment, and the leader output matrix estimate of the target follower at the next moment is calculated.

[0041] The estimated value of the leader output matrix of the target follower at the current moment is determined according to the first-order derivative of the leader output matrix of the target follower at the previous moment.

[0042] At the initial moment, the estimated values ​​of the leader output information and the estimated values ​​of the leader output matrix of the target follower and each adjacent follower can be arbitrarily specified, such as specified as 0.

[0043] Step 105: According to the estimated value of the 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, a distributed formation tracking controller is used to perform calculations to obtain a control input vector of the target follower at the current moment.

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

[0045]

[0046] Among them, θ i (t) represents the estimated value of θ by follower i at time t, 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 represents the estimate of the leader's state vector v0(t) by follower i at time t, ξ i1 (t), ξ i2 (t),......,ξ in (t) are the leader state vector v o The n components of the estimate of (t); and They are θ i (t) and ξ i (t) the first-order differential with respect to time t; I m represents the identity matrix of dimension m×m, represents the tensor product operation; μ1>0, is a constant in the observer; N represents the number of followers in the time-varying conformational formation; and are the state variables of the second group of filters respectively.

[0047] a ij Indicates whether followers i and j have a communication relationship. When followers i and j have a communication relationship, a ij = 1, when followers i and j do not have a communication relationship, a ij =0; a i0 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. That is, a ij ,a i0 The communication topology diagrams are as follows: The corresponding submatrix of the Laplacian matrix L Items in In this application, we consider the case where 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 follower j’s estimate of the leader’s 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] in, is a bounded vector, representing the leader state vector (i.e., leader state information); represents the leader output vector (i.e., the leader output information), For the leader system matrix, is the leader output matrix. This set of equations is the dynamic model established for the leader in this application.

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

[0054]

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

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

[0057]

[0058] in, k>0 is a scalar gain, which is used to ensure the stability of the filter; is the derivative of v0(t), and 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) according to p(t) = v0(t) - e -kt v0(0)-kf(t) is calculated, where

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

[0060]

[0061] in, represents the estimated value of the leader's output information z0(t) by follower i at time t, represents the estimated value of the leader output matrix F by follower i at time t; for The first order differential of ; a ik Indicates whether follower i and follower k have a communication relationship (a ik ,a i0 They are the communication topology diagrams The Laplacian matrix L of the neutron matrix ), represents the estimated value of the leader's output information z0(t) by follower k at time t; z0(t) and F satisfy 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:

[0063]

[0064] in, represents the control input vector of follower i at time t; Ψ i (·) represents the regression matrix, and They represent the position and velocity of follower i at time t respectively; for The first-order differential with respect to time t is represents the estimated value of the leader's output information z0(t) by follower i at time t, h i (t) represents the time-varying formation vector of follower i at time t, h i (t) the first-order differential with respect to time t; for The first-order differential with respect to time t; is the parameter vector; k s Normal amount; 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)), used to represent the expected time-varying formation, h i (t) is the i-th variable in h(t).

[0066] In another exemplary embodiment of the present application, the method for tracking a time-varying conformational formation with an unknown leader further includes:

[0067] Step 106: Calculate the motion state of the target follower at the next moment according to 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, according to the current moment control input vector u i (t) and the position and speed (i.e., motion state) of the target follower, the acceleration variable at the current moment is obtained, and then the position and speed at the next moment, i.e., the motion state at the next moment, are calculated. This cycle repeats.

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

[0070]

[0071] in, represents the control input vector of follower i at time t; and They represent the position, velocity and acceleration of follower i at time t respectively; and G i (x i (t)) are the inertia matrix, Coriolis and centrifugal matrix, and gravity matrix of the i-th follower, respectively.

[0072] The follower dynamics model has the following characteristics: For the regression matrix in as well as is a parameter vector, and 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 perform each moment according to the leader state information and the system matrix distributed observer. Calculate and get the estimated value of the next moment, 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 estimated value at the next moment is written as θ i (t+Δt),ξ(t+Δt), where Δt represents the control step size in practical applications.

[0075] The effectiveness of this observer has a premise assumption: the communication topology corresponding to the formation cluster is connected. If there is a pair of isolated followers, each of which only has a communication relationship with each other, the observer cannot converge in this case. However, the communication topology in this case is not connected, which no longer meets the assumptions in this application.

[0076] The following describes the leader-unknown time-varying conformational formation tracking method from the perspective of scheme design. Figure 2 .

[0077] Step 201: Obtain the communication topology of the heterogeneous formation. The communication topology in the time-varying heterogeneous formation cluster is abstracted into an undirected graph, and the corresponding Laplace matrix L and other related quantitative variables are calculated to provide a basis for the design of the observer and controller in the subsequent steps 203 to 205.

[0078] Step 202: Establish the Euler-Lagrangian dynamics model of the follower and the dynamics model of the leader. Obtain the corresponding characteristic equations, which provide a basis for the design of the observer and controller in the subsequent steps 203 to 205. The Euler-Lagrangian dynamics model of the follower refers to the mathematical model of the follower dynamics model.

[0079] Step 203: construct leader state information and system matrix distributed observer for the follower cluster, wherein firstly, two groups of filters are constructed, namely, the first group of filters and the second group of filters, and then a distributed adaptive observer (namely, leader state information and system matrix distributed observer) is constructed.

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

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

[0082] Step 206: According to the distributed time-varying formation tracking controller, a control input vector of the follower is obtained to control the time-varying formation of the follower cluster. According to the Euler-Lagrangian dynamics model in step 202, the motion state of the follower cluster under the control of the controller can be obtained.

[0083] The two sets of distributed observers and controllers designed in this application can realize the time-varying heterogeneous formation motion of heterogeneous Eulerian-Lagrangian systems with unknown leaders.

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

[0085] In an exemplary embodiment, Figure 3 As shown, a leader-unknown time-varying conformational formation tracking device is provided, comprising:

[0086] The modeling module M1 is used to establish the Euler-Lagrangian dynamics model of the follower and the dynamics model of the leader.

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

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

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

[0090] The control module M5 is used 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, the signal that only meets the initial excitation condition needs to have a value at the initial moment, corresponding to the continuous excitation condition (PE). The initial excitation condition proposed in the present application refers to the continuous provision of the signal for a period of time at the beginning. What is described here is actually a signal (referring to the filtered signal D(t)) that meets the initial excitation condition, which does not mean that there is a specific "excitation" or a specific object of action. The signal meeting the initial excitation condition means that the signal itself has a value at the initial moment, rather than the continuous value required in the continuous excitation condition.

[0092] Specifically, this application requires the form In the second set of filters, the filtered signal D(t) satisfies the initial excitation condition, which can be expressed mathematically as:

[0093]

[0094] Among them, t0 represents a finite time; δ1 represents a constant greater than zero; Indicates the dimension is m 2 The identity matrix of .

[0095] If G(t) satisfies Then the following lemma holds:

[0096] For the variable D(t) defined in the filter, we can find a positive constant δ′1 such that

[0097]

[0098] in, The Laplace matrix representing the communication relationship of the follower cluster (excluding the leader); Indicates the dimension is Nm 2 The identity matrix of .

[0099] Construct Lyapunov function based on observer:

[0100]

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

[0102] Then we can get:

[0103]

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

[0105] Then, the lemma condition obtained by the initial excitation condition When t≥t0, it can be further proved that:

[0106]

[0107] Then we can get This proves the convergence of the observer.

[0108] In other words, if the above initial excitation conditions are met, the observer convergence can be ensured. This means that the two sets of distributed observers designed can achieve convergence based on relatively easy-to-achieve initial excitation conditions, which is one of the advantages of the two sets of distributed observers designed in this application.

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

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

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

[0112] See also Figure 4 Consider a cluster of 5 agents, including 1 drone and 4 unmanned vehicles. The drone is the leader and the unmanned vehicles are followers. Unmanned vehicles 1, 3, 2, 4, 3, 4 can communicate with each other in a two-way manner, and unmanned vehicles 1 and 2 can communicate with the drone (leader).

[0113] Figure 4 In the text, UAV stands for Unmanned Aerial Vehicle (UAV) and UGV stands for Unmanned Vehicle (UG

[0114] (2) Establishment of the follower Euler-Lagrangian dynamics model and the leader dynamics model

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

[0116]

[0117] Among them, x i =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 x i The two components of m i represents the mass of the i-th follower, and I2 represents the 2×2 identity matrix.

[0118] for There are 4 followers in the network, and their masses are as follows: m1=0.5, m2=0.6, m3=1.0, m4=1.5.

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

[0120]

[0121] Among them, E=[0,1,2;-1,0,3;-2,-3,0], F=[1,0,0;0,1,0].

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

[0123] Here, the desired time-varying formation is set as a circular rotating formation. For 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] Construct the first set of filters:

[0127]

[0128] Among them, the constant k=0.5.

[0129] Construct the second set of filters as follows:

[0130]

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

[0132]

[0133] Among them, 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 settings

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

[0139]

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

[0141]

[0142] Among them, the constant k s =0.5.

[0143] (7) Simulation condition settings and results

[0144] For the agents in the heterogeneous cluster (drones and unmanned vehicles), the experiment was conducted on a two-dimensional plane, and the initial position was 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 The estimated error curves of the leader state vector v0(t) and the system matrix E by 2 and 4 followers are shown respectively. Figure 7is the tracking error variation curve of the formation of 4 followers, Figure 8 It shows the positions of the four followers and the leader at different times. Figures 5 to 8 In the figure, (a) shows the numerical simulation results, and (b) shows the physical experiment results.

[0146] pass Figure 5 and Figure 6 It can be seen that the distributed observer provided by this application can effectively converge to the true value of the leader state information and the system matrix; Figure 7 and Figure 8 It can be seen that on the basis of the observer converging to the true value, the distributed formation controller provided by the present application can also make the formation error converge to 0, effectively controlling the followers to achieve the desired circular rotation formation. This example verifies the effectiveness of the method proposed in the present application.

[0147] Compared with the existing technology, the distributed adaptive observer and controller designed in this application can realize the tracking control of multi-agent formations with unknown leaders. The main advantages are as follows:

[0148] 1) This application solves the problem of observer design for parameter estimation of heterogeneous multi-agent formations when the leader is unknown, and can ensure that the relevant adaptive parameters converge to their true values ​​under the initial incentive (IE) condition, rather than being restricted by the traditional persistent incentive (PE) condition.

[0149] 2) This application proposes a distributed adaptive observer and a time-varying formation tracking controller for each follower, that is, it is not necessary to know the leader's system matrix E, output matrix F or the leader's state derivative information And ensure that the heterogeneous formation system can achieve the desired time-varying formation and track the state trajectory generated by the unknown leader without knowing the rest of the information of the entire cluster.

[0150] 3) In order to verify the effectiveness of the observer and time-varying formation tracking controller proposed in this application, an actual physical experiment of a heterogeneous air-ground cluster system with 4 unmanned vehicles and 1 drone was carried out, realizing time-varying heterogeneous formation tracking with an unknown leader (drone).

[0151] The present application also provides an application scenario, which applies the above-mentioned leader-unknown time-varying configuration formation tracking method. Specifically: the leader-unknown time-varying configuration formation tracking method provided in this embodiment can be applied in the leader-unknown time-varying configuration formation tracking scenario.

[0152] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Fig. 9As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. 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 formation-related data. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a time-varying formation tracking method with an unknown leader is implemented.

[0153] Those skilled in the art will understand that Fig. 9 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components. In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0154] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0155] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

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

[0157] Those of ordinary skill 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, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the 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 memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0158] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0159] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0160] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for tracking a time-varying conformational formation with an unknown leader, characterized in that: The leader-unknown time-varying conformational formation tracking method comprises: According to the communication topology relationship diagram of the time-varying structural formation, all adjacent followers corresponding to the target follower are determined; the communication topology relationship diagram 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 the communication relationship 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; Obtaining the leader state information estimation value and the leader output information estimation value of each adjacent follower at the current moment; when the adjacent follower is a follower having a communication relationship with the leader, the leader state information estimation value and the leader output information estimation value of the adjacent follower are both directly obtained from the leader; when the adjacent follower is a follower not having a communication relationship with the leader, the leader state information estimation value and the leader output information estimation value of the adjacent follower are respectively the values ​​obtained by the adjacent follower estimating the leader state information and the leader output information; According to the leader state information estimation value of each adjacent follower at the current moment, the leader state information estimation value of the target follower at the current moment and the leader system matrix estimation value, the leader state information of the target follower and the first-order derivative of the leader system matrix are estimated using the leader state information and system matrix distributed observer, and the leader state information estimation value and the leader system matrix estimation value of the target follower at the next moment are calculated; 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 output matrix distributed observer of the target follower are used to estimate the leader output information and the first-order derivative estimation value of the leader output matrix of the target follower at the current moment, and the leader output matrix estimation value of the target follower at the next moment is calculated; According to the estimated value of the 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, a distributed formation tracking controller is used to calculate to obtain a control input vector of the target follower at the current moment.

2. The method for tracking a time-varying conformational formation with an unknown leader according to claim 1, characterized in that: The mathematical model of the leader state information and the system matrix distributed observer is expressed as: Among them, θ i (t) represents the estimated value of θ by follower i at time t, 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 represents the estimate of the leader's state vector v0(t) by follower i at time t, ξ i1 (t), ξ i2 (t),......,ξ in (t) are the leader state vector v o The n components of the estimate of (t); and They are θ i (t) and ξ i (t) the first-order differential with respect to time t; I m represents the identity matrix of dimension m×m, represents the tensor product operation; μ1>0, which is a constant; a ij Indicates whether followers i and j have a communication relationship. When followers i and j have a communication relationship, a ij = 1, when followers i and j do not have a communication relationship, a ij =0; a i0 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 temporal isomerization formation; and are the state variables of the second group of filters respectively; ξ j (t) represents the follower j’s estimate of the leader’s state vector v0(t) at time t.

3. The method for tracking a time-varying formation with an unknown leader according to claim 2, characterized in that: The mathematical model of the second group of filters is expressed as: in, and are the first-order differentials of D(t) and P(t) respectively; and are the state variables of the first group of filters respectively; The mathematical model of the first group of filters is expressed as: in, k>0 is a scalar gain, is the derivative of v0(t), and are the first-order differentials of G(t) and p(t), respectively; p(t) is calculated according to p(t) = v0(t) - e -kt v0(0)-kf(t) is calculated, f(0)=0.

4. The method for tracking a time-varying formation with an unknown leader according to claim 2, characterized in that: The mathematical model of the leader output information and the output matrix distributed observer is expressed as: in, represents the estimated value of the leader's output information z0(t) by follower i at time t, represents the estimated value of the leader output matrix F by follower i at time t; for The first order differential of a ik Indicates whether follower i and follower k have a communication relationship, represents the estimated value of the leader's output information z0(t) by follower k at time t; z0(t) and F satisfy is the first-order differential of z0(t).

5. The method for tracking a time-varying conformational formation with an unknown leader according to claim 1, characterized in that: The mathematical model of the distributed formation tracking controller is expressed as: in, represents the control input vector of follower i at time t; Ψ i (·) represents the regression matrix, and They represent the position and velocity of follower i at time t respectively; for The first-order differential with respect to time t is represents the estimated value of the leader's output information z0(t) by follower i at time t, h i (t) represents the time-varying formation vector of follower i at time t, h i (t) the first-order differential with respect to time t; for The first-order differential with respect to time t; is the parameter vector; k s Normal amount; s i (t) is the sliding vector, 6. The method for tracking a time-varying conformational formation with an unknown leader according to claim 1, characterized in that: The leader-unknown time-varying conformational formation tracking method further includes: The motion state of the target follower at the next moment is calculated according to 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.

7. The method for tracking a time-varying conformational formation with an unknown leader according to claim 6, characterized in that: The mathematical model of the follower dynamics model is expressed as: in, represents the control input vector of follower i at time t; and They represent the position, velocity and acceleration of follower i at time t respectively; and G i (x i (t)) are the inertia matrix, Coriolis and centrifugal matrices, 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, wherein the processor executes the computer program to implement the leader-unknown time-varying heterogeneous formation tracking method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for tracking a time-varying heterogeneous formation with an unknown leader as described in any one of claims 1 to 7 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method for tracking a time-varying heterogeneous formation with an unknown leader as described in any one of claims 1 to 7 is implemented.

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