CN114879484B - Collaborative controller design method for connection maintenance of multiple incomplete mobile agents - Google Patents
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Abstract
The invention relates to a method for designing a cooperative controller for connecting and maintaining a plurality of incomplete mobile intelligent agents, which is used for solving the problem of cooperative control formed by formation and comprises the following steps: constructing a kinetic equation of a multi-agent system, wherein the multi-agent system comprises N followers and 1 leader; acquiring a time-varying communication diagram of a leader and follower system; constructing a closed loop system corresponding to the multi-intelligent system through coordinate transformation; design distributed dynamic state feedback controller u i So that for any initial conditions, theThe connection is such that the closed loop system has the following properties: (1) For any of the values of t,connecting; (2)And is also provided withCompared with the prior art, the intelligent agent capable of initially maintaining communication can maintain communication all the time, and meanwhile, the intelligent agents can cooperate to achieve a formation effect.
Description
Technical Field
The invention belongs to the technical field of control science, relates to a cooperative controller, and particularly relates to a cooperative controller design method for connection maintenance of a plurality of incomplete mobile intelligent agents.
Background
In the case where the communication network satisfies a certain connectivity assumption, various cooperative control problems of a plurality of incomplete mobile agents have been widely studied by using a distributed controller. For example, synchronization problems, no leader formation problems, leader follower formation problems, and the like.
In the literature "Cooperative output regulation with application to multi-agent consensus under switching network" (Su Young et al IEEE Transactions on Systems, man, and Cybernetics, part B (Cybernetics), 2012,42 (3): 864-875), for a plurality of incompletely mobile agents, it is assumed that communication patterns can remain connected frequently enough during motion evolution. However, for a given initial state and parameter set, it is difficult or even impossible in practice to meet and verify this assumption. In fact, the connectivity of the original network generally cannot guarantee connectivity of the entire network during long-time movement, and is limited by the sensing and communication capabilities of the agents, the interaction topology between the agents may change over time. Therefore, it is of great practical importance to study the problem of maintaining connectivity of an agent.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for designing a cooperative controller for connecting and maintaining a plurality of incomplete mobile intelligent agents, which can realize that the intelligent agents which initially maintain communication can always maintain communication and can realize that the intelligent agents cooperate to achieve a formation effect.
The aim of the invention can be achieved by the following technical scheme:
a design method of a cooperative controller for maintaining connection of a plurality of incomplete mobile agents is used for solving the problem of cooperative control formed by formation, and is characterized by comprising the following steps:
s1, constructing a kinetic equation of a multi-agent system, wherein the multi-agent system is provided with N+1 agents and comprises N followers and 1 leader;
s2, acquiring a time-varying communication diagram of a leader and follower systemWherein the set of pointsIs an edge set and defines the neighbor node set of i as: /> t represents the moment;
s3, constructing a closed loop system corresponding to the multi-agent system through coordinate transformation:
wherein r is i Is the position after the coordinate conversion and is used for the coordinate conversion,is a new input, ψ (·) is the potential energy function, a ij (t) is an edge set parameter;
s4, designing a distributed dynamic state feedback controller u i So that for any initial condition x 0 (0)、x i (0)、y i (0)、θ i (0)、v i (0)、w i (0) I=1, … N, letThe connection is such that the closed loop system has the following properties: (1) For any t->Connecting; (2)/>And->Obtained distributed dynamic state feedback controller u i Expressed as:
wherein θ i Is the angle, v, of agent i i Is the linear velocity omega i Is the angular velocity, m i Is of mass, J i Is the moment of mass inertia.
Further, the kinetic equation of the follower is:
wherein for i=1, …, N, (x) i ,y i (ii) is the Cartesian coordinates of the center of agent i, f i Is force τ i Is the moment acting on the agent.
Further, the dynamics equation of the leader is based on the leader signal x 0 Building the leader signal x 0 Is generated by a linear system of the following form:I 2 is a second order identity matrix.
Further, the time trace of the leader is: h is a i (t)＝[at+x di ,ct+y di ]Wherein a, c, x di And y di Are all constant.
Further, an effective communication distance constant r & gt0 and a constant E [0, r ] of any sensor are given, and for any t is more than or equal to 0, a time-varying communication diagram is providedEdge set of->The following conditions were used: (1)/> (2) If r i (t)-r j (t) ||gtoreq.r, then +.>(3)/>(4) For i=0, 1, …, N, j=1, …, N, if +.>And r i (t)-r j (t) | < (r-E), then +.>(5) For i=0, 1, …, N, j=1, …, N, if +.>And r i (t)-r j (t) || < r, then +.>Wherein, at time t, if +.>Then call ||r i (t)-r j (t) || is the length of the edge (i, j).
Further, the coordinate conversion specifically includes:
r i ＝q i -d i0 ，i＝1,…,N
wherein q i Position of i-th agent axle, d i0 Is the distance between the ith follower and the leader, f i Is force τ i Is the moment acting on the agent.
Further, the q i Expressed as:
further, the value of the edge set parameter is determined by:
for i=1, …, N, j=0, 1, …, N, e.g.Fruit setThen a ij =1, otherwise a ij ＝0。
Further, the potential energy function ψ(s) is designed as follows:s is more than or equal to 0 and less than r, wherein r is the effective communication distance constant of the sensor.
The present invention also provides an electronic device including:
one or more processors;
a memory; and
one or more programs stored in memory, the one or more programs comprising instructions for performing the collaborative controller design method as described in any of the above.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention combines the problem of cooperative output adjustment with the potential function technology, and further researches the problem of formation and connectivity maintenance of leader followers of a plurality of incomplete mobile agents.
2. The invention does not set up a communication diagram to meet any connectivity assumption, so that the controller has the capability of maintaining the connectivity of an initial connection network, and meanwhile, the formation of a leader follower formation of a mobile agent group is realized when the leader moves along a straight line. The invention requires the initial communication diagram to be a connection diagram instead of the assumption that the communication diagram can keep frequent enough connection, so that the intelligent agents which initially keep communication can keep communication all the time, and meanwhile, the intelligent agents can cooperate to achieve the formation effect.
3. The control algorithm of the invention can lead the intelligent body with limited communication distance to finally reach the cooperative control target.
4. The method is suitable for formation tasks with limited effective communication distances of some intelligent body sensors, and has good practical application value.
Drawings
FIG. 1 is a schematic diagram of a controller design flow according to the present invention;
FIG. 2 is a schematic diagram of the expected formation of a plurality of incomplete mobile robots according to the present invention;
FIG. 3 is a diagram of the length change of the initial connection topology edge of a plurality of incomplete mobile robots;
FIG. 4 is a graph of distance variation between a follower and a leader;
fig. 5 is a diagram of the formation situation at different moments.
Detailed Description
The invention will now be described in detail with reference to the drawings and specific examples. The present embodiment is implemented on the premise of the technical scheme of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.
The invention provides a method for designing a cooperative controller for connection and maintenance of a plurality of incomplete mobile intelligent agents, which solves the problem that formation of connection and maintenance of communication diagrams can form cooperative control under the condition that no communication diagram is set to meet any connectivity assumption, and provides important technical support for formation control of leader followers of a mobile intelligent agent group.
As shown in fig. 1, the cooperative controller design method includes the following steps:
step S1, constructing a multi-agent system, wherein the multi-agent system is provided with N+1 agents and comprises N followers and 1 leader, and acquiring a dynamics equation of the multi-agent system.
(1) Kinetic equation of follower
In this embodiment, a system kinematics equation of the follower of the following form is constructed: wherein for i=1, …, N, (x) i ,y i ) Is the Cartesian coordinate, θ, of the center of the agent i Is the angle v i Is the linear velocity omega i Is the angular velocity, m i Is of mass, J i Is the moment of inertia of mass, f i Is force τ i Is the moment acting on the agent.
(2) Kinetic equation of leader
In this embodiment, the time trace of the leader is defined as h d (t)＝[at+x d0 ,ct+y d0 ]Wherein a is a constant, c is a constant, x d0 Is a constant, y d0 Is a constant. Thus, give the leader signal x 0 Is generated by a linear system of the following form:wherein I is 2 Is a second order identity matrix, by selecting an initial condition x 0 (0)＝[x d0 ,y d0 ,a,c]Can be derived +.>
Step S2, a time-varying communication diagram of the leader and follower system is obtained.
In a multi-agent system, generally, the control input u of the ith agent is due to communication impairment between the leader and follower i Information of all the remaining nodes cannot be accessed. In order to describe communication disorders more intuitively, a time-varying communication diagram is defined as follows:wherein the dot set->Node 0 is associated with the leader system, nodes i, i=1, …, N is associated with the ith agent (i.e. the ith follower) in the follower system,/-, and _>Is an edge set. Edge setThe definition is as follows: for the followingi=1, …, N, j=0, 1, …, N, i+notej, if and only if at time t the control input u of the i-th agent i Can access the information of the jth agent, there is +.>Defining neighbor node sets of agent i as:
in this embodiment, a distributed state feedback method is adopted to enable the follower to follow a certain straight line h i (t)＝[at+x di ,ct+y di ]Moving and forming a geometric profile, as shown in FIG. 2, which presents a problem of formation, where x di And y di Is a constant.
And S3, carrying out coordinate transformation on a kinetic equation of the follower to form a double-integrator multi-agent system.
To define a communication diagramLet q i At a distance d i Representing the position of the ith mobile agent axle:the following coordinate transformations are formed in step S1:
r i ＝q i -d i0 ,i＝1,…,N
the following dual integrator follower system is thus derived:p i is an intermediate parameter. Wherein r is i Is the converted position, +.>Is a new input. At the same time let r 0 (t)＝h d0 (t), then>
The dual integrator follower system and the domain person kinetic equation together form a dual integrator multi-agent system.
Step S4, defining a time-varying communication diagramEdge set of->The condition is satisfied.
Providing an effective communication distance constant r > 0 and a constant E [0, r ] of any sensor, and for any t is more than or equal to 0,is defined as satisfying the following conditions: (1)/> (2) If r i (t)-r j (t) ||gtoreq.r, then +.>(3)/>For i=0, 1, …, N; (4) For i=0, 1, …, N, j=1, …, N, if +.>And r i (t)-r j (t) | < (r-E), then +.>(5) For i=0, 1, …, N, j=1, …, N, if +.>And r i (t)-r j (t) || < r, thenAt time t, if->Then call ||r i (t)-r j (t) || is the length of the edge (i, j).
Step S5, designing a distributed state feedback controller aiming at the double-integrator multi-intelligent system in step S3.
The general form of the distributed dynamic state feedback controller is designed as: wherein design h i Is a sufficiently smooth function.
The designed distributed state feedback controller has the specific form that: wherein for i=1, …, N, j=0, 1, …, N, if>Then a ij =1, otherwise a ij =0. The following closed loop system is generated:
in this embodiment, to deal with the connectivity maintenance problem, the potential energy function ψ(s) is designed as follows:
thus, it can be derived that the differential form of ψ(s) is +.>
Step S6, designing a controller aiming at the formation problem of the original multi-agent system.
It is proposed to enable formation of communication graph connection maintenance to form a cooperative control problem. For the multi-agent system in step S1, r > 0, ε [0, r), the distributed controller is designed such that for any initial condition x 0 (0)、x i (0)、y i (0)、θ i (0)、v i (0)、w i (0) I=1, … N, letThe connection is such that the closed loop system has the following properties: (1) For arbitrary->Connecting; (2)/>And->
For the multi-intelligent system formation problem in step S1, the distributed dynamic state feedback controller is specifically designed to:wherein->In step S5.
And S7, simulation verification.
In this embodiment, the system parameters of the original multi-agent in step S1 are: m is m i ＝1，J i ＝1，d i =1, i=1, …,4. Let the sensing distance r=8, e=0.5. The control objective is to find a distributed control input u i So that the proper d 10 ＝[-2,2]、d 20 ＝[-2,-2]、d 30 ＝[-4,-4]And d 40 ＝[-4,4]In the time-course of which the first and second contact surfaces, the initial values of the variables are set as follows: (x) 1 (0),y 1 (0))＝[4 4] T 、(x 2 (0),y 2 (0))＝[10 0] T 、(x 3 (0),y 3 (0))＝[2 0] T 、(x 4 (0),y 4 (0))＝[0 8] T 、θ 1 (0)＝1、θ 2 (0)＝0、θ 3 (0)＝1、θ 4 (0)＝0、(v 1 (0),w 1 (0))＝[7 2] T 、(v 2 (0),w 2 (0))＝[0 0] T 、(v 3 (0),w 3 (0))＝[0 -1] T 、(v 4 (0),w 4 (0))＝[0 0] T And x 0 (0)＝[8 0 1 1] T . It can be derived that these initial values enable +.>A connected communication map is formed. The simulation effect of the controller designed in step S6 is shown in FIGS. 3-5. FIG. 3 shows the length of edges { (0, 1), (1, 4), (0, 2), (1, 3) } at t.gtoreq.0, as can be seen, all less than sensor distance 8, and thus, the communication map connection remains. FIG. 4 shows 4 followers to leader d i0 Is a distance of (3). Fig. 5 shows the formation positions of 5 multi-agents at t=0s, 20s,50s,100s, respectively. As can be seen from the simulation results of fig. 3 to 5, the distributed dynamic state in step S6The feedback controller can solve the problem that the proposed formation which can enable the communication diagram connection to be maintained forms cooperative control.
The above-described method, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (5)
1. A design method of a cooperative controller for maintaining connection of a plurality of incomplete mobile agents is used for solving the problem of cooperative control formed by formation, and is characterized by comprising the following steps:
s1, constructing a kinetic equation of a multi-agent system, wherein the multi-agent system is provided with N+1 agents and comprises N followers and 1 leader;
s2, acquiring a time-varying communication diagram of a leader and follower systemWherein the set of pointsIs an edge set and defines the neighbor node set of i as: /> t represents the moment;
s3, constructing a closed loop system corresponding to the multi-agent system through coordinate transformation:
wherein r is i Is the position after the coordinate conversion and is used for the coordinate conversion,is a new input, ψ (·) is the potential energy function, a ij (t) is an edge set parameter;
s4, designing a distributed dynamic state feedback controller u i So that for any initial condition x 0 (0)、x i (0)、y i (0)、θ i (0)、v i (0)、ω i (0) I=1, N, letThe connection is such that the closed loop system has the following properties: (1) For any of the values of t,connecting; (2)/>And->Obtained distributed dynamic state feedback controller u i Expressed as:
wherein θ i Is the angle, v, of agent i i Is the linear velocity omega i Is the angular velocity, m i Is of mass, J i Is the mass moment of inertia;
the kinetic equation of the follower is:
wherein, for i=1,.. i ，y i (ii) is the Cartesian coordinates of the center of agent i, f i Is force τ i Is the moment acting on the intelligent body;
the time track of the leader is as follows: h is a i (t)＝[at+x di ，ct+y di ]Wherein a, c, x di And y di Are all constants;
the coordinate conversion specifically includes:
r i ＝q i -d i0 ，i＝1，…，N
wherein q i Position of i-th agent axle, d i0 Is the distance between the ith follower and the leader, f i Is force τ i Is the moment acting on the intelligent body;
the q is i Expressed as:
the potential energy function ψ(s) is designed as follows:where r is the sensor effective communication distance constant.
2. The method for collaborative controller design for multiple incomplete mobile agent connection maintenance according to claim 1, wherein the dynamics equation of the leader is based on a leader signal x 0 Building the leader signal x 0 Is generated by a linear system of the following form:I 2 is a second order identity matrix.
3. The method for designing a cooperative controller for connection and maintenance of a plurality of incomplete mobile agents according to claim 1, wherein an effective communication distance constant r > 0 and a constant e 0, r of any sensor are given, and a time-varying communication map is given for any t.gtoreq.0Edge set of->The following conditions were used: (1)/> (2) If r i (t)-r j (t) ||gtoreq.r, then +.>(3)/>(4) For i=0, 1, …, N, j=1, …, N, if +.>And r i (t)-r j (t) | < (r-E), then +.>(5) For i=0, 1, …, N, j=1, …, N, if +.>And r i (t)-r j (t) || < r, then +.>Wherein, at time t, if +.>Then call ||r i (t)-r j (t) || is the length of the edge (i, j).
4. The method of collaborative controller design for multiple incomplete mobile agent connection maintenance according to claim 1, wherein the value of the edge set parameter is determined by:
for i=1, …, N, j=0, 1, …, N, ifThen a ij =1, otherwise a ij ＝0。
5. An electronic device, comprising:
one or more processors;
a memory; and
one or more programs stored in a memory, the one or more programs comprising instructions for performing the collaborative controller design method of any of claims 1-4.
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| CN113325852A (en) * | 2021-06-10 | 2021-08-31 | 浙江大学 | Leader follower mode-based control method for formation change of multiple intelligent agents in advancing process |
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