Linear formation cooperative control method and device

Abstract

The invention discloses a linear formation cooperative control method and device, and belongs to the technical field of cooperative control. The method specifically comprises the following steps of: 1, selecting nl agents from multiple agents as pilots, and constructing a feasible nominal configuration r; 2, setting an interactive stress matrix omega, wherein the stress matrix and the nominal configuration r meet a stress balance relationship; and step 3, according to the interaction stress matrix omega, carrying out distributed linear formation controller design.

Description

Technical Field

[0001] This invention belongs to the field of cooperative control technology, specifically relating to a linear formation cooperative control method and device. Background Technology

[0002] With the development of individual autonomous intelligence technology, the demand for multi-agent systems has become increasingly apparent. Compared to a single agent, the collaborative cooperation of multiple agents can significantly enhance task execution efficiency; for example, collaborative exploration by multiple UAVs can accelerate a swarm's understanding of unknown environments. Formation control, as a method for managing large-scale swarms, has attracted widespread attention. The goal of formation control is to guide a group of agents to a specified desired formation, and changes in formation can enhance the flexibility and maneuverability of the formation.

[0003] Affine formation control methods construct a stress matrix to describe the interaction weights between agents and design a distributed formation control method that enables the formation to achieve the desired affine transformation. However, due to the limited types of affine transformations, the number of feasible formations is also limited. Summary of the Invention

[0004] In view of this, the present invention proposes a linear formation cooperative control method and device for the multi-agent cooperative control problem. By setting an interactive stress matrix, richer formation transformations can be achieved.

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

[0006] Firstly, this application provides an embodiment of a linear formation cooperative control method, the specific process of which is as follows:

[0007] Step 1: Select n from the multi-agent pool l One acts as the leader, constructing a feasible nominal configuration r;

[0008] Step 2: Define the interactive stress matrix Ω, which satisfies the stress balance relationship with the nominal configuration r;

[0009] Step 3: Design a distributed linear formation controller based on the interaction stress matrix Ω.

[0010] Furthermore, the feasible nominal configuration described in this invention is: the navigator's augmented nominal configuration r l Linear spanning forms an f-dimensional Euclidean space, where

[0011] Furthermore, the stress balance relationship described in this invention is as follows:

[0012]

[0013] in, Represents the Kronecker product, r represents the feasible nominal configuration, and I f Let f represent the f-dimensional identity matrix.

[0014] Furthermore, in step two of this invention, the constructed stress matrix Ω is required to satisfy the following two conditions:

[0015] Condition 1: For the framework Its corresponding stress matrix Ω is positive semi-definite and satisfies rank(Ω) = nf⁻¹, where r represents the nominal configuration. This represents the connection topology graph between agents, where n represents the number of agents;

[0016] Condition 2: Ω ff It is a non-singular matrix, where Ω ff The blocks of Ω correspond to the followers, i.e.

[0017]

[0018] Furthermore, in step three of this invention, the designed distributed formation controller is as follows:

[0019]

[0020] Where, k f A positive control gain Let p represent the set of neighbors of agent i. i and p j ω represents the positions of agents i and j respectively. ij This represents the element in row i and column j of the stress matrix Ω.

[0021] Secondly, according to an embodiment of this application, a linear formation cooperative control device includes:

[0022] The nominal configuration model is used to select n from a multi-agent system. l One acts as the leader, constructing a feasible nominal configuration r;

[0023] The stress matrix module is used to set the interactive stress matrix Ω, and the stress matrix satisfies the stress balance relationship with the nominal configuration r.

[0024] The controller is configured to calculate the distributed formation control input u based on the interaction stress matrix Ω. i To achieve linear formation cooperative control;

[0025]

[0026] Where, k f A positive control gain Let p represent the set of neighbors of agent i. i and pj ω represents the positions of agents i and j respectively. ij This represents the element in row i and column j of the stress matrix Ω.

[0027] Beneficial effects:

[0028] This invention, by setting a stress matrix, allows followers to autonomously follow the desired formation determined by the navigator based on the stress matrix relationship, enabling multiple formation switching. Compared to traditional formation control methods that require broadcasting the desired formation for formation switching, this invention requires less information and is more lightweight. Attached Figure Description

[0029] 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.

[0030] Figure 1 The results are for the simulation trajectory of a linear formation.

[0031] Figure 2 This represents the convergence result of the formation position error. Detailed Implementation

[0032] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0033] 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.

[0034] 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 can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on this disclosure, it should be understood by those skilled in the art that an 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 described herein can be used to implement an apparatus and / or practice a method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this apparatus and / or practice this method.

[0035] This application provides a distributed formation control method based on linear transformation, the specific process of which is as follows:

[0036] Step 1: Construct a feasible nominal configuration

[0037] Select n from the multi-agent group l As a leader, construct a feasible nominal configuration r.

[0038] First, let's introduce some concepts used to describe linear formation control:

[0039] Nominal configuration: r = [r1…r n ] T Let f represent a configuration in f-dimensional Euclidean space, where Represents coordinates.

[0040] Framework: A framework located in f-dimensional Euclidean space. It consists of a nominal configuration r and a topological graph Composed of various elements.

[0041] Augmented nominal configuration: Indicates the augmented nominal configuration, in which

[0042] 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:

[0043]

[0044] in, It is a linear transformation matrix. It is a translation vector. Ar i b and 'b' represent shape and translation, respectively.

[0045] Assume the dynamics of n agents satisfy a first-order integrator dynamics model:

[0046]

[0047] in, Indicates control input, Indicates the location of the agent.

[0048] The control objective will be achieved using a leader-follower framework, assuming there are n... l There is one leader, and the rest are followers. The leader guides the expected linear transformation matrix. Therefore, the desired position can be reached, but the follower does not know this matrix and thus needs to move according to the actions of its neighbors. Therefore, the objective of linear formation control is to design the control input u... i This allows the follower agents to reach the desired formation, i.e. t→+∞.

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

[0051] Step 2: Design of Interactive Stress Matrix

[0052] To achieve linear formation control, a suitable stress matrix needs to be defined. The stress matrix Ω is defined as follows:

[0053]

[0054] Where, ω ij This represents the interaction weights between agents i and j. Let i represent the set of neighbors of agent i.

[0055] Since the stress matrix is ​​for the nominal configuration, the following stress balance relationship must be satisfied:

[0056]

[0057] in, Indicates the Kronecker product. r indicates the nominal configuration, I f Represents an f-dimensional identity matrix;

[0058] For this stress matrix Ω, it is required to satisfy the following two conditions:

[0059] Condition 1: For the framework Its corresponding stress matrix is ​​positive semi-definite and satisfies:

[0060] rank(Ω) = nf-1

[0061] Where f is the dimension of the nominal configuration linearly spanned Euclidean space, and n represents the total number of agents in the formation;

[0062] Condition 2: Ω ff It is a non-singular matrix, where Ω ff The blocks of Ω correspond to the followers, i.e.

[0063]

[0064] In the stress matrix Ω above, the larger id represents the follower and the smaller id represents the leader. The resulting stress matrix adopts the block form shown above.

[0065] Step 3: Design a distributed linear formation controller based on the stress matrix Ω.

[0066] Based on the stress balance relationship in step two It was noted that the equation still holds after a linear transformation of the equilibrium relationship, i.e., by multiplying both sides by matrix A. At this point, the stress equilibrium relationship after the linear transformation becomes the relationship between the formation position coordinates. Based on this characteristic, a formation controller was designed.

[0067] Based on the stress matrix constructed in step two, this step proposes the following distributed formation controller:

[0068]

[0069] Among them, k f For a positive control gain, Let p represent the set of neighbors of agent i. i and p j ω represents the positions of agents i and j respectively. ij This represents the element in row i and column j of the stress matrix Ω.

[0070] Secondly, according to an embodiment of this application, a linear formation cooperative control device includes:

[0071] The nominal configuration model is used to select n from a multi-agent system. l One acts as the leader, constructing a feasible nominal configuration r;

[0072] The stress matrix module is used to set the interactive stress matrix Ω, and the stress matrix satisfies the stress balance relationship with the nominal configuration r.

[0073] The controller is configured to calculate the distributed formation control input u based on the interaction stress matrix Ω. i To achieve linear formation cooperative control;

[0074]

[0075] Among them, k f For a positive control gain, Let p represent the set of neighbors of agent i. i and p j ω represents the positions of agents i and j respectively. ij This represents the element in row i and column j of the stress matrix Ω.

[0076] The present invention can realize rich formation transformations. Compared with the affine formation control method, which only supports a square transformation matrix, the method proposed in this invention supports a rectangular transformation matrix A, which is more general and universal.

[0077] A simulation experiment was conducted using this linear formation controller, and the results are as follows: Figures 1-2 As shown, a simulation of 10 agents switching between formations is performed. Figure 1 The trajectory during the formation switching process was shown. Figure 2 The convergence of position error after each formation switch is demonstrated, and the results show that the position error converges to zero after each formation switch.

[0078] 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 linear formation cooperative control method, characterized in that: The specific process is: Step 1: Select n from multiple agents l As a pilot, construct a feasible nominal configuration r; Step 2: Set the interaction stress matrix Ω, and the stress matrix and the nominal configuration r satisfy the stress equilibrium relationship; Step 3: Design a distributed linear formation controller based on the interaction stress matrix Ω.

2. The linear formation cooperative control method according to claim 1, characterized in that: The feasible nominal configuration is: the augmented nominal configuration of the navigator Linearly spans an f-dimensional Euclidean space, where 3. The linear formation cooperative control method according to claim 1, characterized in that: The stress balance relationship is: in, represents the Kronecker product, r represents the feasible nominal configuration, I f represents the f-dimensional identity matrix.

4. The linear formation cooperative control method according to claim 1, characterized in that: In step 2, the stress matrix Ω is required to meet the following two conditions: Condition 1: Targeting the framework The corresponding stress matrix Ω is semi-positive definite and satisfies rank(Ω)=nf-1, where r represents the nominal configuration, represents the connection topology between agents, and n represents the number of agents; Condition 2: Ω ff is a non-singular matrix, where Ω ff is a block of Ω, corresponding to the follower, that is, 5. The linear formation cooperative control method according to claim 4, characterized in that: In step 3, the designed distributed formation controller is: Among them, k f is a positive control gain, represents the neighbor set of agent i, p i and p j denote the positions of agents i and j respectively, ω ij Represents the element in the stress matrix Ω located in row i and column j.

6. A linear formation cooperative control device, characterized in that: include: Nominal configuration model for selecting n from multiple agents l As a pilot, construct a feasible nominal configuration r; The stress matrix module is used to set the interaction stress matrix Ω, which satisfies the stress equilibrium relationship between the stress matrix and the nominal configuration r; A controller is used to calculate the distributed formation control input u according to the interaction stress matrix Ω i , achieving coordinated control of linear formations; Among them, k f is a positive control gain, represents the neighbor set of agent i, p i and p j denote the positions of agents i and j respectively, ω ij Represents the element in the stress matrix Ω located in row i and column j.

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