Multi-agent time-varying linear formation parameter estimation method and parameter estimator

Abstract

The application belongs to the technical field of cooperative control, and particularly relates to a multi-agent time-varying linear formation parameter estimation method and a parameter estimator. The specific process of the method is as follows: constructing a feasible nominal configuration: the nominal configuration of the leader linearly spans an f-dimensional Euclidean space; constructing a measurable topology: the topology between agents satisfies: (1) the topology graph between followers is undirected and connected, and (2) the nominal formation corresponding to all measurable edges is linearly spanned in an f-dimensional Euclidean space; time-varying formation shape parameter estimator design: based on the consistent estimation results of all agents and the fact that the local formation corresponding to all edges of agent i and the local estimation results are the same, the formation state parameter estimator is designed; time-varying formation translation parameter estimator design: by comparing the difference between the transformed formation position and the actual position, the translation parameter estimator is designed.

Description

Technical Field

[0001] This invention belongs to the field of cooperative control, specifically relating to a method and estimator for estimating parameters of multi-agent time-varying linear formations. Background Technology

[0002] Using associated information to calculate target information is the basic idea of ​​estimation. In recent years, multi-agent systems have developed rapidly, and the problem of multi-agent cooperative estimation has also come into people's view. For example, the UWB-based cooperative localization problem requires a group of agents to collaboratively determine the target's location based on their own distance information from the target.

[0003] Formation control, as an elegant way to describe the cooperative behavior of multi-agent systems, also faces the problem of cooperative estimation, such as estimating the current formation size parameters based on changes in neighbors. However, the size parameter is a simple single parameter. In affine formation control, which has been proposed in recent years, the formation can be described using an affine transformation matrix. Estimating this affine transformation matrix is ​​much more difficult, and there is currently no research on relevant estimation methods. Summary of the Invention

[0004] This invention addresses the problem of multi-agent cooperative control by proposing a time-varying linear formation parameter estimation method and parameter estimator, which can achieve accurate estimation of agent parameters.

[0005] The technical solution for implementing the present invention is as follows:

[0006] Firstly, this application provides a method for estimating parameters of a multi-agent time-varying linear formation, the specific process of which is as follows:

[0007] Constructing a feasible nominal configuration: the navigator's nominal configuration r l Linear spanning forms an f-dimensional Euclidean space;

[0008] Construct a measurable topology: Make the topology between agents satisfy: (1) the topology between followers For undirected connectivity, (2) the nominal formations corresponding to all displacement-measurable edges are linearly spanned into an f-dimensional Euclidean space;

[0009] Design of a time-varying formation shape parameter estimator: Based on the fact that all agents have consistent estimation results and all edges of agent i are the same as the local formation corresponding to the local estimation results, a formation state parameter estimator is designed.

[0010] Design of a time-varying formation translation parameter estimator: By comparing the difference between the transformed formation position and the actual position, a translation parameter estimator is designed.

[0011] Furthermore, the distributed time-varying formation parameter estimator designed in this invention is as follows:

[0012]

[0013] Where α is a positive control gain, and the gain γ i Satisfying γ i >2m i δ2, the gain k satisfies k > δ1, where δ2 represents the upper bound of the navigator's velocity, and δ1 represents the upper bound of the desired time-varying formation change, i.e., δ1 = ||x * ||2,m i The set represents the number of measurable leader displacements for follower i. It consists of all followers who can measure the displacement of the leader, and is a set. It consists of all followers who cannot measure the displacement of the navigator. Let represent the set of all follower neighbors of agent i. The edge p contains all measurable navigators of agent i. jk =p j -p k p j and p k These represent the positions of agents j and k, respectively. The nominal configuration corresponding to the edges of all measurable navigators of agent i. r jk =r j -r k r j and r k Let || || represent the nominal configurations of agents j and k respectively. ∞ I represents the infinite norm. d This represents a d-dimensional identity matrix.

[0014] Furthermore, the distributed time-varying formation translation parameter estimator designed in this invention is as follows:

[0015]

[0016] Where σ1, σ2, and σ3 are three gains, satisfying σ1 > 0, σ2 > n f δ3, σ3 > 0. Where n f This indicates the number of follower agents. This indicates the upper bound of the change in the translation parameter. Let represent the set of all follower neighbors of agent i. Let i represent the set of all navigator neighbors of agent i.

[0017] Furthermore, the present invention also includes the design of a controller based on the formation parameter estimator and the translation parameter estimator.

[0018] Furthermore, the controller described in this invention is designed as follows:

[0019]

[0020] Where ρ is a positive control gain, x i and Let x represent the vectorized formation shape parameters x of agent i respectively. * The estimate and the derivative of the estimate; y i and Let y represent the vectorized formation translation parameters of agent i respectively. * The estimate and the derivative of the estimate, r i and Let represent the nominal formation and the derivative of the nominal formation of agent i, respectively.

[0021] Secondly, embodiments of this application provide a multi-agent time-varying linear formation parameter estimator, wherein the parameter estimator is a distributed time-varying formation parameter estimator.

[0022]

[0023]

[0024] Where α is a positive control gain, and the gain γ i Satisfying γ i >2m i δ2, the gain k satisfies k > δ1, where δ2 represents the upper bound of the navigator's velocity, and δ1 represents the upper bound of the desired time-varying formation change, i.e., δ1 = ||x * ||2,m i The set represents the number of measurable leader displacements for follower i. It consists of all followers who can measure the displacement of the leader, and is a set. It consists of all followers who cannot measure the displacement of the navigator. Let represent the set of all follower neighbors of agent i. The edge p contains all measurable navigators of agent i. jk =p j -p k p j and p k These represent the positions of agents j and k, respectively. The nominal configuration corresponding to the edges of all measurable navigators of agent i. r jk =r j -r k r j and r k Let j and k represent the nominal configurations of agents j and k, respectively.

[0025] Thirdly, embodiments of this application provide a multi-agent time-varying linear formation parameter estimator, wherein the parameter estimator is a distributed time-varying formation translation parameter estimator.

[0026]

[0027] Where σ1, σ2, and σ3 are three gains, satisfying σ1 > 0, σ2 > n f δ3, σ3>0, n f This indicates the number of follower agents. This indicates the upper bound of the change in the translation parameter. Let represent the set of all follower neighbors of agent i. Let i represent the set of all navigator neighbors of agent i.

[0028] Fourthly, embodiments of this application provide a multi-agent time-varying linear formation controller, which... i for

[0029]

[0030] Where ρ is a positive control gain, x i and Let x represent the vectorized formation shape parameters x of agent i respectively. * The estimate and the derivative of the estimate; y i and Let y represent the vectorized formation translation parameters of agent i respectively. * The estimate and the derivative of the estimate, r i and Let represent the nominal formation and the derivative of the nominal formation of agent i, respectively.

[0031] Beneficial effects:

[0032] First, the present invention can realize rich formation transformations. Compared with scaling formation control and affine formation control methods, which only support one scaling parameter and one square transformation matrix, the design of the time-varying formation shape parameter estimator proposed in this invention expands the transformation matrix and supports more types of formations. Based on the estimation results of local formation parameters, an error-driven translation parameter estimator is implemented by comparing the difference between the transformed formation position and the actual position, making the present invention more general and universal.

[0033] Secondly, this invention can solve the problem of collaborative estimation of local incomplete measurements. Specifically, the formation parameter information to be estimated in this invention cannot be completely obtained by a single agent. Compared with information that can be completely obtained, such as formation scaling parameters and rotation parameters, it is more complex. The distributed estimation method proposed in this invention can solve this challenging problem, and therefore has theoretical advancement.

[0034] Third, the quantity to be estimated in this invention is time-varying. Compared with the usual estimation of time invariants, the problem studied in this invention is more complex, and therefore challenging and cutting-edge. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 The results are for the simulation trajectory of a time-varying linear formation. Detailed Implementation

[0037] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0038] It should be noted that, in the absence of conflict, the following embodiments and features can be combined with each other; and, based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0039] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0040] To describe richer formation shapes, this invention uses a linear transformation matrix to describe the formation shape, overcoming the limitation that feasible formations are restricted to a predetermined affine image space. Furthermore, it proposes a distributed estimation method to estimate this time-varying linear transformation matrix, thereby achieving the desired time-varying formation maneuvers.

[0041] This application provides a method for estimating parameters of a multi-agent time-varying linear formation, the specific process of which is as follows:

[0042] Step 1: Construct a feasible nominal configuration

[0043] First, let's introduce some concepts used to describe linear formation control:

[0044] Nominal configuration: r = [r1…r n ] T Let f represent a configuration in f-dimensional Euclidean space, where Represents coordinates, r i This represents the nominal configuration of agent i.

[0045] Augmented nominal configuration: Indicates the augmented nominal configuration, in which This represents the augmented nominal configuration of agent i.

[0046] Target formation: target configuration is a vector located in d-dimensional Euclidean space, describing the desired position of the agent. This target configuration is determined by the following linear transformation:

[0047]

[0048] in, It is a linear transformation matrix. It is a translation vector. Ar i b and 'b' represent shape and translation, respectively.

[0049] This application will use a leader-follower framework to achieve the control objective, assuming there are n... l There is one leader, and the rest are followers. The leader knows the expected time-varying linear transformation matrix. Therefore, the desired position can be reached. However, the followers do not know the time-varying matrix. Thus, the followers need to estimate the formation parameters based on the movement of their neighbors to achieve formation control. Therefore, the objective of this time-varying linear formation control is to design an estimator so that each follower can obtain the desired time-varying formation shape parameters A and time-varying translation parameters b.

[0050] Therefore, the first step is to find a feasible nominal configuration, requiring: the navigator's augmented nominal configuration Linear spanning forms an f-dimensional Euclidean space, where

[0051] Step 2: Construct a measurable topology

[0052] First, we define the concept of measurable displacement:

[0053] Displacement measurable: If the edge between navigator j and k can be measured by follower i, then the corresponding topology graph... In the graph, i and j, and i and k must be connected, i.e., they are subgraphs. It must exist, where v i v j and v k Let i, j, and k represent the agents respectively, and let the subgraphs represent the subgraphs. It contains three nodes and two edges, that is in Represents the node set, ε s ={(v j ,v i ),(v k ,v i )} represents the edge set.

[0054] The following topological conditions are given to ensure that the formation parameters are measurable, which require the following two conditions to be met:

[0055] Condition 1: Topological graph among followers It is undirected and connected.

[0056] Condition 2: The nominal alignments corresponding to all measurable displacement edges linearly span an f-dimensional Euclidean space, i.e.

[0057]

[0058] Where, r jk =r j -r k r j and r k This indicates the nominal configuration of navigators j and k.

[0059] Step 3: Design of Time-Varying Formation Shape Parameter Estimator

[0060] Since the navigator knows the desired time-varying linear transformation matrix Therefore, the desired position can be reached, but the follower does not know the changing formation shape parameter A. Therefore, the time-varying formation shape parameter estimator designed in this step is used to estimate the formation parameter A.

[0061] Assume n f The local formation shape parameters of the followers satisfy the following first-order integrator dynamics model:

[0062]

[0063] in, Indicates control input, Let x represent the estimate of agent i for x*, where x is the sum of x* and ... * =vec(A) represents the vectorized formation parameters.

[0064] The applicant discovered that the goal of the estimator is to ensure that all agents obtain correct and consistent formation parameters. To achieve this goal, two conditions need to be met: 1) all agents have consistent estimation results, and 2) the local estimation results do not contradict the local observations, that is, all edges of agent i are the same as the local formations corresponding to the local estimation results. Therefore, in the estimator, g is designed respectively. i and f i To satisfy these two objectives respectively, the following shape parameter estimator was designed:

[0065]

[0066]

[0067] Where α is a positive control gain, and the gain γ i Satisfying γ i >2m i δ2, the gain k satisfies k > δ1, where δ2 represents the upper bound of the navigator's velocity, and δ1 represents the upper bound of the desired time-varying formation change, i.e., δ1 = ||x * ||2,m i The set represents the number of measurable leader displacements for follower i. It consists of all followers who can measure the displacement of the leader, and is a set. It consists of all followers who cannot measure the displacement of the navigator. Let represent the set of all follower neighbors of agent i. The edge p contains all measurable navigators of agent i. jk =p j -p k p j and p k These represent the positions of agents j and k, respectively. The nominal configuration corresponding to the edges of all measurable navigators of agent i. r jk =r j -r k r j and r k Let || || represent the nominal configurations of agents j and k respectively. ∞ I represents the infinite norm. d This represents a d-dimensional identity matrix.

[0068] Step 4: Design of Time-Varying Formation Translation Parameter Estimator

[0069] Since the navigator knows the desired time-varying linear transformation matrix Therefore, the desired position can be reached, but the follower does not know the time-varying translation parameter b. Therefore, the time-varying formation translation parameter estimator designed in this step is used to estimate the translation parameter b.

[0070] Assume n f The local formation shape parameters of the followers satisfy the following first-order integrator dynamics model:

[0071]

[0072] in, Indicates the update rate. This indicates that agent i has a relationship with the formation translation parameter y. * =Estimation of b.

[0073] Based on the estimation results of the local formation parameters, and by comparing the difference between the transformed formation position and the actual position, the following error-driven translation parameter estimator was designed:

[0074]

[0075] Where σ1, σ2, and σ3 are three gains, satisfying σ1 > 0, σ2 > n f δ3, σ3 > 0. Where n f This indicates the number of follower agents. This indicates the upper bound of the change in the translation parameter. Let represent the set of all follower neighbors of agent i. p represents the set of all navigator neighbors of agent i. j This indicates the position of agent j.

[0076] The following assumes that the dynamics of n agents satisfy a first-order integrator dynamics model:

[0077]

[0078] in, Indicates control input, Indicates the location of the agent.

[0079] Based on the estimator's results, the following controller can be used to guide a multi-agent system to the desired formation:

[0080]

[0081] Where ρ is a positive control gain, x iand Let x represent the vectorized formation shape parameters x of agent i respectively. * The estimate and the derivative of the estimate; y i and Let y represent the vectorized formation translation parameters of agent i respectively. * The estimate and the derivative of the estimate, r i and Let represent the nominal formation and the derivative of the nominal formation of agent i, respectively.

[0082] Based on the proposed time-varying formation parameter estimator, and using the given controller, the following simulation experiments were conducted, and the results are as follows: Figure 1 Sixteen intelligent agents performed formation obstacle avoidance maneuvers in the simulation. Figure 1 It demonstrates that multi-agent systems can achieve flexible formation changes to adapt to obstacle environments.

[0083] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for estimating parameters of multi-agent time-varying linear formations, characterized in that, The specific process is as follows: Constructing a feasible nominal configuration: the navigator's nominal configuration Linear spanning forms an f-dimensional Euclidean space; Construct a measurable topology: Make the topology between agents satisfy: (1) the topology between followers For undirected connectivity, (2) the nominal formations corresponding to all displacement-measurable edges are linearly spanned into an f-dimensional Euclidean space; Design of a time-varying formation shape parameter estimator: Based on the fact that all agents have consistent estimation results and all edges of agent i are the same as the local formation corresponding to the local estimation results, a formation state parameter estimator is designed. Design of a time-varying formation translation parameter estimator: By comparing the difference between the transformed formation position and the actual position, a translation parameter estimator is designed. It also includes the design of a controller based on the formation parameter estimator and translation parameter estimator; The controller is designed as follows: Where ρ is a positive control gain, x i and Let x represent the vectorized formation shape parameters x of agent i respectively. * The estimate and the derivative of the estimate; y i and Let y represent the vectorized formation translation parameters of agent i respectively. * The estimate and the derivative of the estimate, r i and Let p represent the nominal formation and the derivative of the nominal formation of agent i, respectively. i I represents the position of agent i. d This represents a d-dimensional identity matrix.

2. The multi-agent time-varying linear formation parameter estimation method according to claim 1, characterized in that, The distributed time-varying formation parameter estimator designed is as follows: Where, x i Indicates agent i's relationship with x * The estimate, x * =vec(A) represents the vectorized formation parameters; α is the positive control gain, and γ is the gain. i Satisfying γ i >2m i δ2, the gain k satisfies k > δ1, where δ2 represents the upper bound of the navigator's velocity, and δ1 represents the upper bound of the desired time-varying formation change, i.e., δ1 = ||x * ||2,m i The set represents the number of measurable leader displacements for follower i. It consists of all followers who can measure the displacement of the leader, and is a set. It consists of all followers who cannot measure the displacement of the navigator. Let represent the set of all follower neighbors of agent i. The edge p contains all measurable navigators of agent i. jk =p j -p k p j and p k These represent the positions of agents j and k, respectively. The nominal configuration corresponding to the edges of all measurable navigators of agent i. r jk =r j -r k r j and r k Let j and k represent the nominal configurations of agents j and k, respectively.

3. The multi-agent time-varying linear formation parameter estimation method according to claim 1, characterized in that, The distributed time-varying formation translation parameter estimator is designed as follows: in, This indicates that agent i has a relationship with the formation translation parameter y. * = b is estimated to have three gains σ1, σ2, and σ3, satisfying σ1 > 0, σ2 > n f δ3, σ3>0, where n f This indicates the number of follower agents. This indicates the upper bound of the change in the translation parameter. Let represent the set of all follower neighbors of agent i. Let i represent the set of all navigator neighbors of agent i.

4. A multi-agent time-varying linear formation parameter estimator, applied to the method described in any one of claims 1-3, characterized in that, The parameter estimator is a distributed time-varying formation parameter estimator. Where α is a positive control gain, and the gain γ i Satisfying γ i >2m i δ2, the gain k satisfies k > δ1, where δ2 represents the upper bound of the navigator's velocity, and δ1 represents the upper bound of the desired time-varying formation change, i.e., δ1 = ||x * ||2,m i The set represents the number of measurable leader displacements for follower i. It consists of all followers who can measure the displacement of the leader, and is a set. It consists of all followers who cannot measure the displacement of the navigator. Let represent the set of all follower neighbors of agent i. The edge p contains all measurable navigators of agent i. jk =p j -p k p j and p k These represent the positions of agents j and k, respectively. The nominal configuration corresponding to the edges of all measurable navigators of agent i. r jk =r j -r k r j and r k Let j and k represent the nominal configurations of agents j and k, respectively.

5. A multi-agent time-varying linear formation parameter estimator, applied to the method described in any one of claims 1-3, characterized in that, The parameter estimator is a distributed time-varying formation translation parameter estimator. Where σ1, σ2, and σ3 are three gains, satisfying σ1 > 0, σ2 > n f δ3, σ3>0, n f This indicates the number of follower agents. This indicates the upper bound of the change in the translation parameter. Let represent the set of all follower neighbors of agent i. Let i represent the set of all navigator neighbors of agent i.

6. A multi-agent time-varying linear formation controller, characterized in that, This controller is implemented based on claims 4-5, controller u i for Where ρ is a positive control gain, x i and Let x represent the vectorized formation shape parameters x of agent i respectively. * The estimate and the derivative of the estimate; y i and Let y represent the vectorized formation translation parameters of agent i respectively. * The estimate and the derivative of the estimate, r i and Let represent the nominal formation and the derivative of the nominal formation of agent i, respectively.

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