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

Multi-agent formation control method under visual field angle constraint condition Download PDF

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CN114115334A
CN114115334A CN202111303464.6A CN202111303464A CN114115334A CN 114115334 A CN114115334 A CN 114115334A CN 202111303464 A CN202111303464 A CN 202111303464A CN 114115334 A CN114115334 A CN 114115334A
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formation
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CN114115334B (en
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杨庆凯
赵欣悦
方浩
潘云龙
曾宪琳
李若成
肖凡
刘奇
陈杰
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Beijing Institute of Technology BIT
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Abstract

The multi-agent formation control method under the visual field angle constraint condition is characterized in that an agent system model is established; constructing an angular speed controller of an orientation intelligent body based on an intelligent body system model; controlling the orientation intelligent agent to meet the visual field angle constraint condition by utilizing an angular speed controller of the orientation intelligent agent; establishing a linear speed 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 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; and controlling the formation of the multiple agents under the visual field angle constraint condition according to the linear speed control law of the orientation agent and the linear speed control law of the distance agent. Under the condition that the intelligent agent only has azimuth information and no position information or distance information, the intelligent agent can select relatively fewer paths to move from an undesired side to a desired side and finally to a desired position, and formation, maintenance and transformation of multi-intelligent-agent formation under the condition of view angle constraint are realized.

Description

Multi-agent formation control method under visual field angle constraint condition
Technical Field
The invention belongs to the technical field of multi-agent control, and particularly relates to a multi-agent formation control method under a visual field angle constraint condition.
Background
In recent years, due to the fact that the multi-agent cooperative control has a great number of practical applications in search rescue, cooperative operation in industrial production, intelligent entertainment and the like in complex dangerous environments, research on the multi-agent cooperative control has attracted extensive attention in academia and industry. When a search task in a complex environment is executed, the multi-agent formation technology plays an important role in expanding the search range, improving the search efficiency and improving the accuracy of target identification; when the intelligent agent flies at high altitude, the formation flying can not only enhance the stability of the system, but also reduce the overall energy consumption. Therefore, a great deal of research is maintained on the formation. However, at present, most research considerations are ideal, and few considerations are taken into consideration of the limitation of the measurement range, for example, a camera generally used for acquiring the azimuth information is not usually an omnidirectional angle, but has a certain view angle.
For the formation control problem under the visual angle constraint condition, the following main solutions exist: scheme 1: in the references "Li X, Tan Y, marels I, et al, compatible formation set for use with visual presentation constraint [ C ]. In 2018 annular American Control Conference (ACC),2018:2497 ″, by introducing the concept of barrier function (barrier function), it is ensured that the neighbor agent is always In the visual field during the exercise, but this method assumes that the visual field angle is 300 ° and the visual distance is large enough (i.e. the visual distance constraint can not be considered) to ensure that the entire formation topology is fully connected and it is required that each agent can acquire the relative position information of the neighbor agent. The designed control method realizes formation and maintenance of the formation.
Scheme 2: the documents "Frank D, Zelazo D,
Figure BDA0003339239980000011
F.Bearing-only formation control with limited visual sensing:Two agent case[J]IFAC-paperOnLine, 2018,51(23): 28-33 ", where two agents are considered on the basis of azimuth control, orientation angle control is added so that the other agent is always in the center of the viewing angle, thereby completing the formation task. The designed control method can realize formation and maintenance of the formation.
Scheme 3: in the literature "Renaud P, Cervera E, Martiner P. Towards a reusable vision-based mobile robot formation control [ C ]. In 2004IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS),2004: 3176-.
Disclosure of Invention
The invention overcomes one of the defects of the prior art, provides a multi-agent formation control method under the condition of visual field angle constraint, and can enable an agent to select relatively fewer paths to move from an undesired side to a desired side and finally to move to a desired position under the condition that the agent only has azimuth information but no position information or distance information, thereby realizing the formation, the maintenance and the transformation of the multi-agent formation under the condition of the visual field angle constraint.
According to one aspect of the present disclosure, the present invention provides a multi-agent formation control method under a viewing angle constraint condition, 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.
In one possible implementation, the model of the intelligent system is:
Figure BDA0003339239980000021
wherein,
Figure BDA0003339239980000031
indicating the position of the agent at two adjacent moments,
Figure BDA0003339239980000032
is the control input of the linear velocity of the intelligent body, T is the material sample time,
Figure BDA0003339239980000033
representing the orientation angle, u, of the agent at two timesω(k) Is the control input of the angular speed of the intelligent body.
In one possible implementation, the constructing an angular velocity controller of an orientation agent based on the agent system model includes:
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.
In a possible implementation manner, the visual field angle constraint condition is the visual field angle θf∈(0,π]。
In one possible implementation, 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:
Figure BDA0003339239980000034
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.
In one possible implementation, the f (k) ═ k (θ (k) - θ) is equal to*) Where θ (k) is the controlled angle of the orientation agent, θ*(k) Representing the desired controlled angle.
In one possible implementation, the distance agent switching function
Figure BDA0003339239980000035
Wherein S is the area with symbol, S*Is the desired signed area.
The multi-agent formation control method under the visual field angle constraint condition comprises the steps of establishing an agent system model, wherein the agent comprises an orientation agent and a distance agent; constructing an angular speed controller of an orientation intelligent body based on an intelligent body system model; controlling the orientation intelligent agent to meet the visual field angle constraint condition by utilizing an angular speed controller of the orientation intelligent agent; establishing a linear speed 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 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; and controlling the formation of the multiple agents under the visual field angle constraint condition according to the linear speed control law of the orientation agent and the linear speed control law of the distance agent. Under the condition that the intelligent agent only has azimuth information and no position information or distance information, the intelligent agent can select relatively fewer paths to move from an undesired side to a desired side and finally to a desired position, and formation, maintenance and transformation of multi-intelligent-agent formation under the condition of view angle constraint are realized.
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The accompanying drawings are included to provide a further understanding of the technology or prior art of the present application and are incorporated in and constitute a part of this specification. The drawings expressing the embodiments of the present application are used for explaining the technical solutions of the present application, and should not be construed as limiting the technical solutions of the present application.
FIG. 1 illustrates a flow chart of a multi-agent formation control method under view angle constraints according to one embodiment of the present disclosure;
FIG. 2 shows a schematic diagram of 3 agent formations under a viewing angle constraint according to an embodiment of the present disclosure;
FIG. 3 is a schematic diagram illustrating the motion relationships of 3 agents at any two adjacent time points under the viewing angle constraint according to an embodiment of the disclosure;
FIG. 4 illustrates an angle of view according to an embodiment of the present disclosure
Figure BDA0003339239980000041
Forming a schematic diagram by 3 intelligent agents under a constraint condition;
FIG. 5 illustrates an angle of view according to an embodiment of the present disclosure
Figure BDA0003339239980000042
Forming a process error curve schematic diagram by 3 intelligent agents under a constraint condition;
FIG. 6 illustrates an angle of view according to an embodiment of the present disclosure
Figure BDA0003339239980000043
Forming a schematic diagram by 3 intelligent agents under a constraint condition;
FIG. 7 illustrates an angle of view according to an embodiment of the present disclosure
Figure BDA0003339239980000044
Forming a process error curve schematic diagram by 3 intelligent agents under a constraint condition;
FIG. 8 shows a schematic diagram of formation when the initial position of the number 2 orientation agent is near the number 3 distance agent, according to one embodiment of the present disclosure;
FIG. 9 is a diagram illustrating a formation error when an initial position of a number 2 orientation agent is near a number 3 distance agent, according to one embodiment of the present disclosure;
FIG. 10 shows a formation schematic diagram with the initial position of orientation agent # 2 on the desired side according to an embodiment of the present disclosure;
FIG. 11 shows a diagram of a formation error for position agent # 2 with the initial position on the desired side, according to an embodiment of the present disclosure;
FIG. 12 illustrates a schematic diagram of a multi-agent formation and transformation process under view angle constraints, according to an embodiment of the present disclosure;
FIG. 13 illustrates a schematic diagram of angle error and Bischnian of side length during multi-agent formation under viewing angle constraints according to an embodiment of the present disclosure.
Detailed Description
The following detailed description of the embodiments of the present invention will be provided with reference to the accompanying drawings and examples, so that how to apply the technical means to solve the technical problems and achieve the corresponding technical effects can be fully understood and implemented. The embodiments and the features of the embodiments can be combined without conflict, and the technical solutions formed are all within the scope of the present invention.
The invention relates to a multi-agent formation control method under the condition of visual field angle constraint, which considers the motion of multi-agents at the same height (two-dimensional plane) and aims at the multi-agent triangular formation control problem under the condition of visual field angle constraint. The method considers the situation that a plurality of agents can obtain expected formation information defined by the azimuth and the distance, and adds a visual field angle constraint condition to the agents capable of measuring the azimuth. The design angular speed controller ensures that the intelligent agent can always see the neighbor intelligent agent, and on the basis, the speed control is respectively designed for the intelligent agent capable of measuring azimuth information and distance information, so that the intelligent agent can move to a desired position.
The invention respectively designs the control law of the intelligent agent capable of sensing the azimuth information and the distance information. For an intelligent body for measuring the azimuth, the control law design is decomposed into angular velocity control and speed control, the angular velocity ensures that the visual field angle constraint is met, and the speed control ensures that the intelligent body moves to a desired position.
FIG. 1 shows a flow chart of a multi-agent formation control method under view angle constraints according to an embodiment of the present disclosure. The method can be used in the formation movement process of a plurality of intelligent agents with direction intelligent agents and distance intelligent agents, and the following description takes 1 direction intelligent agent and 2 distance intelligent agents as examples. As shown in fig. 1, the method may include:
step S1: an agent system model is established, wherein the agents include a position agent and a distance agent.
FIG. 2 shows a schematic diagram of 3 agent formations under a viewing angle constraint according to an embodiment of the present disclosure.
As shown in fig. 2, the multiple agents move at the same altitude (i.e. two-dimensional plane), and for the convenience of description, 1 orientation agent is labeled as number 1, and 2 distance agents are labeled as numbers 1 and 3, respectively.
In one example, the intelligent system model is:
Figure BDA0003339239980000061
wherein,
Figure BDA0003339239980000062
indicating the position of the agent at two adjacent moments,
Figure BDA0003339239980000063
is the control input of the linear velocity of the intelligent body, T is the material sample time,
Figure BDA0003339239980000064
representing the orientation angle, u, of the agent at two timesω(k) Is the control input of the angular speed of the intelligent body.
For writing convenience, order
Figure BDA0003339239980000065
uω＝uω(k) In that respect Thus, the intelligent system model can be expressed as follows:
Figure BDA0003339239980000066
step S2: and constructing an angular speed controller of the azimuth intelligent body based on the intelligent body system model.
In an example, the step may specifically include:
establishing a perception orientation model of an orientation intelligent agent based on an intelligent 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.
For example, the direction-intelligent-perception-direction model No. 2 shown in fig. 2 is:
Figure BDA0003339239980000071
wherein b is2i(k) For direction, that is, the No. 2 direction agent can sense the directions of the No. 1 distance agent and the No. 3 distance agent as b21And b23B can be obtained from the formula 321And b23The value of (c).
Angle of view theta due to orientation agentf∈(0,π]The constraint of the angle of view of the orientation agent is then between 0 ° and 180 °. Under such constraints, if the neighbor agent (distance 1 agent and distance 3 agent in fig. 2) is within the field of view of the direction 2 agent, the following equation is satisfied:
Figure BDA0003339239980000072
let b (k) be [ < x >b yb]TRepresenting the orientation of the smart-agent handpiece,
Figure BDA0003339239980000073
representing the transpose of agent number 2 and agent number 1 orientations,
Figure BDA0003339239980000074
representing the transpose of the orientations of agent 2 and agent 3, then
Figure BDA0003339239980000075
Formula (5) is
Figure BDA0003339239980000076
Representing a desired orientation corresponding to the agent, respectively
Figure BDA0003339239980000077
Wherein
Figure BDA0003339239980000078
To expect the orientation, according to equation (3) and equation (6), it can be obtained that No. 2 intelligent agent can perceive that No. 1 distance intelligent agent and No. 3 distance intelligent agent's orientation is:
Figure BDA0003339239980000079
the included angle between the actual orientation and the expected orientation of the orientation intelligent agent can be calculated according to the formula (6) and the formula (7)
Figure BDA00033392399800000710
Comprises the following steps:
Figure BDA00033392399800000711
wherein,
Figure BDA00033392399800000712
the calculation method is the following as a symbolic function:
Figure BDA00033392399800000713
i.e. the angle between the desired orientation of the orientation agent and the current orientation is directional, where the desired orientation is directed towards the current orientation, where it is specified that the counter-clockwise direction is positive and the clockwise direction is negative.
Due to the angle of view thetafNext, it is the first task to ensure that the direction number agent can see the neighbor distance agent, and the heading angle is controlled first, i.e. the angular speed controller is designed.
Will uωThe design is as follows:
Figure BDA0003339239980000081
formula (10) wherein kwIs a positive control gain.
Through the angular velocity controller of the design position intelligent agent for the position intelligent agent satisfies the visual field angle constraint all the time, and then guarantees that the neighbor distance intelligent agent remains in the visual field range all the time, has guaranteed that the position measurement information can not lose.
Step S3: and controlling the orientation intelligent agent to meet the visual field angle constraint condition by utilizing the angular speed controller of the orientation intelligent agent.
Step S4: 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;
the position of the orientation intelligent agent is divided into a desired side and an undesired side, and different control inputs are acted on different sides.
In one example, the linear velocity control law u for the orientation agent is:
Figure BDA0003339239980000082
g is a discriminant function of the position of the orientation intelligent agent, and when the position of the orientation intelligent agent is on the expected side, f (k) influences the linear velocity control law of the orientation intelligent agent, and finally the orientation intelligent agent can move to an expected balance point; when the position of the orientation intelligent agent is on the unexpected side, (1-g) influences the linear velocity control law of the orientation intelligent agent, and the orientation intelligent agent selects a detour mode to move to the expected side.
In one example, design f (k) ═ k (θ (k) - θ*) Equation (12), where θ (k) is the controlled angle of the orientation agent, θ*(k) Representing the desired controlled angle.
For example, the azimuth measured by the azimuth agent is φj(k) E [0,2 pi) ' U-1, starting from the X-axis direction of the local coordinate system of the orientation number agent, the anticlockwise direction is positive, and the clockwise direction is negative, wherein, ' -1 ' means that the orientation number agent cannot observe the j number agent in the visual field of the orientation number agent.
Introducing an auxiliary angular variable δ (k), then:
δ(k)＝φ21(k)-φ23(k) a compound of the formula (13),
the controlled angle θ (k) is:
Figure BDA0003339239980000091
in the following, the linear velocity control law is designed by taking three agents as an example as shown in fig. 2, and the controlled angle of the No. 2 azimuth agent can be known from equation (15):
Figure BDA0003339239980000092
introducing an auxiliary variable psi (k), so that psi (k) is equal to phi23(k)+γ2θ2(k) Formula (16), wherein γ2Is a positive constant coefficient and satisfies 0 < gamma2< 1, generally γ2The value was chosen to be 0.5.
Introducing a direction vector b perpendicular to the current orientation⊥(k) As shown in FIG. 2, then
Figure BDA0003339239980000093
Beta to be designed2(k) Comprises the following steps:
Figure BDA0003339239980000094
a compound of the formula (18),
wherein h is1Is related to b (k-1). times.b⊥(k-1) a function calculated as:
Figure BDA0003339239980000095
and (3) introducing a discriminant function g to judge whether the No. 2 azimuth intelligent agent is on the expected side, wherein the judging method comprises the following steps:
Figure BDA0003339239980000096
it is specified that when the No. 2 orientation agent is judged to be on the undesired side, the initial moving direction is the moving to the No. 1 distance agent side, as shown in FIG. 2B in (1)⊥(k) As shown.
Introducing auxiliary variables η (k) and ε (k), η (k) being defined as follows:
η(k)＝h2(b(k)×b21(k) a compound of the formula (21),
wherein h is2And h1The same, which is not described herein. From the equation (21), the auxiliary variable ∈ (k) can be obtained,
Figure BDA0003339239980000101
defining a rotation matrix r (k) ∈ (k) ×, wherein,
Figure BDA0003339239980000102
thus, b⊥(k) (k) b (k) formula (23).
Fig. 3 shows a schematic diagram of the motion relationship of 3 agents at any two adjacent time points under the visual field angle constraint according to an embodiment of the disclosure.
As shown in FIG. 3, Δ L > 0 is the distance traveled by the agent at position 2 between two times, d21And d23Is the distance at time k + 1.
As can be seen from fig. 3, according to the triangular geometric relationship, the following is calculated:
Figure BDA0003339239980000103
wherein alpha is21Is the included angle formed by the current time of the No. 2 intelligent agent, the position of the next time and the No. 1 intelligent agent, alpha23Is the included angle formed by the current moment of the No. 2 intelligent agent, the next moment position and the No. 3 intelligent agent, and can be obtained by the sine theorem:
Figure BDA0003339239980000104
where Δ L is the distance between the current time and the next time position of agent # 2, and edge d23(k +1) and d21(k +1) represents the distance between agent No. 2 and agents No. 3 and 1 at the next moment, respectively, and the difference Δ D between them is:
Figure BDA0003339239980000111
since it is apparent that Δ L is greater than zero, the sign of Δ D is determined by the latter term. The latter term is defined as Δ d, and the expression is as follows:
Figure BDA0003339239980000112
the direction of movement corresponding to the closer side can be selected according to the sign of ad.
The linear speed control law of the No. 2 azimuth intelligent agent is as follows:
Figure BDA0003339239980000113
wherein k is2And kgControl gain, sgn (Δ d), which are all greater than zero, is as follows:
Figure BDA0003339239980000114
when the initial position of the No. 2 orientation intelligent agent is on the unexpected side, the closer path can be selected to fly to the expected side through the action of the formula (28), and the intelligent agent finally moves to the expected point after reaching the expected side.
By means of the agent which can acquire the orientation, the visual angle constraint problem is decomposed into an angular velocity control problem and a linear velocity control problem. The design angular speed controller makes the intelligent body satisfy the visual field angle constraint all the time, and then guarantees that the neighbor intelligent body remains in the visual field range all the time, has guaranteed that the position measurement information can not lose. Under the prerequisite that satisfies the visual angle constraint, according to the initial position difference of the intelligent body, be promptly initially in expectation one side and in unexpected one side, divide into two kinds of situations with speed control, design control law respectively, design switching function realizes the switching of two kinds of control laws, and this formation and the transform that not only can realize the formation of formation can also be under the prerequisite that does not have position and distance information, and the intelligent body just can select a nearer route to move to expectation one side from unexpected one side by the position information alone.
Step S5: and designing a distance intelligent agent switching function, and establishing a linear velocity control law of the distance intelligent agent according to the switching function and the multi-intelligent agent system model.
Aiming at an intelligent agent capable of measuring relative distance information, the concept of signed area is introduced, a discriminant function is designed, the intelligent agent starts to move only when the intelligent agent for measuring the direction is on the expected side, and finally the control of the expected distance is realized.
Taking distance agent No. 1 and distance agent No. 3 shown in fig. 2 as an example, it is explained to ensure that agent No. 2 can move to a desired side. It is necessary that when the direction agent No. 2 is on the undesired side, the distance agents No. 1 and No. 3 are in a static state, and when the direction agent No. 2 moves to the desired side, the direction agent No. 2 finally moves to the desired balance point.
For this purpose, firstly, a signed area S is introduced, and the signed triangle area calculation method is as follows:
Figure BDA0003339239980000121
in the formula,
Figure BDA0003339239980000122
the symbol of S is represented by z1、z2And z3Is determined. When the sequence is counterclockwise, S is positive, otherwise, S is negative. A unique triangle whose vertex order is also uniquely determined can be determined by equation (31). The expected signed triangle area S is calculated as follows:
Figure BDA0003339239980000123
wherein a is equal to {1, -1}, when z is1、z2And z3In the case of counterclockwise alignment, a is 1, in the case of clockwise alignment, a is-1,
Figure BDA0003339239980000124
defining a distance agent switching function f (S) based on the signed area S and the expected signed area S,
Figure BDA0003339239980000125
thus, controllers for agents No. 1 and No. 3 were obtained, in the form:
Figure BDA0003339239980000126
wherein k isi>0 is a control gain.
By combining the step 1, the total control laws of three agents can be obtained:
Figure 1
formula (34), wherein ki>0 is a constant.
Step S6: and controlling the formation of the multi-agent under the visual field angle constraint condition according to the linear speed control law of the orientation agent and the linear speed control law of the distance agent.
The following is a simulation and physical experiment of the multi-agent formation control method. Due to the view angle constraint, the parameters when k is 0 and k is 0 are set as follows:
Figure BDA0003339239980000132
Figure BDA0003339239980000133
wherein e is>0, and sufficiently small;
sgn(Δd)＝1。
three sets of simulation experiments were performed for the following three cases. The three cases are:
(1) different angular size of field of view, i.e.
Figure BDA0003339239980000134
And
Figure BDA0003339239980000135
(2) the undesired side different initial positions. Namely, the initial position is respectively close to the No. 1 intelligent agent and the initial position is close to the No. 3 intelligent agent;
(3) the initial position is on the desired side and the undesired side.
Simulation one: different view angle size constraints
Fig. 4 and 5 respectively illustrate at viewing angles according to an embodiment of the present disclosure
Figure BDA0003339239980000136
And forming a schematic diagram of 3 intelligent agents under the constraint condition and forming an error curve schematic diagram.
In that
Figure BDA0003339239980000137
Under the condition, the view angle is set to be
Figure BDA0003339239980000138
Desired angle
Figure BDA0003339239980000139
The initial positions of agents No. 1, 2 and 3 are respectively z1＝[-1.0 0.0]T、z2＝[-1.8 1.5]TAnd z3＝[1.0 0.0]T. The formation process of agents No. 1, No. 2 and No. 3 shown in fig. 2 is shown in fig. 4, and the error curve of the formation process is shown in fig. 5.
FIGS. 6 and 7 illustrate at viewing angles, respectively, according to an embodiment of the present disclosure
Figure BDA0003339239980000141
And 3 intelligent agents are formed into a schematic diagram and a schematic diagram of an error curve of the formation process under the constraint condition.
In that
Figure BDA0003339239980000142
Under the condition, the viewing angle theta is setfSize pi, desired angle
Figure BDA0003339239980000143
The initial positions of agents No. 1, 2 and 3 are respectively z1＝[-1 0]T、z2＝[-0.5 0.8]TAnd z3＝ [1 0]T. The formation process of agents No. 1, No. 2 and No. 3 shown in fig. 2 is shown in fig. 6, and the error curve of the formation process is shown in fig. 5.
Simulation II: different view angle size constraints
Fig. 8 and 9 respectively show a formation forming diagram and a formation forming process error diagram when the initial position of the number 2 orientation agent is close to the number 3 distance agent according to an embodiment of the present disclosure.
Wherein, the simulation result of the No. 2 azimuth intelligent agent when the initial position is close to the No. 1 distance intelligent agent and the view angle thereof
Figure BDA0003339239980000144
Simulation results under the constraint condition are consistent, and a formation forming schematic diagram and a formation forming process error schematic diagram of the intelligent agent with the number 2 azimuth when the initial position is close to the intelligent agent with the number 1 distance are respectively shown in fig. 4 and 5.
In that
Figure BDA0003339239980000145
Under the condition, the view angle is set to be
Figure BDA0003339239980000146
Desired angle
Figure BDA0003339239980000147
The initial positions of agents No. 1, 2 and 3 are respectively z1＝[-1 0]T、z2＝[1.8 1.5]TAnd z3＝ [1 0]T. The formation process of agents No. 1, No. 2 and No. 3 shown in fig. 2 is shown in fig. 8, and the error curve of the formation process is shown in fig. 9.
And (3) simulation: the initial position is at the desired side and the undesired side
Fig. 10 and 11 show a formation schematic diagram and a formation process error schematic diagram, respectively, of a position agent No. 2 with its initial position on the desired side according to an embodiment of the present disclosure.
On the desired side, the viewing angle is set to a value of
Figure BDA0003339239980000148
Desired angle
Figure BDA0003339239980000149
The initial positions of agents No. 1, 2 and 3 are respectively z1＝[-1 0]T、z2＝[0.55-6]TAnd z3＝[1 0]T. The formation process of agents No. 1, No. 2 and No. 3 shown in fig. 2 is shown in fig. 10, and the error curve of the formation process is shown in fig. 11.
FIG. 12 illustrates a schematic diagram of a multi-agent formation and transformation process under view angle constraints, according to an embodiment of the present disclosure; FIG. 13 shows a schematic diagram of angle error and side length transformation in a multi-agent formation process under view angle constraints according to an embodiment of the present disclosure.
Next, a set of experiments of the drones is given, the formation process is shown in fig. 11, and the error and side length variation curve is shown in fig. 12.
The multi-agent formation control method under the visual field angle constraint condition comprises the steps of establishing an agent system model, wherein the agent comprises an orientation agent and a distance agent; constructing an angular speed controller of an orientation intelligent body based on an intelligent body system model; controlling the orientation intelligent agent to meet the visual field angle constraint condition by utilizing an angular speed controller of the orientation intelligent agent; establishing a linear speed 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 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; and controlling the formation of the multiple agents under the visual field angle constraint condition according to the linear speed control law of the orientation agent and the linear speed control law of the distance agent. Under the condition that the intelligent agent only has azimuth information and no position information or distance information, the intelligent agent can select relatively fewer paths to move from an undesired side to a desired side and finally to a desired position, and formation, maintenance and transformation of multi-intelligent-agent formation under the condition of view angle constraint are realized.
Although the embodiments of the present invention have been described above, the above descriptions are only for the convenience of understanding the present invention, and are not intended to limit the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

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:
Figure FDA0003339239970000011
wherein z (k +1),
Figure FDA0003339239970000012
indicating the position of the agent at two adjacent moments,
Figure FDA0003339239970000013
is the control input of the linear velocity of the intelligent body, T is the material sample time,
Figure FDA0003339239970000014
representing the orientation angle, u, of the agent at two timesω(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 θf∈(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:
Figure FDA0003339239970000021
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
Figure FDA0003339239970000022
Wherein S is the area with symbol, S*Is the desired signed area.
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