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

Abstract

The invention 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: linearly expanding the nominal configuration # imgabs0 # of a navigator into an f-dimensional Euclidean space; a measurable topology is constructed, wherein the topology between the intelligent agents meets the conditions that (1) a topological graph # imgabs1 # between followers is undirected communication, and (2) nominal formations corresponding to all sides with measurable displacement are linearly tensioned into an f-dimensional Euclidean space; designing a time-varying formation shape parameter estimator: designing a formation state parameter estimator on the basis that all agents have consistent estimation results and all edges of the agent i are the same as a local formation corresponding to a local estimation result; and designing a time-varying formation translation parameter estimator: comparing the difference between the transformed formation position and the actual position, and designing the translation parameter estimator.

Description

Technical Field

[0001] The present invention belongs to the field of collaborative control, and in particular relates to a multi-agent time-varying linear formation parameter estimation method and a parameter estimator. Background Art

[0002] Using correlation information to calculate target information is the basic idea of ​​estimation. In recent years, multi-agent systems have developed vigorously, and the problem of collaborative estimation of multi-agents has also come into people's attention. For example, the problem of collaborative positioning based on UWB requires a group of agents to collaboratively determine the direction of the target based on the distance information between themselves and the target.

[0003] Formation control, as an elegant way to describe the collaborative behavior of multiple agents, also has the problem of collaborative estimation, such as estimating the current size parameters of the formation based on the changes in neighbors. However, the size parameter is a simple single parameter. In the affine formation control proposed in recent years, an affine transformation matrix can be used to describe the formation. The estimation of the affine transformation matrix is ​​much more difficult, and there is no research on related estimation methods. Summary of the invention

[0004] Aiming at the problem of multi-agent collaborative control, the present invention proposes a multi-agent 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] In the first aspect, the embodiment of the present application provides a method for estimating parameters of a multi-agent time-varying linear formation, and the specific process is as follows:

[0007] Constructing a feasible nominal configuration: the nominal configuration of the navigator l Linearly span f-dimensional Euclidean space;

[0008] Construct a measurable topology: Make the topology between agents satisfy: (1) Topological graph between followers is undirectedly connected, (2) the nominal formations corresponding to all edges with measurable displacements are linearly spanned into an f-dimensional Euclidean space;

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

[0010] Design of time-varying formation translation parameter estimator: Compare the difference between the transformed formation position and the actual position, and design the translation parameter estimator.

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

[0012]

[0013] Among them, α is a positive control gain, and the gain γ i Satisfaction i >2m i δ 2 , the gain k satisfies k>δ 1 , where δ 2 represents the upper bound of the leader’s speed, δ 1 represents the upper bound of the expected time-varying formation, that is, δ 1 =||x * || 2 , m i represents the number of leader displacements that can be measured by follower i, the set It consists of all followers that can measure the displacement of the leader, the set It consists of all followers that cannot measure the displacement of the leader, represents the set of all follower neighbors of agent i, The edges containing all leaders that agent i can detect, p jk =p j -p k , p j and p k denote the positions of agents j and k respectively, The nominal configuration corresponding to the edge containing all leaders that agent i can detect, r jk =r j -r k , r j and r k denote the nominal configurations of agents j and k, respectively, || || ∞ represents the infinite norm, I d represents the d-dimensional identity matrix.

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

[0015]

[0016] where σ 1 , σ 2 and σ 3 For three gains, satisfying σ 1 >0,σ 2 >n f δ 3 , σ 3 >0. Among them, n f represents the number of follower agents, represents the upper bound of the translation parameter change, represents the set of all follower neighbors of agent i, represents the set of all leader neighbors of agent i.

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

[0018] Furthermore, the controller of the present invention is designed as follows:

[0019]

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

[0021] In a second aspect, the present application provides a multi-agent time-varying linear formation parameter estimator, wherein the parameter estimator is a distributed time-varying formation parameter estimator.

[0022]

[0023]

[0024] Among them, α is a positive control gain, and the gain γ i Satisfaction i >2m i δ 2 , the gain k satisfies k>δ 1 , where δ 2 represents the upper bound of the leader’s speed, δ 1 represents the upper bound of the expected time-varying formation, that is, δ 1 =||x * || 2 , m i represents the number of leader displacements that can be measured by follower i, the set It consists of all followers that can measure the displacement of the leader, the set It consists of all followers that cannot measure the displacement of the leader, represents the set of all follower neighbors of agent i, The edges containing all leaders that agent i can detect, p jk=p j -p k , p j and p k denote the positions of agents j and k respectively, The nominal configuration corresponding to the edge containing all leaders that agent i can detect, r jk =r j -r k , r j and r k denote the nominal configurations of agents j and k, respectively.

[0025] In a third aspect, an embodiment of the present application provides a multi-agent time-varying linear formation parameter estimator, wherein the parameter estimator is a distributed time-varying formation translation parameter estimator.

[0026]

[0027] Among them, σ 1 , σ 2 and σ 3 For three gains, satisfying σ 1 >0,σ 2 >n f δ 3 , σ 3 >0,n f represents the number of follower agents, represents the upper bound of the translation parameter change, represents the set of all follower neighbors of agent i, represents the set of all leader neighbors of agent i.

[0028] In a fourth aspect, the present application embodiment provides a multi-agent time-varying linear formation controller, the controller u i for

[0029]

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

[0031] Beneficial effects:

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

[0033] Second, the present invention can solve the problem of collaborative estimation of local incomplete measurements. Specifically, the formation parameter information to be estimated in the present invention cannot be fully acquired by one intelligent agent. Compared with those that can be fully acquired, such as formation scaling parameters and rotation parameters, it is more complex. The distributed estimation method proposed in the present invention can solve this challenging problem, and is therefore theoretically advanced.

[0034] Third, the estimated quantity considered in the present invention is time-varying. Compared with the usual estimation of time-invariant variables, the problem studied in the present invention is more complex and therefore challenging and cutting-edge. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, 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 invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0036] Figure 1 This is the simulation trajectory result of time-varying linear formation. DETAILED DESCRIPTION

[0037] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0038] It should be noted that the following embodiments and features in the embodiments may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

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

[0040] In order to describe richer formation shapes, the present invention uses a linear transformation matrix to describe the formation shape, breaking through the defect that the feasible formation is limited to a predetermined affine image space, and proposes a distributed estimation method for estimating the time-varying linear transformation matrix, thereby realizing the desired time-varying formation maneuver.

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

[0042] Step 1: Construct a feasible nominal configuration

[0043] First, some concepts used to describe linear formation control:

[0044] Nominal configuration: r = [r 1 …r n ] T represents a configuration in f-dimensional Euclidean space, where Represents coordinates, r i represents the nominal configuration of agent i.

[0045] Augmented nominal configuration: represents the augmented nominal configuration, where represents the augmented nominal configuration of agent i.

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

[0047]

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

[0049] This application will use a leader-follower framework to achieve the control goal. Assume that there are n l There are leaders, and the rest are followers. The leader knows the expected time-varying linear transformation matrix Therefore, the desired position can be reached, but the follower does not know the time-varying matrix. Therefore, the follower needs to estimate the formation parameters according to the movement of the neighbors to achieve formation control. Therefore, the task goal of this time-varying linear formation control is to design an estimator so that each follower can obtain the desired time-varying formation shape parameter A and time-varying translation parameter b.

[0050] To this end, we first need to find a feasible nominal configuration, requiring: the augmented nominal configuration of the navigator Linearly spans an f-dimensional Euclidean space, where

[0051] Step 2: Build a testable topology

[0052] First, the concept of measurable displacement is given:

[0053] Displacement is measurable: If the edge between leaders j and k can be measured by follower i, then the corresponding topological graph In the graph, i and j, i and k must be connected, that is, the subgraph There must exist, where v i , v j and v k Represents agents i, j and k respectively, subgraph Contains three nodes and two edges, namely in represents a node set, ε s ={(v j ,v i ),(v k ,v i )} represents an edge set.

[0054] The following are the topological conditions to ensure that the formation parameters are measurable. The following two conditions need to be met:

[0055] Condition 1: Topology between followers is undirectedly connected.

[0056] Condition 2: The nominal formations corresponding to all edges with measurable displacements are linearly spanned into an f-dimensional Euclidean space, that is

[0057]

[0058] Among them, r jk =r j -r k , r j and r k represents the nominal configuration of pilots j and k.

[0059] Step 3: Design of time-varying formation shape parameter estimator

[0060] Since the pilot knows the expected time-varying linear transformation matrix Therefore, the desired position can be reached, but the follower does not know the variable 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 that n f The local force shape parameters of each follower satisfy the following first-order integrator dynamic model:

[0062]

[0063] in, represents the control input, represents agent i’s estimate of x*, x * =vec(A) represents the vectorized formation parameters.

[0064] The applicant has found that the goal of the estimator is to make 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 are consistent with the local observations, that is, all sides of agent i are the same as the local formation corresponding to the local estimation results. Therefore, in the estimator, g i and f i In order to meet these two goals respectively, the following shape parameter estimator is designed:

[0065]

[0066]

[0067] Among them, α is a positive control gain, and the gain γ i Satisfaction i >2m i δ 2 , the gain k satisfies k>δ 1 , where δ 2 represents the upper bound of the leader’s speed, δ 1 represents the upper bound of the expected time-varying formation, that is, δ 1 =||x * || 2 , mi represents the number of leader displacements that can be measured by follower i, the set It consists of all followers that can measure the displacement of the leader, the set It consists of all followers that cannot measure the displacement of the leader, represents the set of all follower neighbors of agent i, The edges containing all leaders that agent i can detect, p jk =p j -p k , p j and p k denote the positions of agents j and k respectively, The nominal configuration corresponding to the edge containing all leaders that agent i can detect, r jk =r j -r k , r j and r k denote the nominal configurations of agents j and k, respectively, || || ∞ represents the infinite norm, I d represents the d-dimensional identity matrix.

[0068] Step 4: Design of time-varying formation translation parameter estimator

[0069] Since the pilot knows the expected time-varying linear transformation matrix So 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 that n f The local force shape parameters of each follower satisfy the following first-order integrator dynamic model:

[0071]

[0072] in, represents the update rate, Represents the translation parameter y of the formation by agent i * = an estimate of b.

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

[0074]

[0075] Among them, σ 1 , σ 2 and σ 3 For three gains, satisfying σ1 >0,σ 2 >n f δ 3 , σ 3 >0. Among them, n f represents the number of follower agents, represents the upper bound of the translation parameter change, represents the set of all follower neighbors of agent i, represents the set of all the leaders’ neighbors of agent i, p j represents the position of agent j.

[0076] It is assumed that the dynamics of n agents satisfy the first-order integrator dynamics model:

[0077]

[0078] in, represents the control input, Represents the position of the agent.

[0079] Based on the estimation results of the estimator, the following controller can be used to make the multi-agent system reach the desired formation:

[0080]

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

[0082] Based on the proposed time-varying formation parameter estimator and the given controller, the following simulation experiments were carried out. The results are as follows Figure 1 , 16 agents perform formation obstacle avoidance maneuvers simulation, Figure 1 It is demonstrated that the multi-agent system can achieve flexible formation changes to adapt to obstacle environments.

[0083] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A multi-agent time-varying linear formation parameter estimation method, characterized in that: The specific process is: Constructing a feasible nominal configuration: the nominal configuration of the navigator Linearly span f-dimensional Euclidean space; Construct a measurable topology: Make the topology between agents satisfy: (1) Topological graph between followers is undirectedly connected, (2) the nominal formations corresponding to all edges with measurable displacements are linearly spanned into an f-dimensional Euclidean space; Design of time-varying formation shape parameter estimator: Based on the fact that all agents have consistent estimation results and all sides of agent i have the same local formation as the local estimation results, a formation state parameter estimator is designed; Design of time-varying formation translation parameter estimator: Compare the difference between the transformed formation position and the actual position, and design the translation parameter estimator.

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 designed as: Among them, x i Represents agent i's response to x * The estimate of x * =vec(A) represents the vectorized formation parameter; α is a positive control gain, and the gain γ i Satisfaction i >2m i δ2, the gain k satisfies k>δ1, where δ2 represents the upper bound of the leader's speed, and δ1 represents the upper bound of the expected time-varying formation, that is, δ1=||x * ||2, m i represents the number of leader displacements that can be measured by follower i, the set It consists of all followers that can measure the displacement of the leader, the set It consists of all followers that cannot measure the displacement of the leader, represents the set of all follower neighbors of agent i, The edges containing all leaders that agent i can detect, p jk =p j -p k , p j and p k denote the positions of agents j and k respectively, The nominal configuration corresponding to the edge containing all leaders that agent i can detect, r jk =r j -r k , r j and r k denote 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 designed is designed as: in, Represents the translation parameter y of the formation by agent i * =b's estimates σ1, σ2 and σ3 are three gains, satisfying σ1>0, σ2>n f δ3,σ3>0, where n f represents the number of follower agents, represents the upper bound of the translation parameter change, represents the set of all follower neighbors of agent i, represents the set of all leader neighbors of agent i.

4. The method for estimating parameters of a multi-agent time-varying linear formation according to any one of claims 1 to 3, characterized in that: It also includes designing a controller based on the formation parameter estimator and the translation parameter estimator.

5. The multi-agent time-varying linear formation parameter estimation method according to claim 4, characterized in that: The controller is designed as follows: Where ρ is a positive control gain, x i and They represent the quantized formation shape parameters x of agent i respectively. * The estimate and derivative of the estimate; y i and They represent the translation parameters y of the quantized formation for agent i respectively. * The estimate and estimated derivative of r i and denote the nominal formation and nominal formation derivative of agent i respectively.

6. A multi-agent time-varying linear formation parameter estimator, characterized in that: The parameter estimator is a distributed time-varying formation parameter estimator, Among them, α is a positive control gain, and the gain γ i Satisfaction i >2m i δ2, the gain k satisfies k>δ1, where δ2 represents the upper bound of the leader's speed, and δ1 represents the upper bound of the expected time-varying formation, that is, δ1=||x * ||2, m i represents the number of leader displacements that can be measured by follower i, the set It consists of all followers that can measure the displacement of the leader, the set It consists of all followers that cannot measure the displacement of the leader, represents the set of all follower neighbors of agent i, The edges containing all leaders that agent i can detect, p jk =p j -p k , p j and p k denote the positions of agents j and k respectively, The nominal configuration corresponding to the edge containing all leaders that agent i can detect, r jk =r j -r k , r j and r k denote the nominal configurations of agents j and k, respectively.

7. A multi-agent time-varying linear formation parameter estimator, characterized in that: The parameter estimator is a distributed time-varying formation translation parameter estimator, Among them, σ1, σ2 and σ3 are three gains, satisfying σ1>0, σ2>n f δ3,σ3>0,n f represents the number of follower agents, represents the upper bound of the translation parameter change, represents the set of all follower neighbors of agent i, represents the set of all leader neighbors of agent i.

8. A multi-agent time-varying linear formation controller, characterized in that: The controller is implemented based on claims 6-7. i for Where ρ is a positive control gain, x i and They represent the quantized formation shape parameters x of agent i respectively. * The estimate and derivative of the estimate; y i and They represent the translation parameters y of the quantized formation for agent i respectively. * The estimate and estimated derivative of r i and denote the nominal formation and nominal formation derivative of agent i respectively.

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