Multi-agent linear formation design method and device

Abstract

The invention belongs to the technical field of cooperative control, and particularly relates to a multi-agent linear formation design method and device. The specific process of the method comprises the following steps: step 1, selecting multiple agents from multiple agents as pilots, and constructing a feasible nominal configuration; 2, constructing a formation mapping relation between a navigator and a follower based on the changed configuration; and step 3, based on the mapping relation, performing linear formation optimization design.

Description

Technical Field

[0001] The present invention belongs to the technical field of collaborative control, and specifically relates to a multi-agent linear formation design method and device. Background Art

[0002] Collaboration between agents can enhance work efficiency. Classically, the collaborative control of multiple agents has been studied in depth for nearly 20 years and has been widely used in tasks such as regional surveillance, collaborative search, and cooperative transportation. Formation control, as an important collaborative control technology, has also attracted widespread attention. There have been many studies on how to converge the formation to the desired formation, but the research on how to design the desired formation is not sufficient. Although the desired position of each agent can be assigned, such as the light show of a drone, such a design lacks the ability to adapt to the environment. The formation design method based on optimization can find a set of the most suitable formation maneuvering solutions, so it is considered to be the preferred method for solving the formation design problem. Summary of the invention

[0003] This application aims at the problem of multi-agent collaborative control and proposes a multi-agent linear formation design method and device, which can realize linear formation optimization and support the design of more formations.

[0004] The technical solution for implementing the present invention is as follows:

[0005] In the first aspect, the embodiment of the present application provides a multi-agent linear formation design method, the specific process is:

[0006] Step 1: Select multiple agents from the multi-agents as navigators to construct a feasible nominal configuration;

[0007] Step 2: Based on the transformation configuration, a formation mapping relationship between the leader and the follower is constructed;

[0008] Step 3: Based on the mapping relationship, perform linear formation optimization design.

[0009] Furthermore, in step 1 of the present invention, the nominal configuration to be constructed is required to meet the following conditions: Linearly spans f-dimensional space, where

[0010] Furthermore, in step 2 of the present invention, the mapping relationship between the leader and a single follower is:

[0011]

[0012] in, represents the augmented nominal formation of agent i, represents the target formation of all navigators, represents the target formation of agent i, I d represents the d-dimensional identity matrix, Represents a linear formation The vector representation of .

[0013] Furthermore, in step 3 of the present invention, the formation optimization problem of the design is:

[0014]

[0015] Among them, l k >0, l>0 represent the safe distance between agents and between agents and obstacles, respectively. is a preset reference formation, Q is a positive definite gain diagonal matrix, and represents the target formation of agent i and agent j, q k represents the position of obstacle k.

[0016] In a second aspect, an embodiment of the present application provides a multi-agent linear formation design device, which optimizes according to the following formation optimization problem to obtain:

[0017]

[0018] Among them, l k >0, l>0 represent the safe distance between agents and between agents and obstacles, respectively. is the preset reference formation, Q is a positive definite gain diagonal matrix, and represents the target formation of agent i and agent j, q k represents the position of obstacle k.

[0019] Beneficial effects:

[0020] First, the present invention solves the formation design problem of linear formation. In the linear formation control problem, since the formation between intelligent agents is managed by the linear transformation matrix, the position of the intelligent agent cannot be optimized directly, and it is necessary to build the relationship between the position of the intelligent agent and the linear transformation matrix to indirectly design the formation. Therefore, it is complex and challenging. The present invention analyzes the formation mapping relationship between the leader and the follower to perform linear formation optimization design, so it can support the design of more formations.

[0021] Second, 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 a square transformation matrix, the method proposed in the present invention expands the transformation matrix, supports more types of formations, and is more general and universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] 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.

[0023] Figure 1 This is the simulation trajectory result of time-varying linear formation. DETAILED DESCRIPTION

[0024] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0025] 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.

[0026] 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.

[0027] The linear formation control method is a formation control method of a leader-follower architecture, and the transformation of its formation is determined by a linear transformation matrix. Therefore, the present invention proposes a design method of the linear transformation matrix according to the environment in which the multi-agent system is located, that is, a formation design method, which can design a smooth and continuously changing time-varying formation for the multi-agent system to adapt to the dynamic environment. The embodiment of the present application is a multi-agent linear formation formation design method, and the specific process is:

[0028] Step 1: Construct a feasible nominal configuration

[0029] First, some concepts used to describe linear formation control:

[0030] Nominal configuration: r = [r1…r n ] Trepresents a configuration in f-dimensional Euclidean space, where Represents coordinates.

[0031] Augmented nominal configuration: represents the augmented nominal configuration, where

[0032] 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:

[0033]

[0034] in, is a linear transformation matrix, is a translation vector, Ar i and b represent the shape and translation, respectively.

[0035] 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. According to the environment, a linear formation will be designed for these agents, that is, Used to achieve obstacle avoidance maneuvers.

[0036] To this end, we first need to find a feasible nominal configuration, requiring: the augmented nominal configuration of the navigator Linearly spans f-dimensional space, where

[0037] Step 2: Construct a formation mapping relationship between the leader and the followers

[0038] Under the feasible nominal configuration relationship, the leader and follower have a unique target formation mapping:

[0039]

[0040] in, represents the augmented nominal formation of agent i, and Represent the target formations of all leaders and all followers, namely

[0041]

[0042] in, Represents the target formation of agent i.

[0043] According to the definition of the target formation, the following relationship can be obtained:

[0044]

[0045] in, express MP inverse of the matrix, I d represents the d-dimensional identity matrix, Representation Matrix The vector representation of .

[0046] Therefore, the mapping relationship between the leader and a single follower is:

[0047]

[0048] in,

[0049] Step 3: Linear formation optimization design

[0050] According to the results of step 2, the target formation of all agents can be expressed by the target formation of the leader. Therefore, the constraints constructed in step 2 are integrated into the following optimization problem for formation design:

[0051]

[0052] Among them, l k >0 and l>0 represent the safe distance between agents and between agents and obstacles, respectively. is a preset reference formation, and Q is a positive definite gain diagonal matrix. and represents the target formation of agent i and agent j, q k Represents the obstacle coordinates.

[0053] The expected formation is given by p * Determine, solve the optimization problem, and get a set of p * , and p * and The relationship between can be determined by the relationship given in step 2. Therefore, by solving the above optimization problem, the desired linear formation can be obtained. The following simulation experiment is conducted, considering the obstacle avoidance formation task of 5 intelligent agents. Figure 1 The maneuverability of the designed formation is demonstrated, and it can be seen that the agent can flexibly avoid obstacles and safely reach the target point, which proves the effectiveness of the formation design method.

[0054] 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 linear formation design method, characterized in that: The specific process is: Step 1: Select multiple agents from the multi-agents as navigators to construct a feasible nominal configuration; Step 2: Based on the transformation configuration, a formation mapping relationship between the leader and the follower is constructed; Step 3: Based on the mapping relationship, perform linear formation optimization design.

2. The multi-agent linear formation design method according to claim 1, characterized in that: In step 1, the nominal configuration to be constructed is required to meet the following conditions: Linearly spans f-dimensional space, where 3. The multi-agent linear formation design method according to claim 1, characterized in that: In step 2, the mapping relationship between the leader and a single follower is: in, represents the augmented nominal formation of agent i, represents the target formation of all navigators, represents the target formation of agent i, I d represents the d-dimensional identity matrix, Represents a linear formation The vector representation of .

4. The multi-agent linear formation design method according to claim 1, characterized in that: In step 3, the formation optimization problem of the design is: Among them, l k >0, l>0 represent the safe distance between agents and between agents and obstacles, respectively. is a preset reference formation, Q is a positive definite gain diagonal matrix, and represents the target formation of agent i and agent j, q k represents the position of obstacle k.

5. A multi-agent linear formation design device, characterized in that: The device is optimized according to the following formation optimization problem, and the result is: Among them, l k >0, l>0 represent the safe distance between agents and between agents and obstacles, respectively. is the preset reference formation, Q is a positive definite gain diagonal matrix, and represents the target formation of agent i and agent j, q k represents the position of obstacle k.

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