CN115598970A - Multi-robot fuzzy adaptive angle formation control method with nonlinear dead zone - Google Patents

Multi-robot fuzzy adaptive angle formation control method with nonlinear dead zone Download PDF

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CN115598970A
CN115598970A CN202211343570.1A CN202211343570A CN115598970A CN 115598970 A CN115598970 A CN 115598970A CN 202211343570 A CN202211343570 A CN 202211343570A CN 115598970 A CN115598970 A CN 115598970A
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robot
angle
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沈庆成
吴楠
陈子韬
王芹
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Jiangsu Qingya Electronic Technology Co ltd
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Abstract

The invention discloses a multi-robot fuzzy self-adaptive angle formation control method with a nonlinear dead zone, which comprises the following steps of: (1) The unmodeled dynamic state exists in the multi-robot system model, and the unknown nonlinear dynamic state is approximated by using a fuzzy system to model the system; (2) Designing a distributed formation control strategy based on angle information by using a potential energy function method, calculating the error between an actual angle and an expected angle, and designing a virtual control law, namely speed control, by using a negative gradient algorithm; (3) Local information and virtual control obtained by communication are utilized, a self-adaptive dynamic estimator is introduced to estimate unknown dead zone parameters, and a global stable angle rigid formation control law and a self-adaptive law are designed; (4) And (4) calculating the control input of each robot by combining the steps. The method has the characteristics of simplicity, reliability, higher precision and convenience for practical application, and the multi-robot system after formation is widely applied to the fields of military, aerospace, industry and the like.

Description

Multi-robot fuzzy adaptive angle formation control method with nonlinear dead zone
Technical Field
The invention relates to the technical field of multi-robot formation control, in particular to a multi-robot fuzzy self-adaptive angle formation control method with a nonlinear dead zone.
Background
In recent years, with the development and progress of disciplines such as computer technology, communication technology, digital signal processing, sensor technology and the like, a vision or distance sensor, an autonomous or passive controller and a shared communication topology network system are combined to realize new functions of an intelligent agent or improve the effectiveness so as to discover and create greater potential value, and the development and progress of the disciplines become a new trend hot research problem at present. Due to the development of a system embedded technology, the improvement and breakthrough of 5-nanometer and 3-nanometer precise processes, the function of a microprocessing chip is stronger and faster, and the microprocessing chip has the operational capability which is comparable with that of a large-scale computer in the past, so that the microprocessing chip becomes a micro controlled device individual with certain communication, sensing, calculation and execution capabilities, and the development of an automatic control technology and a network communication technology causes the micro autonomous mobile robot [1] to be widely concerned by people. However, due to the increasing production requirements of industrial life and the high development cost of a single robot, the weak function expansibility, the large limitation and other factors, in some dynamic and complex scenes, a single individual physical device is not enough to complete complex tasks and meet practical requirements, so that scholars combine a plurality of robots into a whole on the basis of the intelligent agent theory to study, and provide the concept of a multi-robot system. In terms of practical application, compared with a single robot, the sensing capability and the execution capability of a multi-robot system are better, and a single robot capable of being grouped generally has a self dynamic evolution function, and can exchange information in a non-global range according to adjacent neighbor information to continuously make self attitude or position adjustment, so that the system has the characteristics of communication topology, feedback control and dynamic characteristics. In the application of investigation tasks, exploration surveying and mapping and the like, the robot moves into a certain geometric shape and follows the designed formation, and jump of system functions and energy efficiency is realized. For example, data collection, forest fire monitoring, searching and rescue can be carried out in a severe environment which cannot enter, and a multi-robot system can be used for scanning terrain detection conditions in a greatly improved mode; in space, the artificial satellites can form a formation network and form a planet image; the weight can be measured at multiple points in industrial transportation, so that the supporting points are evenly distributed for reinforcement and safety; in military affairs, submarines, ships and aircraft carriers can keep formation, and the enemy information is investigated in a labor division manner to be gathered and captured; in the aspect of agricultural production, the fertilizer and pesticide can be uniformly applied and sprayed, and the health degree of crops and the like can be recorded. By forming an ideal formation, the robot can not only successfully complete tasks, but also improve performance, such as the quality of collected data, and the robustness of group motion to random environmental disturbances. Therefore, the multi-robot formation system has better stability, stronger fault tolerance and higher efficiency than a single robot, and is also more and more applied to the production and life of people, for example, the multi-robot formation system has vital functions and good prospects in the fields of search and rescue, agricultural plant protection, disaster management, networked unmanned aerial vehicle cruise and the like in dangerous environments, so that the establishment of a scientific and efficient multi-robot cooperative formation control strategy has important practical significance and application value.
At present, most of the existing formation control methods are formation based on relative position information, control input is phenomenon input, and research on multi-robot angle rigid formation control with nonlinear dead zones is few. In addition, most of the existing research objects are first-order integrator models, however, in practical application, many physical objects cannot be depicted by the first-order integrator models, such as mobile robots, unmanned aircrafts, autonomous underwater submarines and the like, and most of the objects must meet incomplete constraint conditions. Because technical limitations or limitations of actual measurement environments are frequently encountered in life, angle measurement information can be easily obtained through a visual sensor or a wireless sensor array, and meanwhile, more and more products are installed on the robot to change the mode of obtaining the environment information, so that formation control can be performed on the multi-robot system only through measuring the angle information. Therefore, a special attention is paid to such a formation situation that each robot can only measure the relative orientation information of its neighboring robots. Most of the existing formation control researches based on relative angles ignore researches of comprehensive models facing external environment interference existing in practical engineering application and specific characteristic information in application problems, most of the existing researches on multi-robot collaborative formation control internationally do not consider uncertain factors such as input nonlinearity or environmental influence, and no learner can provide a new control strategy to globally stabilize an angle rigid formation system aiming at a multi-robot system with nonlinear dead zone input.
Disclosure of Invention
The invention aims to provide a multi-robot fuzzy adaptive angle formation control method with a nonlinear dead zone, which is particularly suitable for a distributed formation control system which only knows relative angle information of multiple robots and has a dead zone nonlinear input.
In order to achieve the purpose, the invention provides the following technical scheme:
the multi-robot fuzzy adaptive angle formation control method with the nonlinear dead zone comprises the following steps of:
(1) The unmodeled dynamic state exists in the multi-robot system model, and the unknown nonlinear dynamic state is approximated by using a fuzzy system to model the system;
(2) Designing a distributed formation control strategy based on angle information by using a potential energy function method, calculating the error between an actual angle and an expected angle, and designing a virtual control law, namely speed control, by using a negative gradient algorithm;
(3) Local information and virtual control obtained by communication are utilized, a self-adaptive dynamic estimator is introduced to estimate unknown dead zone parameters, and a global stable angle rigid formation control law and a self-adaptive law are designed;
(4) And (4) calculating the control input of each robot by combining the steps.
Further, multi-robot systems have typical nonlinear dead zone inputs, and the control algorithm relies only on the relative angles of adjacent robots, each reaching the desired angle and moving at the same speed.
Further, in the step (1), in order to approximate the non-linear unmodeled dynamics of the system, a first class of fuzzy system is selected, and a modeling formula for the robot system is as follows by using the approximation capability of the fuzzy system to the non-linear function:
definition of x i ＝[x i T ,v i T ]Definition of tight set
Figure BDA0003917421230000031
Wherein
Figure BDA0003917421230000032
Is an arbitrarily large normal number limit;
let f 1i (x 1i ,v 1i ,θ x1i ),…,f ki (x ki ,v ki ,θ xki ) Is an I-type fuzzy system in the region
Figure BDA0003917421230000033
Approximation of the upper component, i.e.
Figure BDA0003917421230000034
Wherein theta is xpi ＝[θ 1i ,θ 2i ,…θ Mi ] T ,
Figure BDA0003917421230000035
M i Is the number of rules, phi, of the fuzzy system li (x pi ) Represents the sign of the fuzzy basis function, which is in the form of the equation:
Figure BDA0003917421230000036
wherein theta is li Is an adjustable parameter that is,
Figure BDA0003917421230000037
is a given membership function and is usually taken as
Figure BDA0003917421230000041
Wherein b is i ∈R,c i >0, letting:
Figure BDA0003917421230000042
Figure BDA0003917421230000043
additional equipment
Figure BDA0003917421230000044
Is theta xki The estimated value at the time, at which the optimal approximation error is defined as:
Figure BDA0003917421230000045
at the same time
Figure BDA0003917421230000046
Then the
Figure BDA0003917421230000047
To obtain
f i (x i ,v i )＝φ i (χ i )θ i +δ i
Wherein
Figure BDA0003917421230000048
Substituting the above formula into the dynamic model can obtain
Figure BDA0003917421230000049
Further, the step (2) comprises the following steps:
(2.1) measuring a relative angle between adjacent robots by using a sensor, and calculating an error between an actual angle and an expected angle;
(2.2) introducing a potential energy function according to the error between the actual angle and the expected angle, and designing a virtual control law based on a negative gradient algorithm;
the potential energy function between the robot i and the neighbor robot j is constructed, and the form is as follows:
Figure BDA0003917421230000051
defining:
Figure BDA0003917421230000052
wherein the content of the first and second substances,
Figure BDA0003917421230000053
I d ∈R k×k is an identity matrix, and
Figure BDA0003917421230000054
therefore, the method comprises the following steps:
Figure BDA0003917421230000055
the total potential energy function of robot i is:
Figure BDA0003917421230000056
at the same time, let x = [ x ] 1 T ,x 2 T ,…,x i T ] T ，v＝[v 1 T ,v 2 T ,…,v i T ] T ，u＝[u 1 T ,u 2 T ,…,u i T ] T
Then the non-linear equation can be rewritten as:
Figure BDA0003917421230000057
further, the step (3) comprises the following steps:
(3.1) calculating the error between the actual speed and the virtual control according to the virtual control;
(3.2) calculating a derivative of the error system according to the above steps;
(3.3) selecting a proper Lyapunov function, and deriving the time t;
(3.4) designing a dead zone parameter self-adaptive law by using a parameter self-adaptive dynamic estimation method according to the relative angle information and the virtual control law;
and (3.5) designing a proper global stable angle formation control law by utilizing a back-stepping design method.
Further, to ensure that a specified desired angle can be achieved between each pair of robots, the step (3.3) selects a Lyapunov candidate function as:
Figure BDA0003917421230000061
because the communication topology is undirected, we have
Figure BDA0003917421230000062
For function V 1 (t) derivation may give:
Figure BDA0003917421230000063
selecting a virtual control law v = z (x) as follows:
Figure BDA0003917421230000064
v＝z(x)
then obtain
Figure BDA0003917421230000065
Comprises the following steps:
Figure BDA0003917421230000066
second, introduce an error variable
Figure BDA0003917421230000067
Taking derivatives of the above equation, i.e.
Figure BDA0003917421230000068
For the above system, the Lyapunov candidate function is chosen as:
Figure BDA0003917421230000069
differentiating the above equation with respect to time t, we can obtain:
Figure BDA0003917421230000071
and (3.5) designing a global stable formation control law as follows:
Figure BDA0003917421230000072
the adaptive law is designed as follows:
Figure BDA0003917421230000073
Figure BDA0003917421230000074
further, in which, among others,
Figure BDA0003917421230000075
0<α min <α i ，u max ，α min is a normal number. Symbol letterThe number sgn (a) is defined as: when a is<0,sgn(a)＝-1；a＝0,sgn(a)＝0；a>0,sgn(a)＝1，
Figure BDA0003917421230000076
Compared with the prior art, the invention has the beneficial effects that:
the method has the characteristics of simplicity, reliability, high precision and convenience for practical application, and the multi-robot system after formation is widely applied to the fields of military, aerospace, industry and the like.
Drawings
FIG. 1 is a diagram of a nonlinear input dead-zone model of the present invention;
FIG. 2 is a topology diagram of the present invention;
FIG. 3 is a flow chart of a multi-robot fuzzy adaptive angle formation control method with nonlinear dead zones according to the present invention.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
Example 1, please refer to fig. 1-3:
FIG. 3 is a flow chart of the design of the present invention, which is composed of modules P1, P2 and P3, each of which is described below:
module P1
In the invention, in order to approximate the non-linear unmodeled dynamics of the system, a first class fuzzy system is introduced. Definition of x i ＝[x i T ,v i T ]Definition of tight set
Figure BDA0003917421230000081
Wherein
Figure BDA0003917421230000082
At an arbitrarily large normal number limit. Let f 1i (x 1i ,v 1i ,θ x1i ),…,f ki (x ki ,v ki ,θ xki ) Is an I-type fuzzy system in the region
Figure BDA0003917421230000083
Approximation of the upper component, i.e.
Figure BDA0003917421230000084
Wherein theta is xpi ＝[θ 1i ,θ 2i ,…θ Mi ] T ,
Figure BDA0003917421230000085
M i Is the number of rules, phi, of the fuzzy system li (x pi ) Represents the sign of the fuzzy basis function, which is in the form of the equation:
Figure BDA0003917421230000086
wherein theta is li Is an adjustable parameter that is,
Figure BDA0003917421230000087
is a given membership function and is usually taken as
Figure BDA0003917421230000088
Wherein b is i ∈R,c i >0。
Order to
Figure BDA0003917421230000089
Figure BDA00039174212300000810
Wherein the normal number M xki Is a design parameter. Additional equipment
Figure BDA0003917421230000091
Is theta xki An estimate of the time of day.
The optimal approximation error is now defined as:
Figure BDA0003917421230000092
at the same time
Figure BDA0003917421230000093
Wherein epsilon x1i ,…,ε xki Is a constant number that is unknown to be bounded.
Then
Figure BDA0003917421230000094
We can get
f i (x i ,v i )＝φ i (χ i )θ i +δ i
Wherein
Figure BDA0003917421230000095
Substituting the above formula into the dynamic model can obtain
Figure BDA0003917421230000096
In addition, the
Figure BDA0003917421230000097
Are each theta i ，h i An estimate at time t, and
Figure BDA0003917421230000098
and a module P2:
because the invention considers the angle rigid formation control of a multi-robot system with unknown dead zone and nonlinear disturbance, the formation control problem to be solved is as follows: under the condition that the input has unknown dead zone, a backward pushing method is adopted to construct a model which only uses anglesFormation control strategy u of information i (t)∈R k So as to be moved from an arbitrary initial position x i (0)∈R k×k The robots starting from i =1,2 and … and n can reach the expected formation, and the multi-robot system can realize the global asymptotic stable formation. That is, the system converges to the following set:
Figure BDA0003917421230000101
a module P3:
the module P2 is a control target to be realized by the invention, the module P3 designs a global stable controller according to the requirement of the module P2, and the design is realized according to the following steps:
the first step is as follows: constructing a potential energy function between the robot i and the neighboring robot j, wherein the potential energy function is in the following form:
Figure BDA0003917421230000102
defining:
Figure BDA0003917421230000103
wherein the content of the first and second substances,
Figure BDA0003917421230000104
I d ∈R k×k is an identity matrix, and
Figure BDA0003917421230000105
therefore, the method comprises the following steps:
Figure BDA0003917421230000106
the total potential energy function of robot i is:
Figure BDA0003917421230000107
at the same time, let x = [ x ] 1 T ,x 2 T ,…,x i T ] T ，v＝[v 1 T ,v 2 T ,…,v i T ] T ，u＝[u 1 T ,u 2 T ,…,u i T ] T
Then the non-linear equation can be rewritten as:
Figure BDA0003917421230000108
the second step is that: a control law is designed by adopting a reverse-thrust design method, and the method comprises the following steps:
first consider the first equation in a nonlinear dynamical equation:
Figure BDA0003917421230000109
we treat the variable v as a virtual control input and then design the feedback controller
v＝z(x)＝[z 1 T ,z 2 T ,…,z i T ],i＝1,2,…,n
To ensure that a specified desired angle can be achieved between each pair of robots, the virtual control law v = z (x) is selected as follows:
Figure BDA0003917421230000111
v＝z(x)
secondly, error variables are introduced
Figure BDA0003917421230000112
Taking the derivative of the above equation, i.e.
Figure BDA0003917421230000113
For the above system, the global stable formation control law is designed as follows
Figure BDA0003917421230000114
The adaptive law is designed as follows:
Figure BDA0003917421230000115
Figure BDA0003917421230000116
wherein the content of the first and second substances,
Figure BDA0003917421230000117
0<α min <α i ，u max ，α min is a normal number. The sign function sgn (a) is defined as: when a is<0,sgn(a)＝-1；a＝0,sgn(a)＝0；a>0,sgn(a)＝1。
Figure BDA0003917421230000118
Figure BDA0003917421230000119
The invention utilizes the Barbalt theorem to analyze the global property of the whole closed-loop angle rigid formation control system and provides the following theorem:
the invention utilizes the Barbalt theorem to analyze the global property of the whole closed-loop angle rigid formation control system and provides the following theorem:
considering a nonlinear system, the communication topology G is an infinite angle rigid graph, the dead zone input meets the assumed conditions, and the control law is represented by the u i ，k i (t)，
Figure BDA0003917421230000121
Determining that the desired angular rigid formation is globally asymptotically stable, the relative angles among all communication robots reach the desired angle, and the system converges to the following set:
Figure BDA0003917421230000122
as shown in fig. 1 and 2:
the invention relates to a multi-robot fuzzy adaptive angle formation control method with a nonlinear dead zone, which considers a robot moving in a k-dimensional space, and has the following dynamic model without loss of generality:
Figure BDA0003917421230000123
wherein x i Representing the position of robot i, k =1,2,3 … v i Representing the speed of robot i, i =1,2, …, n. Psi i (u i ) Representing an input of u i The dead zone model of (2). f. of i (x i ,v i )＝[f 1i (x 1i ,v 1i ),...,f ki (x ki ,v ki )] T Is a continuous differentiable vector function and is used for expressing a nonlinear dynamical equation of the robot i. d i Is an unknown bounded perturbation, let | d | | i ||≤D i ，D i Is an unknown normal number.
Representing the input as u i The output is psi i (u i ) The dead zone model of (a) is described as follows:
Figure BDA0003917421230000124
parameter α in the above equation ri ，α li ，u ri ，u li Is an unknown bounded non-zero constant.
To facilitate subsequent analysis, 0 is set<α i ＝min{α li ,α ri }，
Figure BDA0003917421230000125
The dead zone model of the above equation may then be redefined as:
Figure BDA0003917421230000126
when a plurality of robots move cooperatively, information interaction between the robots is indispensable. The information interaction relationship can be described by an undirected graph G = { V, E }, where V = {1,2, k, n } is a set of nodes,
Figure BDA0003917421230000131
representing a collection of edges. If a path exists between node i and node j, this means that the moving body i can obtain the information of the moving body j, and the moving body j is the adjacent node of the moving body i. The set of adjacent nodes of moving body i may be N i And { (i, j) ∈ E }. Designing a scalar parameter z ij * It indicates that each robot should maintain the required angle with its neighbors. The edge vector and the angle vector are defined as follows:
Figure BDA0003917421230000132
||x ij | | denotes an euclidean distance value between the robot i and the robot j, z ij Representing the relative angle of robot i to its neighbor robot j. Since we use the undirected topology (FIG. 2), there is x ij ＝-x ji ，z ij ＝-z ji And all angle vectors are based on this global coordinate system. Position information of the robot is x = [ x ] 1 T ,…,x n T ] T An undirected graph is represented and considered. If each edge of G has a specific direction, namely the direction of any edge in G is calibrated, namely a direction is added to an undirected graph, the undirected graph is called a directed graph and is used
Figure BDA0003917421230000133
And (4) showing. The edges in the label graph G are in the order of 1 to m, where m is the number of directed edges. Is provided with
Figure BDA0003917421230000134
All edges in (1) are E 1 ,E 2 ，…,E m Then obtain the corresponding correlation matrix undirected graph G with the edges marked as 1 to m and the directed graph
Figure BDA0003917421230000135
The edge in (A) is denoted as E 1 To E m Then we can have the corresponding correlation matrix H = H (G) ∈ R m×m . Wherein the correlation matrix H is a matrix consisting of 0,1, -1. The elements on the rows of the correlation matrix are indexed by the edge E ∈ V × V, and the elements on the columns are indexed by the vertices V = {1,2, … n }, that is: except for [ H ]] li And [ H] lj In addition, all elements in the kth row of the correlation matrix are zero. Wherein when vertex i is the last vertex of edge k, [ H ]] li =1, [ H ] when the vertex j is the first vertex of the edge k] lj And =1. From the definition of the correlation matrix we can get:
Figure BDA0003917421230000136
FIG. G is a minimum angle stiffness graph according to the present invention; the angle rigidity diagram refers to a diagram that the angle between any pair of robots is kept constant if enough angles between adjacent pairs of robots are kept constant. The minimum rigidity graph refers to the rigidity of the graph which cannot be ensured if the graph is rigid and the angle information between any pair of robots is reduced; i.e. a stiffness map with 2n-3 sides. Fig. 2 shows a minimum graph G with 8 nodes. When in design, the information interaction relation between the robots is known, and then the neighborhood N of the robot i at each moment i Are all constant. In engineering application, a wireless communication mode and a wireless sensing mode can be flexibly adopted according to actual conditions to realize information interaction among multiple robots.
G (x) is R d One ofFormation is carried out by undirected graph G = (V, E) and node position vector
Figure BDA0003917421230000141
Composition, where node i ∈ V in graph G = (V, E) maps to location x i . The core problem discussed by the angle rigidity theory is that by setting relative angles for all edges in the topological graph G = (V, E), and determining the scale factor and the translation factor at the same time, the formation G (x) can be determined and unique. In other words, if two convoy G (x) and G (x ') specify the same relative angle, the convoy G (x) and G (x') have the same convoy form.
In the present invention, the potential energy function between robot i and robot j is defined as:
Figure BDA0003917421230000142
defining:
Figure BDA0003917421230000143
wherein the content of the first and second substances,
Figure BDA0003917421230000144
I d ∈R k×k is an identity matrix, and
Figure BDA0003917421230000145
therefore, the method comprises the following steps:
Figure BDA0003917421230000146
then the overall potential function of robot i is defined:
Figure BDA0003917421230000147
the invention aims to design a distributed formation control law and a self-adaptive law according to the relative angle between adjacent robots measured by a sensor, wherein the rigid formation control law of the angle is as follows:
Figure BDA0003917421230000148
the adaptive law is as follows:
Figure BDA0003917421230000149
Figure BDA00039174212300001410
so that multiple robots can reach a globally stable expected formation form, and the system converges to a unique expected balance state, namely:
Figure BDA0003917421230000151
in the invention, firstly, a fuzzy system is utilized to approximate unknown nonlinear dynamics, and the system is modeled. Then, a negative gradient algorithm is used for designing a virtual control law, namely speed control, and finally, a global stable formation control law and a self-adaptive law are designed by utilizing local information and virtual control obtained through communication; therefore, the problem of angle rigid formation control with nonlinear dead zone input is solved for the first time, the multi-robot system achieves the expected overall stable formation, and all robots achieve the expected speed.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (7)

1. The multi-robot fuzzy adaptive angle formation control method with the nonlinear dead zone is characterized by comprising the following steps of:
(1) The unmodeled dynamic state exists in the multi-robot system model, and the unknown nonlinear dynamic state is approximated by using a fuzzy system to model the system;
(2) Designing a distributed formation control strategy based on angle information by using a potential energy function method, calculating the error between an actual angle and an expected angle, and designing a virtual control law, namely speed control, by using a negative gradient algorithm;
(3) Local information and virtual control obtained by communication are utilized, a self-adaptive dynamic estimator is introduced to estimate unknown dead zone parameters, and a global stable angle rigid formation control law and a self-adaptive law are designed;
(4) And (4) calculating the control input of each robot by combining the steps.
2. The multi-robot fuzzy adaptive angle formation control method with nonlinear dead zones of claim 1, wherein the multi-robot system has typical nonlinear dead zone input and the control algorithm depends only on the relative angles of adjacent robots, each robot reaching the desired angle and moving at the same speed.
3. The multi-robot fuzzy adaptive angle formation control method with the nonlinear dead zone as claimed in claim 1, wherein in the step (1), in order to approximate the nonlinear unmodeled dynamics of the system, a first type of fuzzy system is selected, and the modeling formula of the robot system is as follows by using the approximation capability of the fuzzy system to the nonlinear function:
definition of x i ＝[x i T ,v i T ]Definition of tight set X χi ＝{χ i |||χ i ||≤M χi In which M is χi Is an arbitrarily large normal number limit;
let f 1i (x 1i ,v 1i ,θ x1i ),…,f ki (x ki ,v ki ,θ xki ) Is an I-type blurring system in region X χi Approximation of the upper component, i.e.
Figure FDA0003917421220000011
Wherein theta is xpi ＝[θ 1i ,θ 2i ,…θ Mi ] T ,
Figure FDA0003917421220000012
p∈(1,2,…,k)，M i Is the number of rules, phi, of the fuzzy system li (x pi ) Represents the sign of the fuzzy basis function, which is in the form of the equation:
Figure FDA0003917421220000013
wherein theta is li Is an adjustable parameter that is,
Figure FDA0003917421220000014
is a given membership function and is usually taken as
Figure FDA0003917421220000021
Wherein b is i ∈R,c i >0, letting:
Figure FDA0003917421220000022
Figure FDA0003917421220000023
additional equipment
Figure FDA0003917421220000024
Is theta xki The estimated value at the time, at which the optimal approximation error is defined as:
Figure FDA0003917421220000025
at the same time
Figure FDA0003917421220000026
Then
Figure FDA0003917421220000027
To obtain
f i (x i ,v i )＝φ i (χ i )θ i +δ i
Wherein
Figure FDA0003917421220000028
Substituting the above formula into the dynamic model can obtain
Figure FDA0003917421220000029
4. The multi-robot fuzzy adaptive angle formation control method with the nonlinear dead zone as set forth in claim 1, wherein the step (2) comprises the steps of:
(2.1) measuring a relative angle between adjacent robots by using a sensor, and calculating an error between an actual angle and an expected angle;
(2.2) introducing a potential energy function according to the error between the actual angle and the expected angle, and designing a virtual control law based on a negative gradient algorithm;
the potential energy function between the robot i and the neighbor robot j is constructed, and the form is as follows:
Figure FDA0003917421220000031
defining:
Figure FDA0003917421220000032
wherein the content of the first and second substances,
Figure FDA0003917421220000033
I d ∈R k×k is an identity matrix, and
Figure FDA0003917421220000034
therefore, the method comprises the following steps:
Figure FDA0003917421220000035
the total potential energy function of robot i is:
Figure FDA0003917421220000036
at the same time, let x = [ x ] 1 T ,x 2 T ,…,x i T ] T ，v＝[v 1 T ,v 2 T ,…,v i T ] T ，u＝[u 1 T ,u 2 T ,…,u i T ] T
Then the non-linear equation can be rewritten as:
Figure FDA0003917421220000037
5. the multi-robot fuzzy adaptive angle-queuing control method with nonlinear dead zones as claimed in claim 1, wherein said step (3) comprises the steps of:
(3.1) calculating the error between the actual speed and the virtual control according to the virtual control;
(3.2) calculating a derivative of the error system according to the above steps;
(3.3) selecting a proper Lyapunov function, and deriving the time t;
(3.4) designing a dead zone parameter self-adaptive law by using a parameter self-adaptive dynamic estimation method according to the relative angle information and the virtual control law;
and (3.5) designing a proper global stable angle formation control law by utilizing a back-stepping design method.
6. The multi-robot fuzzy adaptive angular formation control method with nonlinear dead zones according to claim 5,
to ensure that the specified desired angle between each pair of robots is achieved, step (3.3) selects a Lyapunov candidate function as:
Figure FDA0003917421220000041
because the communication topology is undirected, we have x ij ＝-x ji ，
Figure FDA0003917421220000042
For function V 1 (t) derivation may give:
Figure FDA0003917421220000043
selecting a virtual control law v = z (x) as follows:
Figure FDA0003917421220000044
v＝z(x)
then obtain
Figure FDA0003917421220000045
Comprises the following steps:
Figure FDA0003917421220000046
secondly, error variables are introduced
Figure FDA0003917421220000047
Taking derivatives of the above equation, i.e.
Figure FDA0003917421220000048
For the above system, the Lyapunov candidate function is chosen as:
Figure FDA0003917421220000051
differentiating the above equation with respect to time t can obtain:
Figure FDA0003917421220000052
and (3.5) designing a global stable formation control law as follows:
Figure FDA0003917421220000053
the adaptive law is designed as follows:
Figure FDA0003917421220000054
Figure FDA0003917421220000055
7. the multi-robot fuzzy adaptive angular formation control method with nonlinear dead zones according to claim 4, wherein,
Figure FDA0003917421220000056
0<α min <α i ，u max ，α min is a normal number. The sign function sgn (a) is defined as: when a is<0,sgn(a)＝-1；a＝0,sgn(a)＝0；a>0,sgn(a)＝1，
Figure FDA0003917421220000057
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Publication number Priority date Publication date Assignee Title
CN116155965A (en) * 2023-04-21 2023-05-23 天津洪荒科技有限公司 Multi-stage control method of omnidirectional AMR
CN116155965B (en) * 2023-04-21 2023-06-30 天津洪荒科技有限公司 Multi-stage control method of omnidirectional AMR

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