CN114115334A - Multi-agent formation control method under visual field angle constraint condition - Google Patents

Abstract

The multi-agent formation control method under the constraints of the viewing angle of the present disclosure, by establishing an agent system model; constructing an angular velocity controller of an orientation agent based on the agent system model; Constraints on the viewing angle; under the condition that the orientation agent satisfies the viewing angle constraints, the linear velocity control law of the orientation agent is established according to the position of the orientation agent; the switching function of the distance agent is designed, and according to the switching function and the multi-agent system The model establishes the linear velocity control law of the distance agent; according to the linear velocity control law of the azimuth agent and the linear velocity control law of the distance agent, the formation of multiple agents is controlled under the constraints of the viewing angle. Under the condition that the agent only has orientation information but no position information or distance information, the agent can choose relatively few paths to move from the undesired side to the desired side, and finally move to the desired position, so as to realize the view angle constraint Formation, maintenance and transformation of multi-agent formations.

Description

A multi-agent formation control method under the constraint of viewing angle

technical field

The invention belongs to the technical field of multi-agent control, in particular to a multi-agent formation control method under the condition of viewing angle constraints.

Background technique

Due to the large number of practical applications of multi-agent cooperative control in search and rescue in complex and dangerous environments, cooperative operations in industrial production, and agent entertainment performance in recent years, the research on multi-agent cooperative control has received a lot of attention from academia and academia. industry wide attention. When performing search tasks in complex environments, multi-agent formation technology plays an important role in expanding the search range, improving search efficiency, and improving the accuracy of target recognition; when agents fly at high altitudes, formation flying can not only enhance the stability of the system , but also reduce the overall energy consumption. Therefore, there has been a lot of research on formation formation maintenance. However, at present, most studies consider ideal conditions, and rarely consider the limitation of measurement range. For example, cameras generally used to obtain azimuth information are usually not omnidirectional, but have a certain field of view.

For the formation control problem under the constraint of viewing angle, there are the following main solutions: Scheme 1: Reference "Li X, Tan Y, Mareels I, et al. Compatible formation set for uavs with visual sensing constraint [C] .In 2018Annual American Control Conference (ACC), 2018:2497–2502.”, by introducing the concept of barrier function (barrier function) to ensure that the agent is moving, its neighbor agents are always within the field of vision, but this This method assumes that the viewing angle is 300° and the viewing distance is large enough (that is, the limited viewing distance can be ignored) to ensure that the entire formation topology is fully connected, and each agent needs to be able to obtain the relative position of the neighboring agents. information. The designed control method realizes the formation and maintenance of formation.

F.Bearing-only formation controlwith limited visual sensing:Two agent case[J].IFAC-PapersOnLine,2018,51(23):28–33.”中，在基于方位角控制的基础上，考虑了两架智能体的情况下，加入朝向角控制，使得另一架智能体始终在视野角的中央位置，从而完成编队任务。所设计的控制方法能够实现队形的形成和保持。Scenario 2: Literature "Frank D, Zelazo D,

In F.Bearing-only formation control with limited visual sensing:Two agent case[J].IFAC-PapersOnLine,2018,51(23):28–33.”, on the basis of azimuth control, two intelligent In the case of an agent, the orientation angle control is added, so that the other agent is always in the center of the viewing angle, so as to complete the formation task. The designed control method can realize the formation and maintenance of the formation.

Scheme 3: In the document "Renaud P, Cervera E, Martiner P. Towards a reliable vision-based mobile robot formation control [C]. In 2004IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2004:3176–3181." , under the condition of vision, a reliable vision-based formation control method is proposed, which adopts the pilot-following control strategy to realize the one-word formation movement of multiple robots.

SUMMARY OF THE INVENTION

The invention overcomes one of the deficiencies of the prior art, and provides a multi-agent formation control method under the condition of viewing angle constraints, which can make intelligent agents only have orientation information but no position information or distance information. The body chooses relatively few paths to move from the undesired side to the desired side, and finally to the desired position, so as to realize the formation, maintenance and transformation of multi-agent formations under the constraint of viewing angle.

According to an aspect of the present disclosure, the present invention provides a multi-agent formation control method under the condition of viewing angle constraints, the method comprising:

establishing an agent system model, wherein the agent includes an orientation agent and a distance agent;

constructing an angular velocity controller of an azimuth agent based on the agent system model;

Using the angular velocity controller of the orientation agent to control the orientation agent to satisfy the viewing angle constraint;

Under the condition that the orientation agent satisfies the viewing angle constraint, the linear velocity control law of the orientation agent is established according to the position of the orientation agent;

Designing the distance agent switching function, and establishing the linear velocity control law of the distance agent according to the switching function and the multi-agent system model;

According to the linear velocity control law of the orientation agent and the linear velocity control law of the distance agent, the formation of the multi-agents is controlled under the constraints of the viewing angle.

In a possible implementation, the agent system model is:

表示智能体相邻两时刻的位置，

为智能体线速度的控制输入，T为材料样时间，

表示智能体两时刻的朝向角角度，u_ω(k)为智能体角速度的控制输入。in,

represents the position of the agent at two adjacent moments,

is the control input of the linear velocity of the agent, T is the material sample time,

represents the orientation angle of the agent at two moments, and u _ω (k) is the control input of the angular velocity of the agent.

In a possible implementation manner, the constructing an angular velocity controller of an azimuth agent based on the agent system model includes:

establishing a perceived orientation model of the orientation agent based on the agent system model;

Calculate the included angle between the actual orientation and the expected orientation of the orientation agent according to the perceived orientation model;

The angular velocity controller of the orientation agent is constructed according to the included angle between the actual orientation and the expected orientation of the orientation agent.

In a possible implementation manner, the viewing angle constraint is the viewing angle θ _f ∈(0,π].

In a possible implementation manner, the position of the orientation agent is divided into a desired side and an undesired side; the linear velocity control law u of the orientation agent is:

Among them, g is the discriminant function of the position of the position agent, when the position of the position agent is on the desired side, f(k) affects the linear velocity control law of the position agent; when the position of the position agent On the undesired side, (1-g) affects the linear velocity control law of the orientation agent.

In a possible implementation, the f(k)=-k(θ(k)-θ ^* ), where θ(k) is the controlled angle of the orientation agent, and θ ^* (k) Represents the expected charged angle.

式中，S为带符号的面积，S^*为期望的带符号的面积。In a possible implementation, the distance agent switches the function

where S is the signed area and S ^* is the expected signed area.

The multi-agent formation control method under the condition of viewing angle constraints of the present disclosure is established by establishing an agent system model, wherein the agents include an orientation agent and a distance agent; and an angular velocity controller of the orientation agent is constructed based on the agent system model; Using the angular velocity controller of the azimuth agent to control the azimuth agent to meet the viewing angle constraint; when the azimuth agent satisfies the viewing angle constraint, establish the linear velocity control law of the azimuth agent according to the position of the azimuth agent; design the distance agent switching According to the switching function and the multi-agent system model, the linear velocity control law of the distance agent is established; according to the linear velocity control law of the orientation agent and the linear velocity control law of the distance agent, under the constraints of the viewing angle, the Formation of agents. Under the condition that the agent only has orientation information but no position information or distance information, the agent can choose relatively few paths to move from the undesired side to the desired side, and finally move to the desired position, so as to realize the view angle constraint Formation, maintenance and transformation of multi-agent formations.

Description of drawings

The accompanying drawings are used to provide a further understanding of the technical solutions or the prior art of the present application, and constitute a part of the specification. The drawings representing the embodiments of the present application together with the embodiments of the present application are used to explain the technical solutions of the present application, but do not constitute limitations on the technical solutions of the present application.

FIG. 1 shows a flowchart of a method for controlling a formation of multi-agents under the condition of viewing angle constraints according to an embodiment of the present disclosure;

FIG. 2 shows a schematic diagram of a formation of three agents under the condition of viewing angle constraints according to an embodiment of the present disclosure;

3 shows a schematic diagram of the motion relationship of three agents at any two adjacent moments under the condition of viewing angle constraints according to an embodiment of the present disclosure;

约束条件下的3个智能体编队形成示意图；FIG. 4 shows a view angle of view according to an embodiment of the present disclosure.

Schematic diagram of the formation of three agents under the constraints;

约束条件下的3个智能体编队形成过程误差曲线示意图；FIG. 5 shows a view angle of view according to an embodiment of the present disclosure.

Schematic diagram of the error curve of the formation process of the three agents under the constraints;

约束条件下的3个智能体编队形成示意图；FIG. 6 shows a view angle at the viewing angle according to an embodiment of the present disclosure.

Schematic diagram of the formation of three agents under the constraints;

约束条件下的3个智能体编队形成过程误差曲线示意图；FIG. 7 shows a view angle of view according to an embodiment of the present disclosure

Schematic diagram of the error curve of the formation process of the three agents under the constraints;

8 shows a schematic diagram of formation formation when the initial position of the azimuth agent No. 2 is close to the distance agent No. 3 according to an embodiment of the present disclosure;

FIG. 9 is a schematic diagram illustrating a formation error when the initial position of the azimuth agent No. 2 is close to the distance agent No. 3 according to an embodiment of the present disclosure;

FIG. 10 shows a schematic diagram of formation formation when the initial position of the azimuth agent No. 2 is on the desired side according to an embodiment of the present disclosure;

FIG. 11 is a schematic diagram showing a formation error when the initial position of the azimuth agent No. 2 is on the desired side according to an embodiment of the present disclosure;

FIG. 12 shows a schematic diagram of a multi-agent formation formation and transformation process under the condition of viewing angle constraints according to an embodiment of the present disclosure;

FIG. 13 shows a schematic diagram of the angle error and the side length of New Year greetings in the process of multi-agent formation under the constraint of viewing angle according to an embodiment of the present disclosure.

Detailed ways

The embodiments of the present invention will be described in detail below with reference to the accompanying drawings and examples, so as to fully understand and implement the implementation process of how the present invention applies technical means to solve technical problems and achieve corresponding technical effects. The embodiments of the present application and the various features in the embodiments can be combined with each other under the premise of no conflict, and the formed technical solutions all fall within the protection scope of the present invention.

The multi-agent formation control method under the viewing angle constraint condition of the present invention considers the movement of the multi-agent at the same height (two-dimensional plane), and aims at the multi-agent triangular formation control problem under the viewing angle constraint condition. This method considers the situation that multiple agents can obtain the desired formation information specified by the azimuth and distance. For the agents that can measure the azimuth, the viewing angle constraint is added. The angular velocity controller is designed to ensure that the agent can always see its neighbor agents. On this basis, the velocity control is designed for the agent that can measure the azimuth information and the agent that can measure the distance information, so that it can move to the desired position.

The present invention separately designs the control laws for the agents capable of perceiving orientation information and perceiving distance information. For the agent that measures the orientation, the control law design is decomposed into angular velocity control and velocity control. The angular velocity ensures that the viewing angle constraint is satisfied, and the velocity control ensures that it moves to the desired position.

FIG. 1 shows a flowchart of a multi-agent formation control method under the condition of viewing angle constraints according to an embodiment of the present disclosure. This method can be used in the formation movement process of multiple agents with orientation agents and distance agents. The following takes one orientation agent and two distance agents as an example to illustrate. As shown in Figure 1, the method may include:

Step S1: establishing an agent system model, wherein the agents include orientation agents and distance agents.

FIG. 2 shows a schematic diagram of a formation of three agents under the condition of viewing angle constraints according to an embodiment of the present disclosure.

As shown in Figure 2, multiple agents move at the same height (that is, a two-dimensional plane). For the convenience of expression, one orientation agent is marked as No. 1, and two distance agents are marked as No. 1 and No. 3 respectively.

In one example, the agent system model is:

表示智能体相邻两时刻的位置，

为智能体线速度的控制输入，T为材料样时间，

表示智能体两时刻的朝向角角度，u_ω(k)为智能体角速度的控制输入。in,

represents the position of the agent at two adjacent moments,

is the control input of the agent linear velocity, T is the material sample time,

represents the orientation angle of the agent at two moments, and u _ω (k) is the control input of the angular velocity of the agent.

u_ω＝u_ω(k)。因此，智能体系统模型可以得到如下的表达：For the convenience of writing, let

u _ω = u _ω (k). Therefore, the agent system model can be expressed as follows:

Step S2: constructing an angular velocity controller of the azimuth agent based on the agent system model.

In an example, this step may specifically include:

Based on the agent system model, the orientation perception model of the orientation agent is established; the angle between the actual orientation and the expected orientation of the orientation agent is calculated according to the perception orientation model; the orientation intelligence is constructed according to the angle between the orientation agent's real orientation and the expected orientation. body angular velocity controller.

For example, the orientation perception model of the No. 2 orientation agent shown in Figure 2 is:

where b _2i (k) is the orientation, that is, the orientation agent of No. 2 can perceive the orientation of the distance agent No. 1 and the distance agent No. 3 as b ₂₁ and b ₂₃ , respectively. According to formula 3, the b ₂₁ and b ₂₃ can be obtained value.

Since the viewing angle of the orientation agent θ _f ∈ (0, π], the constraint condition of the viewing angle of the orientation agent is between 0° and 180°. Under such constraints, the neighbor agent (1 in Figure 2) The distance agent No. 2 and the distance agent No. 3) are within the field of vision of the azimuth agent No. 2, and the following formula must be satisfied:

代表2号智能体和1号智能体方位的转置，

代表2号智能体和3号智能体方位的转置，则

式(5)，令

代表与该智能体对应的期望朝向，相应的

其中

为期望朝向，根据式(3)和式(6)能够得到2号智能体能够感知到1号距离智能提和3号距离智能体的方位为：Let b(k)=[x _b y _b ] ^T represent the orientation of the agent's head,

represents the transpose of the orientation of agent 2 and agent 1,

represents the transpose of the orientation of agent 2 and agent 3, then

Equation (5), let

represents the desired orientation corresponding to the agent, and the corresponding

in

In order to expect the orientation, according to equations (3) and (6), it can be obtained that the azimuth that the agent No. 2 can perceive the distance agent No. 1 and the distance agent No. 3 is:

为：According to equations (6) and (7), the angle between the actual orientation and the expected orientation of the orientation agent can be calculated

for:

为符号函数，其计算方法如下：in,

is a symbolic function, and its calculation method is as follows:

That is, the angle between the desired orientation of the orientation agent and the current orientation has a direction, and the direction is the desired orientation points to the current orientation. Here, it is stipulated that the counterclockwise direction is positive, and the clockwise direction is negative.

Due to the existence of the field of view angle θ _f , it is the primary task to ensure that the azimuth agent can see the distance between the neighbors. The first task is to control the orientation angle, that is, to design the angular velocity controller.

式(10)，式中，k_w是一个正的控制增益。Design u _ω as the following form:

Equation (10), where _kw is a positive control gain.

By designing the angular velocity controller of the azimuth agent, the azimuth agent always satisfies the viewing angle constraint, thereby ensuring that the neighbor distance agent is always within the field of view, ensuring that the azimuth measurement information will not be lost.

Step S3: Using the angular velocity controller of the azimuth agent to control the azimuth agent to satisfy the viewing angle constraint.

Step S4: establishing a linear velocity control law of the orientation agent according to the position of the orientation agent under the condition that the orientation agent satisfies the viewing angle constraint;

Among them, the position of the orientation agent is divided into two parts: the desired side and the undesired side, and different control inputs work on different sides.

In an example, the linear velocity control law u of the orientation agent is:

Among them, g is the discriminant function of the position of the orientation agent. When the position of the orientation agent is on the desired side, f(k) affects the linear velocity control law of the orientation agent, and finally the orientation agent can move to the desired equilibrium point; when When the position of the orientation agent is on the undesired side, (1-g) affects the linear velocity control law of the orientation agent, and the orientation agent chooses a detour to move to the desired side.

In an example, formula f(k)=-k(θ(k)-θ ^* ) formula (12), where θ(k) is the controlled angle of the orientation agent, and θ ^* (k) represents Expected to be charged angle.

For example, the azimuth angle measured by the azimuth agent is φ _j (k)∈[0,2π)∪-1. Starting from the X-axis direction of the local coordinate system of the azimuth agent, the counterclockwise direction is positive, and the clockwise direction is Negative, where "-1" means that the azimuth agent cannot observe the j agent in its field of view.

Introducing the auxiliary angle variable δ(k), then:

δ(k)=φ ₂₁ (k)-φ ₂₃ (k) Equation (13),

Then the controlled angle θ(k) is:

The following takes the three agents shown in Figure 2 as an example to design the linear velocity control law. From equation (15), it can be known that the controlled angle of the No. 2 azimuth agent is:

Introducing auxiliary variable ψ(k), then ψ(k)=φ ₂₃ (k)+γ ₂ θ ₂ (k) (16), where γ ₂ is a positive constant coefficient and satisfies 0<γ ₂ < 1. Generally, γ ₂ is selected as 0.5.

Introduce a direction vector b _⊥ (k) perpendicular to the current orientation, as shown in Figure 2, then

The β ₂ (k) to be designed is:

Equation (18),

where h ₁ is a function of b(k-1)×b _⊥ (k-1), calculated as:

A discriminant function g is introduced to judge whether the agent No. 2 is on the desired side. The judgment method is as follows:

It is stipulated here that when it is judged that the agent with the No. 2 orientation is on the undesired side, the initial movement direction is to move to the side of the agent with the No. 1 distance, as shown by b _⊥ (k) in Figure 2.

Auxiliary variables η(k) and ε(k) are introduced, and η(k) is defined as follows:

η(k)=h ₂ (b(k)×b ₂₁ (k)) Formula (21),

Among them, the calculation method of h ₂ is the same as that of h ₁ , and will not be repeated here. According to formula (21), the auxiliary variable ∈(k) can be obtained,

因此， b_⊥(k)＝R(k)*b(k) 式(23)。Define the rotation matrix R(k)=∈(k)*r, where,

Therefore, b _⊥ (k)=R(k)*b(k) Equation (23).

FIG. 3 shows a schematic diagram of the motion relationship of three agents at any two adjacent moments under the condition of viewing angle constraints according to an embodiment of the present disclosure.

As shown in Fig. 3, ΔL>0 is the distance of the movement of the agent in orientation 2 between two moments, and d ₂₁ and d ₂₃ are the distances at time k+1.

As can be seen from Figure 3, according to the triangular geometric relationship, the calculation is obtained:

where _α21 is the angle formed between the current moment and the next moment position of agent 2 and agent 1, _α23 is the angle formed between agent 2's current moment and the next moment position and agent 3, and then From the law of sine, we can get:

where ΔL is the distance between the current moment of agent 2 and the position of the next moment, and the edges d ₂₃ (k+1) and d ₂₁ (k+1) represent the distance between agent 2 and agents 3 and 1 at the next moment, respectively distance, their difference ΔD is:

由于ΔL大于零是显然的，因此，ΔD的符号由后一项决定。将后一项定义为Δd，表达式如下：

Since it is obvious that ΔL is greater than zero, the sign of ΔD is determined by the latter term. Defining the latter term as Δd, the expression is as follows:

那么可以根据Δd的符号来选择较近一侧对应的运动方向。

Then the movement direction corresponding to the nearer side can be selected according to the sign of Δd.

The linear velocity control law of the azimuth agent 2 is:

where k ₂ and k _g are both control gains greater than zero, and sgn(Δd) is as follows:

So far, when the initial position of the No. 2 orientation agent is on the undesired side, through the action of formula (28), it can choose a closer path to fly to the desired side, and after reaching the desired side, it will finally move to the desired point.

The view angle constraint problem is decomposed into angular velocity control and linear velocity control by dividing the agent that can obtain the orientation. The angular velocity controller is designed so that the agent always satisfies the viewing angle constraint, thereby ensuring that the neighboring agents always remain within the field of view, and ensuring that the azimuth measurement information will not be lost. On the premise of satisfying the viewing angle constraints, according to the different initial positions of the agent, that is, initially on the desired side and on the undesired side, the speed control is divided into two cases, the control law and the switching function are designed respectively to realize the two cases. It can not only realize the formation and transformation of formations, but also enable the agent to choose a closer path to move from the undesired side to the desired side based on the orientation information alone without the position and distance information. side.

Step S5: Designing a distance agent switching function, and establishing a linear velocity control law of the distance agent according to the switching function and the multi-agent system model.

For the agent that can measure the relative distance information, the concept of signed area is introduced, and the discriminant function is designed to start movement only when the agent measuring the orientation is on the desired side, and finally realize the control of the desired distance.

Taking the distance agent No. 1 and the distance agent No. 3 shown in Figure 2 as an example, in order to ensure that the agent No. 2 can move to the desired side. It is required that when the No. 2 orientation agent is on the undesired side, the No. 1 and No. 3 distance agents are in a static state, and when the No. 2 orientation agent moves to the desired side, it finally moves to the desired equilibrium point.

To this end, the signed area S is first introduced, and the calculation method of the signed triangle area is as follows:

S的符号由z₁、z₂和z₃的顺序决定。当顺序为逆时针时，S则为正，反之，则S为负。通过式(31)可以确定一个唯一且顶点顺序也唯一确定的三角形。则期望的带符号的三角形面积S*计算公式如下：In the formula,

The sign of S is determined by the order of z ₁ , z ₂ and z ₃ . When the order is counterclockwise, S is positive, otherwise, S is negative. A unique triangle whose vertex order is also uniquely determined can be determined by formula (31). Then the expected signed triangle area S* is calculated as follows:

Among them, a∈{1,-1}, when z ₁ , z ₂ and z ₃ are arranged counterclockwise, a=1, and when they are arranged clockwise, a=-1,

Define the distance agent switching function f(S) in terms of the signed area S and the desired signed area S*,

From this, the controllers of agents 1 and 3 are obtained in the following form:

其中，k_i>0是一个控制增益。

where k _i >0 is a control gain.

Combined with step 1, the overall control law of the three agents can be obtained:

Equation (34), where k _i >0 is a constant.

Step S6 : controlling the formation of the multi-agents under the constraint condition of the viewing angle according to the linear velocity control law of the azimuth agent and the linear velocity control law of the distance agent.

The simulation and physical experiments of the multi-agent formation control method are carried out below. Due to the existence of the viewing angle constraint, the parameters when k=0 and k=0 are set as follows:

其中，∈>0，并且足够小；

where ∈>0, and is sufficiently small;

sgn(Δd)=1.

The following three sets of simulation experiments are carried out for the following three situations. The three cases are:

和

(1) Different viewing angle sizes, namely

and

(2) Different initial positions on the undesired side. That is, the initial position is close to agent 1 and the initial position is close to agent 3;

(3) The initial position is on the desired side and the undesired side.

Simulation 1: Different viewing angle size constraints

约束条件下的3个智能体编队形成示意图和编队形成误差曲线示意图。FIG. 4 and FIG. 5 respectively illustrate the viewing angle according to an embodiment of the present disclosure.

Schematic diagram of formation formation and formation formation error curve of 3 agents under constraints.

条件下，设定视野角大小为

期望的角度

1号、2和3号智能体的初始位置分别为z₁＝[-1.0 0.0]^T、z₂＝[-1.8 1.5]^T和 z₃＝[1.0 0.0]^T。则图2中所示的1号、2号和3号智能体的编队形成过程如图 4所示，编队形成过程的误差曲线如图5所示。exist

Under the conditions, the size of the viewing angle is set to be

desired angle

The initial positions of agents No. 1, 2 and 3 are z ₁ =[-1.0 0.0] ^T , z ₂ =[-1.8 1.5] ^T and z ₃ =[1.0 0.0] ^T , respectively. The formation process of agents No. 1, 2 and 3 shown in Figure 2 is shown in Figure 4, and the error curve of the formation formation process is shown in Figure 5.

约束条件为下的3个智能体编队形成示意图和编队形成过程误差曲线示意图。FIG. 6 and FIG. 7 respectively illustrate the viewing angle according to an embodiment of the present disclosure.

Schematic diagram of formation formation of three agents under the constraint condition and error curve diagram of formation formation process.

条件下，设定视野角θ_f大小为π，期望的角度

1号、2和3号智能体的初始位置分别为z₁＝[-1 0]^T、z₂＝[-0.5 0.8]^T和z₃＝ [1 0]^T。则图2中所示的1号、2号和3号智能体的编队形成过程如图6所示，编队形成过程的误差曲线如图5所示。exist

Under the conditions, set the viewing angle θ _f to π, the desired angle

The initial positions of agents No. 1, 2 and 3 are z ₁ =[-1 0] ^T , z ₂ =[-0.5 0.8] ^T and z ₃ =[1 0] ^T , respectively. Then the formation process of agents No. 1, 2 and 3 shown in Figure 2 is shown in Figure 6, and the error curve of the formation formation process is shown in Figure 5.

Simulation 2: Different viewing angle size constraints

8 and 9 respectively show a schematic diagram of formation formation and a schematic diagram of the error of formation formation process when the initial position of the azimuth agent No. 2 is close to the distance agent No. 3 according to an embodiment of the present disclosure.

约束条件下的仿真结果一致，2号方位智能体的初始位置靠近 1号距离智能体时的编队形成示意图和编队形成过程误差示意图分别如图4和5 所示。Among them, the simulation results when the initial position of the azimuth agent No. 2 is close to the distance agent No. 1 is different from that in the field of view.

The simulation results under the constraints are consistent. The initial position of the No. 2 azimuth agent is close to the No. 1 distance agent. The formation diagram and the formation process error diagram are shown in Figures 4 and 5, respectively.

条件下，设定视野角大小为

期望的角度

1号、2和3号智能体的初始位置分别为z₁＝[-1 0]^T、z₂＝[1.8 1.5]^T和z₃＝ [1 0]^T。则图2中所示的1号、2号和3号智能体的编队形成过程如图8所示，编队形成过程的误差曲线如图9所示。exist

Under the conditions, the size of the viewing angle is set to be

desired angle

The initial positions of agents No. 1, 2 and 3 are z ₁ =[-1 0] ^T , z ₂ =[1.8 1.5] ^T and z ₃ =[1 0] ^T , respectively. Then the formation formation process of agents No. 1, 2 and 3 shown in Figure 2 is shown in Figure 8, and the error curve of the formation formation process is shown in Figure 9.

Simulation 3: The initial position is on the desired side and the undesired side

FIGS. 10 and 11 respectively show a schematic diagram of formation formation and a schematic diagram of errors in the formation formation process when the initial position of the azimuth agent No. 2 is on the desired side according to an embodiment of the present disclosure.

期望的角度

1号、2和3号智能体的初始位置分别为z₁＝[-1 0]^T、z₂＝[0.55-6]^T和z₃＝[1 0]^T。则图 2中所示的1号、2号和3号智能体的编队形成过程如图10所示，编队形成过程的误差曲线如图11所示。On the desired side, set the viewing angle size to

desired angle

The initial positions of agents No. 1, 2 and 3 are z ₁ =[-1 0] ^T , z ₂ =[0.55-6] ^T and z ₃ =[1 0] ^T , respectively. Then the formation formation process of agents No. 1, 2 and 3 shown in Figure 2 is shown in Figure 10, and the error curve of the formation formation process is shown in Figure 11.

FIG. 12 shows a schematic diagram of the formation and transformation process of a multi-agent formation under a viewing angle constraint according to an embodiment of the present disclosure; FIG. 13 shows a multi-agent formation under the viewing angle constraint according to an embodiment of the present disclosure. Schematic diagram of the angle error and side length transformation during the process.

Next, a group of UAV experiments are given. The formation process is shown in Figure 11, and the error and side length change curves are shown in Figure 12.

The multi-agent formation control method under the condition of viewing angle constraints of the present disclosure is established by establishing an agent system model, wherein the agents include an orientation agent and a distance agent; based on the agent system model, an angular velocity controller of the orientation agent is constructed; Using the angular velocity controller of the azimuth agent to control the azimuth agent to meet the viewing angle constraint; when the azimuth agent satisfies the viewing angle constraint, establish the linear velocity control law of the azimuth agent according to the position of the azimuth agent; design the distance agent switching According to the switching function and the multi-agent system model, the linear velocity control law of the distance agent is established; according to the linear velocity control law of the orientation agent and the linear velocity control law of the distance agent, under the constraints of the viewing angle, the Formation of agents. Under the condition that the agent only has orientation information but no position information or distance information, the agent can choose relatively few paths to move from the undesired side to the desired side, and finally move to the desired position, so as to realize the view angle constraint Formation, maintenance and transformation of multi-agent formations.

Although the embodiments disclosed in the present invention are as above, the described contents are only the embodiments adopted to facilitate the understanding of the present invention, and are not intended to limit the present invention. Any person skilled in the art to which the present invention belongs, without departing from the spirit and scope disclosed by the present invention, can make any modifications and changes in the form and details of the implementation, but the scope of patent protection of the present invention, The scope as defined by the appended claims shall still prevail.

Claims (7)

1. A method for controlling multi-agent formation under a visual field angle constraint, the method comprising:

establishing an intelligent agent system model, wherein the intelligent agent comprises a position intelligent agent and a distance intelligent agent;

constructing an angular velocity controller of an orientation agent based on the agent system model;

controlling the orientation intelligent agent to meet a visual field angle constraint condition by utilizing an angular speed controller of the orientation intelligent agent;

establishing a linear velocity control law of the orientation intelligent agent according to the position of the orientation intelligent agent under the condition that the orientation intelligent agent meets the visual field angle constraint condition;

designing a switching function of the distance agent, and establishing a linear velocity control law of the distance agent according to the switching function and the multi-agent system model;

and controlling the formation of the multi-agent under the condition of visual field angle constraint according to the linear speed control law of the direction agent and the linear speed control law of the distance agent.

2. The multi-agent formation control method of claim 1, wherein the agent system model is:

wherein z (k +1),

indicating the position of the agent at two adjacent moments,

is the control input of the linear velocity of the intelligent body, T is the material sample time,

representing the orientation angle, u, of the agent at two times_ω(k) Is the control input of the angular speed of the intelligent body.

3. The multi-agent formation control method according to claim 2, wherein said building an angular velocity controller of an orientation agent based on said agent system model comprises:

establishing a perceptual orientation model of the orientation agent based on the agent system model;

calculating an included angle between the real orientation and the expected orientation of the orientation intelligent agent according to the perception orientation model;

and constructing the angular speed controller of the orientation intelligent agent according to the included angle between the real orientation and the expected orientation of the orientation intelligent agent.

4. The multi-agent formation control method as claimed in claim 2, wherein the viewing angle constraint condition is the viewing angle θ_f∈(0,π]。

5. The multi-agent formation control method of claim 4, wherein the location of the orientation agent is divided into a desired side and an undesired side;

the linear velocity control law u of the orientation intelligent agent is as follows:

g is a discriminant function of the position of the orientation intelligent agent, and f (k) influences a linear velocity control law of the orientation intelligent agent when the position of the orientation intelligent agent is on an expected side; (1-g) affecting a linear velocity control law of the orientation agent when the position of the orientation agent is on an undesired side.

6. The multi-agent formation control method of claim 5, wherein f (k) -k (θ (k) - θ) is^*) Where θ (k) is the controlled angle of the orientation agent, θ^*(k) Representing the desired controlled angle.

7. The multi-agent formation control method of claim 1, wherein the distance agent switching function

Wherein S is the area with symbol, S^*Is the desired signed area.

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