CN104865960A - Multi-intelligent-body formation control method based on plane - Google Patents

Abstract

The invention discloses a multi-intelligent-body formation control method based on a plane, which comprises the following steps: a first step, determining a neighbor set Ni(t) of each intelligent body according to a system topology structure, and constructing a system adjacent matrix A, a degree matrix D and a Laplacian matrix L according to the topology structure; a second step, computing a coherence control protocol of the multiple intelligent bodies according to the information of the adjacent nodes; a third step, based on the coherence control protocol, through telescoping transformation of the matrix, distributing the intelligent bodies to different groups, and obtaining a grouped synchronous control protocol; and a fourth step, through rotation transformation, reprocessing the intelligent bodies in different groups, so that each intelligent body is configured to an anticipated formation position. According to the multi-intelligent-body formation control method, the position of the intelligent body in the formation can be randomly set according to the requirement. Furthermore the multi-intelligent-body formation control method has advantages of simple design procedure, clear gradation in the processing process, and clear geometrical meaning. An effective control algorithm is supplied for settling a multi-intelligent-body formation problem.

Description

Based on a kind of multiple agent approach to formation control of plane

Technical field

The present invention relates to multiple agent field, in studying plane, the formation formation problem of multiple agent, proposes formation control method and the order switching method of Arbitrary Formation in a kind of plane.

Background technology

So-called multi-agent system, namely multiple entity with intelligence carrys out a type systematic of the structure of expression system, function and behavioral trait by communication each other, cooperation, coordination, scheduling, control etc.Because one huge, the task of difficulty usually beyond the limit of power of single intelligent body, therefore needs multiple intelligent body mutually to coordinate, cooperating with each other completes jointly, and therefore there is wide Research Prospects in multiple agent field.For multi-agent system, formation problem is a kind of very important approach to cooperation, require under many scenes that multiple intelligent body keeps specific formation when performing a certain task, as: dining room multirobot passes dish service, and the multiple robot in workshop carries out logistics transport and Soccer robot contest etc.Namely this algorithm proposes a formation control method when multiple agent planar runs.

Formation control is that of consistency problem expands and extends, and controls inseparable relation with consistance.The present invention, from consistency problem, carries out a series of linear transformation to the quantity of state of intelligent body, proposes multiple agent formation control protocol algorithm in a kind of plane.This algorithm geometric meaning is clear and definite, technology realizes simple, has extremely strong operability.

Summary of the invention

For solving the deficiency that prior art exists, the invention discloses a kind of multiple agent approach to formation control based on plane, keeping expecting that formation performs a certain task in order to realize intelligent body, strengthening the intelligent processing ability of system.In order to reach above-mentioned effect, each intelligent body needs to keep identical speed when in stable condition, and location gap need keep a numerical value of specifying, and this numerical value depends on concrete formation.

For achieving the above object, concrete scheme of the present invention is as follows:

Based on a kind of multiple agent approach to formation control of plane, comprise the following steps:

Step one: obtain the initial displacement x (0) of each intelligent body and initial velocity v (0), determine that the neighbours of each intelligent body collect N according to system topology _i(t), and according to topological structure tectonic system adjacency matrix A, degree matrix D, and construct Laplacian matrix L thus;

Step 2: utilize the information of neighbor node to calculate multiple agent consistance control protocol u _i, by control protocol u _ibe brought into single intelligent body motion model and obtain corresponding equation;

Step 3: the non-zero characteristics root λ asking Laplacian matrix L ₁, λ ₂..., λ _r, determine multiple agent consistance control protocol u _iin undetermined parameter k, the value of b; The number of the mutually different non-zero characteristics root of r representing matrix L, undetermined parameter k, b demand fulfillment stability condition;

Step 4: structural matrix P meets P ^-1lP=J, and matrix J first diagonal element is 0, wherein P ^-1the inverse matrix of representing matrix P, the Jordans' matrix of matrix J representing matrix L;

Step 5: at consistance control protocol u _ibasis on, by the stretching of matrix, intelligent body position is assigned to different groupings, obtains packet synchronization control protocol u _i';

Step 6: synchro control agreement u _i' basis on, by the rotational transform of matrix, one by one the intelligent body of different grouping is carried out processing again obtaining final control protocol u _i", make each intelligent body be configured to the formation position of expection.

In described step one, initial displacement x (0) and initial velocity v (0), wherein, x (0)=[x ₁(0), x ₂(0) ... x _n(0)] ^t, v (0)=[v ₁(0), v ₂(0) ... v _n(0)] ^t), n represents the number of intelligent body.

In described step one, the relation of adjacency matrix A, degree matrix D and Laplacian matrix L is: L=D-A.

In described step 2, for intelligent body formation control, single intelligent body motion model is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_i=v_i\\ {\stackrel{\·}{v}}_i=u_i\end{array}\right.,i=\mathrm{1,2},...,n,---\left(1\right)$

Wherein, x _i, v _irepresent the Position And Velocity of i-th intelligent body respectively, u _irepresent the control protocol that i-th intelligent body is to be set; represent the first order derivative of displacement and speed respectively, n represents the number of intelligent body, because each intelligent body all planar moves, therefore quantity of state x _i, v _ibe two dimension, i.e. x _i=[x _i1, x _i2] ^t, v _i=[v _i1, v _i2] ^t.

In described step 2, multiple agent consistance control protocol u _ibe specially:

$u_i=\underset{j\∈N_i}{\mathrm{\Σ}}[b(v_j-v_i)+k(x_j-x_i)]$

Wherein k, b are undetermined constant, its value Size-dependent target formation, x _i, v _irepresent the Position And Velocity of i-th intelligent body respectively, x _j, v _jrepresent the displacement when moment t of a jth intelligent body and speed respectively.

In described step 2, by control protocol u _ibe brought into single intelligent body motion model and obtain corresponding equation, be specially:

wherein represent first order derivative and the second derivative of vector x respectively, x=[x ₁, x ₂..., x _n] ^t, k, b are undetermined constant, for guaranteeing the stability of system and the speed regulating formation to restrain, I ₂represent second order unit matrix, i.e. I ₂=diag (1,1), represent that kronecker amasss.

In described step 3, determine multiple agent consistance control protocol u _iin undetermined parameter k, during the value of b,

According to stability theory, work as b, k meets time, (2)

System can reach consistance, determines k with this, the value of b; Wherein, λ _l=α _l+ i β _lfor the non-zero characteristics root of Laplacian matrix L, α _lfor characteristic root λ _lreal part, β _lfor characteristic root λ _limaginary part, r is mutually different non-zero characteristics root number, and i meets i ²=-1;

In described step 4, also comprise, work as b, when k meets stability condition, system speed finally converges on the first two component, be designated as wherein v (0)=[v ₁(0), v ₂(0) ... v _n(0)] ^trepresent the speed of whole n intelligent body initial time, it can thus be appreciated that the angle of intelligent body direction of motion and transverse axis is

In step 4, obtain matrix P, for judging intelligent body direction of motion, direction is vector the cotangent value of ratio of the first two component, this deflection is the reference angle of the rotational transform of step 6.

In described step 5, packet synchronization control protocol wherein η _j, η _irepresent the distance between different grouping, k, b are undetermined constant, its value Size-dependent target formation, x _i, v _irepresent the Position And Velocity of i-th intelligent body respectively, x _j, v _jrepresent the displacement when moment t of a jth intelligent body and speed respectively.

In described step 6, final control protocol u _i":

${u_i}^{\′\′}=\underset{j\∈N_i\left(t\right)}{\mathrm{\Σ}}[\frac{k}{{\mathrm{\η}}_j}{x}_j+b(v_j-v_i)]-\frac{k}{\cos {\mathrm{\θ}}_i}{e}^{{\mathrm{j\θ}}_i}\underset{j\∈N_i\left(t\right)}{\mathrm{\Σ}}\frac{x_i}{{\mathrm{\η}}_i},$ Connect intelligent body x _iwith the line of barycenter, wherein θ _ifor the angle of this line and direction of motion, Size-dependent in expectation formation, η _j, η _irepresent the distance between different grouping, k, b are undetermined constant, its value Size-dependent target formation, x _i, v _irepresent the Position And Velocity of i-th intelligent body respectively, x _j, v _jrepresent the displacement when moment t of a jth intelligent body and speed respectively.

Described intelligent body comprises robot, intelligent vehicle and other unmanned autonomous devices.

Described N _it () represents the neighbours collection of i-th node when moment t.

Beneficial effect of the present invention:

The present invention utilizes neighbours' speed and the position relationship of multiple agent, give the control protocol method for designing of Arbitrary Formation in a kind of plane, and the position of each intelligent body in formation can set arbitrarily, the method design procedure is simple, geometric meaning is clear and definite, has extremely strong practicality and operability.

Accompanying drawing explanation

Fig. 1 topology diagram;

Fig. 2 topological diagram adjacency matrix;

Fig. 3 topology scale matrix;

Fig. 4 topological diagram Laplacian matrix;

Figure 51 6 intelligent body 4 × 4 formation array example;

Fig. 6 control protocol design flow diagram

Embodiment:

Below in conjunction with accompanying drawing, the present invention is described in detail:

Technical solution of the present invention for proposing multiple agent formation control method in a kind of plane, and gives the design proposal of correlation parameter in distributed director.It is simple that the program has realization, the features such as control performance is excellent.

As shown in Figure 1, Fig. 1 gives the topological structure schematic diagram of 6 intelligent bodies, if wherein there is limit to be connected between two intelligent bodies, then these two intelligent bodies claim neighbours mutually; If this limit is unidirectional, then represent that between intelligent body, information transmission is also unidirectional, now claim this topology for digraph, otherwise be called non-directed graph.If there is weight on the limit between neighbours, then claim topology to be weighted graph, for weighted graph, if weights are non-vanishing between two intelligent bodies, then claim these two intelligent bodies for neighbours.

Fig. 2 is the adjacency matrix of topological structure, if wherein adjacency matrix A is weighted graph, then and corresponding a _ijfor concrete weighted value; Fig. 3 is the degree matrix D of topological diagram, and degree matrix is pair of horns matrix, diagonal element d _iiequal this row all elements sum in adjacency matrix; Fig. 4 represents the Laplacian matrix of topological diagram, if topological structure is connected graph, then Laplacian matrix has one zero characteristic roots, and all the other characteristic roots have positive real part.

Multiple agent formation control method in a kind of plane, step one: determine that the neighbours of each intelligent body collect N according to system topology _i(t), and according to topological structure tectonic system adjacency matrix A, degree matrix D and Laplacian matrix L; Step 2: utilize the information of neighbor node to calculate multiple agent consistance control protocol; Step 3: on the basis of consistance control protocol, by the stretching of matrix, is assigned to different groupings by intelligent body, obtains packet synchronization control protocol; Step 4: by rotational transform, processes again by the intelligent body of different grouping one by one, makes each intelligent body be configured to the formation position of expection.

As shown in Figure 6, the specific algorithm of control protocol, is specially when realizing the design cycle of controling parameters:

2-1) obtain the Position And Velocity of each intelligent body of initial time;

2-2) judge whether system topological is communicated with, if cannot be communicated with, then expect that formation cannot realize, if can be communicated with, then proceeds to step 2-3)

2-3) control protocol u1 is set, makes system realize consistance;

2-4) packet synchronization agreement u2 is set on consistance basis;

2-5) rotation displacement is carried out for the intelligent body in same group, agreement u3 is set;

2-6) Comprehensive Control agreement u1, packet synchronization agreement u2 and agreement u3, obtain final control protocol.

The parameter of final control protocol, when calculating, is specially:

3-1) multiple agent consistance calculates, and first calculates coefficient k (1) in final control protocol _ji, k (1) _ii, b, i, j ∈ 1,2 ..., n, make system realize consistance, namely speed is consistent, and position is consistent, wherein k (1) _ji, k (1) _iirepresent the k of first time conversion in the control protocol that formula is final _ji, k _iivalue size, k (1) _ji, k (1) _ii, the Size-dependent of b, in the value of the non-zero characteristics root of Laplacian matrix L, is shown in formula (2);

3-2) carry out grouping to intelligent body to calculate, according to formation needs, intelligent body is divided into groups, namely to the stretching k (2) that the intelligent body of different grouping carries out in various degree _ji, k (2) _ii, i, j ∈ 1,2 ..., n, telescopic level depends on the distance between the different group of specific formation;

3-3) carry out rotary extension conversion with the intelligent body in group, rotational transform k (3) is successively carried out to the intelligent body in same grouping _ji, k (3) _ii, make the intelligent body in same grouping keep the distance of specifying;

3-4) make k _ji=k (3) _jik (2) _jik (1) _ji, k _ii=k (3) _iik (2) _iik (1) _ii, obtain k _ii, k _ji(i, j=1,2 ..., n), and b, be brought in the final control protocol of formula be controller parameter to be asked.

Described N _it () represents the neighbours collection of i-th node when moment t.

Described intelligent body comprises robot, intelligent vehicle and other unmanned autonomous devices.

Described step 3-2) in when intelligent body is divided into groups, first horizontal direction can divide into groups, also can first divide into groups in the vertical direction.

Step 3-2)-step 3-4) be Protocol Design analytical algorithm, intelligent body actual motion route can not according to assemble, divide into groups, rotate three steps run.

In order to realize rate of convergence faster, meet the prerequisite of formula (2) at k, b under, suitably can increase k, the value of b.

Concrete case:

Next how will realize 4 × 4 formation processes by 16 intelligent bodies is example (Fig. 5).

1, synchronize design.Make control protocol by u _ibring formula (1) into and arrange and can obtain: $\stackrel{\·\·}{x}+b(L\⊗I_2)\stackrel{\·}{x}+k(L\⊗I_2)x=0;$

2. theoretical according to system stability, work as k, b > 0, and time (α _l, β _lbe respectively the characteristic root λ of Laplacian matrix L _lreal part and imaginary part, r is the number of the mutual unequal non-zero characteristics root of matrix L, and system speed and displacement can reach consistance;

3. pair intelligent body divides into groups.According to the correlation theory of linear transformation, if reach the effect of expectation after grouping, after system equation being expressed as matrix form be then wherein matrix the spacing of different grouping passes through η ₁, η ₂, η ₃, η ₄size adjust accordingly (in same grouping, η value is identical), be after single subsystem by this system decomposition, for system (1), can control protocol be obtained if wherein x _iwhen belonging to l group, η _i=η _l(l=1,2,3,4), I ₄for quadravalence unit matrix, i.e. I ₄=diag [1,1,1,1];

4. carry out rotary extension conversion with the intelligent body in group.Find the barycenter O under multiagent system steady state (SS), and it can be used as true origin to set up rectangular coordinate system, connect intelligent body x _iwith barycenter, the angle of this line and direction of motion is designated as θ _i.Be, after matrix equation, have multiple agent the Representation Equation wherein $J_2=diag(\frac{1}{{\mathrm{cos\θ}}_1}{e}^{{\mathrm{j\θ}}_1},\frac{1}{{\mathrm{cos\θ}}_2}{e}^{{\mathrm{j\θ}}_2},...,\frac{1}{{\mathrm{cos\θ}}_{16}}{e}^{{\mathrm{j\θ}}_{16}}),$ Can control protocol be obtained thus:

${u_i}^{\′\′}=\underset{j\∈N_i\left(t\right)}{\mathrm{\Σ}}[\frac{k}{{\mathrm{\η}}_j}{x}_j+b(v_j-v_i)]-\frac{k}{\cos {\mathrm{\θ}}_i}{e}^{{\mathrm{j\θ}}_i}\underset{j\∈N_i\left(t\right)}{\mathrm{\Σ}}\frac{x_i}{{\mathrm{\η}}_i}.$

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (10)

1., based on a kind of multiple agent approach to formation control of plane, it is characterized in that, comprise the following steps:

Step one: obtain the initial displacement x (0) of each intelligent body and initial velocity v (0), determine that the neighbours of each intelligent body collect N according to system topology _i(t), and according to topological structure tectonic system adjacency matrix A, degree matrix D, and construct Laplacian matrix L thus;

Step 2: utilize the information of neighbor node to calculate multiple agent consistance control protocol u _i, by control protocol u _ibe brought into single intelligent body motion model and obtain corresponding equation;

Step 3: the non-zero characteristics root λ asking Laplacian matrix L ₁, λ ₂..., λ _r, determine multiple agent consistance control protocol u _iin undetermined parameter k, the value of b; The number of the mutually different non-zero characteristics root of r representing matrix L, undetermined parameter k, b demand fulfillment system stability condition;

Step 4: structural matrix P meets P ^-1lP=J, and matrix J first diagonal element is 0, wherein P ^-1the inverse matrix of representing matrix P, the Jordans' matrix of matrix J representing matrix L;

Step 5: at consistance control protocol u _ibasis on, by the stretching of matrix, intelligent body position is assigned to different groupings, obtains packet synchronization control protocol u _i';

Step 6: synchro control agreement u _i' basis on, by the rotational transform of matrix, one by one the intelligent body of different grouping is carried out processing again obtaining final control protocol u _i", make each intelligent body be configured to the formation position of expection.

2., as claimed in claim 1 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in described step one, initial displacement x (0) and initial velocity v (0),

Wherein, x (0)=[x ₁(0), x ₂(0) ... x _n(0)] ^t, v (0)=[v ₁(0), v ₂(0) ... v _n(0)] ^t), n represents the number of intelligent body.

3. as claimed in claim 1 or 2 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in described step one, the relation of adjacency matrix A, degree matrix D and Laplacian matrix L is: L=D-A.

4., as claimed in claim 1 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in described step 2, for intelligent body formation control, single intelligent body motion model is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_i=v_i\\ {\stackrel{\·}{v}}_i=u_i\end{array}\right.,i=\mathrm{1,2},...,n,---\left(1\right)$

Wherein, x _i, v _irepresent the Position And Velocity of i-th intelligent body respectively, u _irepresent the control protocol that i-th intelligent body is to be set; represent the first order derivative of displacement and speed respectively, n represents the number of intelligent body, because each intelligent body all planar moves, therefore quantity of state x _i, v _ibe two dimension, i.e. x _i=[x _i1, x _i2] ^t, v _i=[v _i1, v _i2] ^t.

5., as claimed in claim 1 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in described step 2, multiple agent consistance control protocol u _ibe specially:

$u_i=\underset{j\∈N_i}{\mathrm{\Σ}}[b(v_j-v_i)+k(x_j-x_i)]$

Wherein k, b are undetermined constant, its value Size-dependent target formation, x _i, v _irepresent the Position And Velocity of i-th intelligent body respectively, x _j, v _jrepresent the displacement when moment t of a jth intelligent body and speed respectively.

6., as claimed in claim 1 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in described step 2, by control protocol u _ibe brought into single intelligent body motion model and obtain corresponding equation, be specially:

wherein represent first order derivative and the second derivative of vector x respectively, x=[x ₁, x ₂..., x _n] ^t, k, b are undetermined constant, for guaranteeing the stability of system and the speed regulating formation to restrain, I ₂represent second order unit matrix, i.e. I ₂=diag (1,1), represent that kronecker amasss.

7., as claimed in claim 1 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in described step 3, determine multiple agent consistance control protocol u _iin undetermined parameter k, during the value of b,

According to stability theory, work as b, k meets time, (2)

System can reach consistance, determines k with this, the value of b; Wherein, λ _l=α _l+ i β _lfor the non-zero characteristics root of Laplacian matrix L, α _lfor the real part of characteristic root, β _lfor the imaginary part of characteristic root, r is mutually different non-zero characteristics root number, and i meets i ²=-1.

8., as claimed in claim 7 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in described step 5, packet synchronization control protocol wherein η _j, η _irepresent the distance between different grouping, k, b are undetermined constant, its value Size-dependent target formation, x _i, v _irepresent the Position And Velocity of i-th intelligent body respectively, x _j, v _jrepresent the displacement when moment t of a jth intelligent body and speed respectively.

9., as claimed in claim 8 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in described step 6, final control protocol u _i":

${u_i}^{\′\′}=\underset{j\∈N_i\left(t\right)}{\mathrm{\Σ}}[\frac{k}{{\mathrm{\η}}_j}{x}_j+b(v_j-v_i)]-\frac{k}{\cos {\mathrm{\θ}}_i}{e}^{j{\mathrm{\θ}}_i}\underset{j\∈N_i\left(t\right)}{\mathrm{\Σ}}\frac{x_i}{{\mathrm{\η}}_i},$ Connect intelligent body x _iwith the line of barycenter, wherein θ _ifor the angle of this line and direction of motion, Size-dependent in expectation formation, η _j, η _irepresent the distance between different grouping, k, b are undetermined constant, its value Size-dependent target formation, x _i, v _irepresent the Position And Velocity of i-th intelligent body respectively, x _j, v _jrepresent the displacement when moment t of a jth intelligent body and speed respectively.

10., as claimed in claim 1 based on a kind of multiple agent approach to formation control of plane, it is characterized in that, in step 4, also comprise: work as b, when k meets stability condition, system speed finally converges on the first two component of v (0), is designated as wherein v (0)=[v ₁(0), v ₂(0) ... v _n(0)] ^trepresent the speed of whole n intelligent body initial time, it can thus be appreciated that the angle of intelligent body direction of motion and transverse axis is