CN115657686B - Multi-robot formation control method based on Backstepping - Google Patents
Multi-robot formation control method based on Backstepping Download PDFInfo
- Publication number
- CN115657686B CN115657686B CN202211594765.3A CN202211594765A CN115657686B CN 115657686 B CN115657686 B CN 115657686B CN 202211594765 A CN202211594765 A CN 202211594765A CN 115657686 B CN115657686 B CN 115657686B
- Authority
- CN
- China
- Prior art keywords
- robot
- virtual
- pilot
- formation
- coordinates
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 230000015572 biosynthetic process Effects 0.000 title claims abstract description 88
- 238000000034 method Methods 0.000 title claims abstract description 32
- 238000013461 design Methods 0.000 claims description 14
- 238000004088 simulation Methods 0.000 claims description 13
- 238000002474 experimental method Methods 0.000 claims description 6
- 230000001133 acceleration Effects 0.000 claims description 3
- 210000004556 brain Anatomy 0.000 claims description 3
- 238000011217 control strategy Methods 0.000 claims description 3
- 206010033799 Paralysis Diseases 0.000 abstract description 5
- 238000005755 formation reaction Methods 0.000 description 75
- 238000010586 diagram Methods 0.000 description 11
- 238000005516 engineering process Methods 0.000 description 5
- 238000004458 analytical method Methods 0.000 description 3
- 238000011161 development Methods 0.000 description 2
- 230000002431 foraging effect Effects 0.000 description 2
- 241000251468 Actinopterygii Species 0.000 description 1
- 238000004220 aggregation Methods 0.000 description 1
- 230000002776 aggregation Effects 0.000 description 1
- 238000013473 artificial intelligence Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 238000000354 decomposition reaction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000010365 information processing Effects 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011002 quantification Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000006641 stabilisation Effects 0.000 description 1
- 238000011105 stabilization Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
Images
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Landscapes
- Feedback Control In General (AREA)
Abstract
The invention discloses a multi-robot formation control method based on Backstepping, which comprises the steps of designing a virtual pilot-following model according to robot kinematics, and converting formation control problems into track tracking problems of a following robot and a virtual pilot; decomposing a nonlinear system of the robot into three subsystems, introducing virtual error variables, and designing a formation controller by combining with a Lyapunov function; according to the invention, a virtual robot is introduced, a virtual pilot-following model is designed, the formation control problem is converted into the track tracking problem of the following robot and a virtual pilot, and the problem that if the pilot robot fails in the actual situation, the whole system is paralyzed is solved; and a stable formation control law is designed, and under the action of the control law, the convergence error of the controller is smaller, and the system error is smaller.
Description
Technical Field
The invention relates to the technical field of automatic control, in particular to a multi-robot formation control method based on Backstepping.
Background
In recent years, with rapid development of robot technology and continuous expansion of task demands, a single mobile robot has been difficult to complete a large number of complex tasks. Inspired by the collaborative behavior of ant foraging, bird colony, fish colony foraging, aggregation, rear-end collision and other populations, researchers have developed exploration for multi-mobile robot formation.
The formation technology has become a hot spot for research in application fields such as daily entertainment, industrial manufacturing, military operations, aerospace and the like at home and abroad. The technology integrates basic knowledge of disciplines such as artificial intelligence, control science, communication technology and the like, and the technical development level represents the state modern automation level. The formation control task is mainly to realize that multiple robots reach target points under the condition of a certain formation. Formation control mainly includes five problems: generating formation, maintaining formation, reconstructing formation, avoiding obstacle and self-adapting. For this reason, researchers have made a great deal of study, and the mainstream formation control methods that have been proposed now are: pilot following method, virtual structure method, behavior-based method, graph theory method, artificial potential field method, etc.
The pilot following method is simple to control, modeling and demonstration are simple, information processing amount is small, a follower does not have formation feedback, the speed of a leader is too high, formation is difficult to stabilize, and in actual conditions, if pilot robots fail, the whole system is paralyzed, the virtual structure method takes formation errors as feedback to control each robot to obtain expected formation more accurately, but the adaptability is insufficient in complex environments; secondly, most methods only consider numerical simulation in MATLAB, and an actual robot needs to carry an ROS platform.
Disclosure of Invention
Aiming at the defects of the background technology, the invention introduces a virtual robot through a multi-robot formation control method based on Backstepping, designs a virtual pilot-following model, converts the formation control problem into a track tracking problem of the following robot and a virtual pilot, and solves the problem that the whole system is paralyzed if the pilot robot fails in the actual situation.
The invention adopts the following technical scheme for solving the technical problems:
the multi-robot formation control method based on Backstepping comprises the following steps:
s1, acquiring coordinates of a pilot robot in a global coordinate system XOY, setting a virtual pilot, acquiring the coordinates of the virtual pilot in the global coordinate system XOY, and acquiring the coordinates of a following robot in the global coordinate system XOY;
s2, obtaining a virtual pose through a robot dynamics model according to a desired distance and a desired angle between a virtual pilot and a pilot robot;
s3, obtaining errors of the virtual robot and the random robot, and obtaining a tracking error kinematic equation, namely an error model;
s4, decomposing the nonlinear system of the robot into three subsystems by adopting a Backstepping method, introducing virtual error variables, and designing a formation controller by combining with a Lyapunov function;
and S5, the controller obtains a control input quantity and inputs the control input quantity into the error model, so that the formation control task is completed.
Further, the step S1 is specifically as follows:
selecting one robot as a pilot of a robot group, wherein the other robots move along with the pilot robot, the pilot robot is equivalent to a brain and is responsible for a pilot, namely, the azimuth trend of a formation, and the other robots are responsible for keeping the relative distance and the relative angle between the robot and the pilot;
setting a virtual pilot for the following robot, and setting the deflection angle, the angular speed, the angular acceleration and the linear speed of the virtual pilot and the pilot robot to be consistent; in addition, the motion trail of the virtual navigator is determined by the relative distance and angle between the virtual navigator and the navigator robot, and the motion trail of the following robot is determined by a set motion control strategy;
order the
Representing coordinates of the piloting robot in the global coordinate system XOY,/for>
Coordinates for virtual navigator, +.>
To follow the coordinates of the robot, < > a->
The angle between the motion direction of the robot and the X axis is represented; />
and />
The desired distance and the desired angle between the pilot robot and the virtual pilot are represented, respectively.
Further, the step S2 specifically includes the following steps:
the dynamics model of the robot is that
wherein ,v, wrespectively representing the linear speed and the angular speed of the robot;
setting the same direction angle of the virtual navigator and the pilot robot, namely
And according to the expected distance and the expected angle between the robot and the robot, the pose of the virtual robot can be obtained
Further, the step S3, specifically as follows,
virtual robot R V And follower robot R F The error of (2) is
in the formula ：
、/>
、/>
error space coordinates>
、/>
、/>
The space coordinates of the virtual robot are obtained; />
、/>
、/>
The space coordinates of the robot are followed;
from (1), (2) and (3), a tracking error kinematic equation is obtained
in the formula 
、/>
For the linear and angular speed of the virtual robot, < >>
、/>
To follow the linear and angular velocity of the robot.
Further, the specific steps of the step S4 are as follows:
the design idea of the Backstepping method is as follows: firstly, converting the whole nonlinear system into a plurality of different subsystems, wherein the number of the subsystems does not exceed the system order; secondly, setting a virtual feedback variable by a designer, and designing a part of Lyapunov function to enable the set function to be negative; finally, selecting a global Lyapunov function, and designing a controller meeting the negative determination of the Lyapunov function, thereby realizing the stability of a nonlinear system;
based on the Backstepping method, the design steps of the controller are as follows:
s41, decomposing the system, namely decomposing the nonlinear system into three subsystems, wherein the three subsystems are shown as the formula (6)
Step S42, introducing virtual feedback variable, selectingxTracking error of direction trackx e For the virtual control quantity and introducing virtual feedback variables:
step S43, designing part Lyapunov functionV 2 Design of
Assume that the system satisfies
,/>
Then
At the position of
, />
Under the condition of (2) tracking errory e Converging to zero;
step S44, designing a global Lyapunov function, and adding a subsystem Lyapunov function meeting the condition of step S23 in the global Lyapunov function design, wherein the global Lyapunov function is designed as follows
(9) Deriving and obtaining
wherein 
Deriving from formula (7), obtaining +.>
Bringing the formulae (7), (8), (11) into (10) to obtain
Step S45, designing a controller,
stabilize the system, i.e. meet
Thus, the system controller is designed to be
wherein ,k 1 >0, k 2 >0，k 1 、k 2 to control gain; if it isw L , v L , 
Is bounded, thenv F , w F Is bounded;
bringing formula (14) into formula (12), and finishing to obtain
Further, the method also comprises the following checking steps:
step S61, controller parametersk 1 ,k 2 The values are obtained through a plurality of experiments, and different values are setk 1 , k 2 Value, comparisonXA shaft(s),YThe convergence speed of the axis and the motion angle tracking error is used for obtaining a relative optimal parameter value;
and step S62, setting different speeds to realize trilateral formation, and carrying out simulation experiments on the system based on the parameter settings.
Compared with the prior art, the technical scheme has the following beneficial effects:
1. according to the multi-robot formation control method based on Backstepping, a virtual robot is introduced, a virtual pilot-following model is designed, the formation control problem is converted into the track tracking problem of the following robot and a virtual pilot, and the problem that if the pilot robot fails in the actual situation, the whole system is paralyzed is solved.
2. The multi-robot formation control method based on Backstepping provided by the invention not only considers MATLAB numerical simulation, but also carries out ROS platform Gazebo experiments, and has more value for practical mobile robot application.
3. The multi-robot formation control method based on Backstepping provided by the invention designs a stable formation control law, and under the action of the control law, the convergence error of a controller is smaller, and the system error is smaller.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of a Leader-Follower model;
FIG. 3 is a diagram of a trilateral formation trajectory;
FIG. 4 is an X-direction position tracking error map;
FIG. 5 is a graph of Y-direction position tracking error;
FIG. 6 is a diagram of motion angular position tracking error;
FIG. 7 is a diagram of a trilateral formation trajectory after changing the initial linear velocity of a pilot;
FIG. 8 is a graph of X-direction position tracking error after changing the initial linear velocity of the pilot;
FIG. 9 is a graph of Y-direction position tracking error after changing the initial linear velocity of the pilot;
FIG. 10 is a graph of movement angle position tracking error after changing the initial linear velocity of the pilot;
FIG. 11 is a square formation trace plot;
FIG. 12 is an X-direction position tracking error plot for square formations;
FIG. 13 is a graph of Y-direction position tracking error for square formations;
FIG. 14 is a graph of motion angular position tracking error for square formations;
FIG. 15 is a pentagonal formation trace plot;
FIG. 16 is an X-direction position tracking error plot for pentagonal formation;
FIG. 17 is a graph of Y-direction position tracking error for pentagonal formation;
FIG. 18 is a graph of motion angular position tracking error for pentagonal formation;
FIG. 19 is a Gazebo simulation environment;
FIG. 20 is a formation pose diagram;
FIG. 21 is a simulated trilateral formation trajectory graph;
FIG. 22 is a simulated X-direction position tracking error plot;
FIG. 23 is a simulated Y-direction position tracking error plot;
fig. 24 is a simulated motion angular position tracking error plot.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The formation control idea based on the piloting following method is to select one robot as a piloter of a robot group, and the rest robots follow the piloting robots to move. The piloting robot is equivalent to the brain and is responsible for the leader, namely, the azimuth trend of the formation, and the rest robots are responsible for keeping the relative distance and the relative angle between the robot and the leader.
In consideration of the problem that if a pilot robot fails under actual conditions, the whole system is paralyzed, the invention sets a virtual pilot for each following robot, and sets the deflection angle, the angular velocity, the angular acceleration, the linear velocity and the like of the virtual pilot and the pilot robot to be consistent; in addition, the motion trail of the virtual navigator is determined by the relative distance and angle between the virtual navigator and the navigator, and the motion trail of the following robot is determined by the set motion control strategy, so that the complex robot formation problem is converted into the simple tracking error convergence problem of the following robot and the virtual navigator.
As shown in the figure1, the present invention uses a Leader-Follower model of a non-full mobile robot, as shown in fig. 2, wherein,
representing coordinates of the piloting robot in the global coordinate system XOY,/for>
Coordinates for virtual navigator, +.>
To follow the coordinates of the robot, < > a->
The angle between the motion direction of the robot and the X axis is represented;
and />
The desired distance and the desired angle between the pilot robot and the virtual pilot are represented, respectively.
As can be taken from fig. 2, the kinetic model of the robot is
wherein ,v, wthe linear and angular speeds of the robot are indicated, respectively.
Setting the same direction angle of the virtual navigator and the pilot robot, namely
And according to the expected distance and the expected angle between the robot and the robot, the pose of the virtual robot can be obtained
Then, the virtual robot R V And follower robot R F The error of (2) is
From (1), (2) and (3), a tracking error kinematic equation is obtained
The analysis described above has transformed the formation problem into a tracking error convergence problem, which translates the tracking error
The formation control requirement can be met by converging in a small neighborhood, and further, the proper control input +.>
And (3) obtaining the product. Next, the present invention will be designed by the Backstepping method>
。
The Backstepping method comprises the following design ideas: firstly, converting the whole nonlinear system into a plurality of different subsystems, wherein the number of the subsystems does not exceed the system order; secondly, setting a virtual feedback variable by a designer, and designing a part of Lyapunov function to enable the set function to be negative; and finally, selecting a global Lyapunov function, and designing a controller meeting the negative setting of the Lyapunov function, thereby realizing the stability of the nonlinear system. The following are design steps and theoretical evidence of the controller of the present invention.
Step S41, system decomposition. Since the robotic system comprises onlyx, y, 
Three kinds of error tracking, the system of the inventionOrder 3, thus decomposing the system into three subsystems, as in equation (6)
Step S42, introducing virtual feedback variables. The virtual control quantity of the invention has three choices, namelyx e ,y e Or (b)
. The invention selectsxTracking error of direction trackx e For virtual control quantity (researchers can choose the other two as virtual control quantity), and introduce virtual feedback variable
Step S43, designing part Lyapunov functionV 2 . Design of
Assume that the system satisfies
,/>
Then
As can be seen from the above, in
,/>
Under the condition of (2) tracking errory e Converging to zero.
Step S44, designing a global Lyapunov function. From Step3, the invention can obtain the negative determination of the partial Lyapunov function, so the invention can add the subsystem Lyapunov function meeting the condition of Step S23 in the global Lyapunov function design, and the global Lyapunov function can be designed as follows
(9) Deriving and obtaining
wherein 
Deriving from (7)
Bringing the formulae (7), (8), (11) into (10) to obtain
Step S45, designing a controller. From the above, it can be seen that if the system is to be stabilized
Namely satisfy
Thus, the system controller is designed to be
wherein ,k 1 >0, k 2 >0. if it isw L , v L , 
Is bounded, thenv F , w F Is bounded.
Bringing formula (14) into formula (12), and finishing to obtain
In a summary of the present invention it is known that,Vthe continuous positive determination can be made slightly,
negative semi-definite and continuous consistency. Is obtained by Lasalle invariant set principle
The establishment is realized, so that the controller can realize formation control tasks;
the analysis proves that the proposed controller meets the system requirement through theory, then numerical simulation experiments are carried out in MATLAB 2018a, trilateral, square row and pentagonal formation of the multiple robots are realized, and the system is formedXA shaft(s),YAnalyzing the axis and motion angle tracking errors; to further verify the effectiveness of the proposed algorithm, a platoon simulation experiment was performed with the algorithm transplanted to the Gazebo simulation environment in ROS.
The controller parameters of the inventionk 1 ,k 2 The values are obtained through a plurality of experiments, and different values are setk 1 , k 2 Value, comparisonXA shaft(s),YThe convergence speed of the axis and motion angle tracking error yields the relative optimum parameter values, table 1 being a partial trial and error result.
Above-mentionedx e , y e , 
Is the convergence value of the algorithm inXA shaft(s),YThe recorded value when the axis and motion angle tracking error is less than 0.001m, x represents that the convergence error is more than 0.001m in a prescribed time. Through the experimental comparison, the most suitable is screenedk 1 ,k 2 Values 0.9,0.8, respectively. />
Firstly, setting different speeds to realize trilateral formation so as to prove that the controller can meet formation control tasks under the condition that the online speed and the angular speed of the pilot robot are bounded; and secondly, selecting a certain linear speed and angular speed to realize quadrilateral formation and pentagonal formation, and further verifying the effectiveness of the controller. Based on the parameter settings, simulation experiments are performed on the system, and the experimental effects and analysis are as follows.
Trilateral formation:
three robots, a pilot and two followers are set, and starting from different initial positions, the requirements of trilateral formation are met. Table 2 is a parameter setting of each robot initial information.
Setting the running time of the system to be 50s, and setting the relative distance between two virtual pilots and the pilot robotL 1 =L 2 =1m, relative angle is
，/>
The pilot robot does uniform linear motion. FIG. 3 is a diagram of a trilateral formation trajectory, and FIGS. 4, 5, and 6 are respectivelyxDirection(s),yDirection and motion angle tracking error map.
As can be seen from fig. 3, the formation has been initially formed at about 10s, with the red solid line being the pilot robot motion trajectory and the green dotted line and the blue dot line being the two follower trajectories. It can be seen from fig. 4, 5, and 6 that the system substantially completes formation generation at 19s and the errors converge within a certain range, where the red and green solid lines represent the error convergence variation between the follower robot and the virtual robot.
And (3) keeping the rest parameters unchanged, only changing the initial linear speed of the pilot to realize trilateral formation, and setting the parameters of each robot in table 3.
Fig. 7 is a diagram of a trilateral formation trajectory, and fig. 8, 9, and 10 are respectively a following robot and a virtual pilotXDirection(s),YDirection and motion angle tracking error map.
The simulation result can be used for obtaining that the controller can realize the formation task at different speeds. The initial linear speed of the pilot robot is used as a quantification, and formation is used as a variable, so that square formation and pentagonal formation of the multiple robots are realized.
Square formation
And setting four robots, namely a navigator, three followers and forming a square formation from different initial positions according to the three-side formation setting. Table 4 shows the parameter settings for four robots.
FIG. 11 is a square formation trace diagram, and FIGS. 12, 13 and 14 are respectivelyXDirection(s),YDirection and motion angle tracking error map.
As can be seen from fig. 11-14, as the number of robots increases and the demand for formation increases, the time required for the controller to perform the formation task increases, and the system completes the formation task demand at about 20 s.
Pentagonal formation
The five robots start from different initial positions to form pentagon formation. Table 5 shows the parameter settings for each robot.
FIGS. 15-18 are pentagonal formation trace diagrams and, respectivelyXDirection(s),YDirection and motion angle tracking error map.
In the Gazebo physical simulation environment, three identical robots were selected for the formation experiments, and fig. 19 is a Gazebo simulation environment. In the experiment, three robots are set at different positions, after the pilot robot advances for a certain distance, the following robot starts to follow, finally, triangle formation is realized, and simulation experiment results are shown in fig. 20-24.
Fig. 20 is a pose diagram after formation stabilization, and fig. 20 is a trilateral trajectory diagram, and it can be seen that the following robot and the piloting robot can maintain a desired distance and angle, and no collision or falling phenomenon occurs; fig. 22-24 are graphs of tracking errors of the follower robot and the virtual pilot robot in the X direction, the Y direction and the motion angle, wherein red represents errors of the follower 1 and the virtual robot 1, green represents errors of the follower 2 and the virtual robot 2, and it can be seen that the error tracking curves of the two follower robots eventually gradually converge into a small neighborhood.
From the experimental results, the controller designed by the invention meets various requirements of formation control tasks and has effectiveness and feasibility.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (3)
1. The multi-robot formation control method based on Backstepping is characterized by comprising the following steps of:
s1, acquiring coordinates of a pilot robot in a global coordinate system XOY, setting a virtual pilot, acquiring the coordinates of the virtual pilot in the global coordinate system XOY, and acquiring the coordinates of a following robot in the global coordinate system XOY;
s2, obtaining a virtual pose through a robot dynamics model according to a desired distance and a desired angle between a virtual pilot and a pilot robot;
s3, obtaining errors of the virtual robot and the random robot, and obtaining a tracking error kinematic equation, namely an error model;
s4, decomposing the nonlinear system of the robot into three subsystems by adopting a Backstepping method, introducing virtual error variables, and designing a formation controller by combining with a Lyapunov function;
s5, the controller obtains a control input quantity and inputs the control input quantity into the error model, so that a formation control task is completed;
the step S2 specifically includes the following steps:
the dynamics model of the robot is that
wherein ,v, wrespectively representing the linear speed and the angular speed of the robot;
setting the same direction angle of the virtual navigator and the pilot robot, namely
And can derive a virtual robot according to a desired distance and a desired angle therebetweenPose is
the step S3, specifically as follows,
virtual robot R V And follower robot R F The error of (2) is
in the formula ：
error space coordinates>
The space coordinates of the virtual robot are obtained; />
The space coordinates of the robot are followed;
from (1), (2) and (3), a tracking error kinematic equation is obtained
in the formula 
For the linear and angular speed of the virtual robot, < >>
The linear speed and the angular speed of the following robot;
the specific steps of the step S4 are as follows:
the design idea of the Backstepping method is as follows: firstly, converting the whole nonlinear system into a plurality of different subsystems, wherein the number of the subsystems does not exceed the system order; secondly, setting a virtual feedback variable by a designer, and designing a part of Lyapunov function to enable the set function to be negative; finally, selecting a global Lyapunov function, and designing a controller meeting the negative determination of the Lyapunov function, thereby realizing the stability of a nonlinear system;
based on the Backstepping method, the design steps of the controller are as follows:
s41, decomposing the system, namely decomposing the nonlinear system into three subsystems, wherein the three subsystems are shown as the formula (6)
Step S42, introducing virtual feedback variable, selectingxTracking error of direction trackx e For the virtual control quantity and introducing virtual feedback variables:
step S43, designing part Lyapunov functionV 2 Design of
Assume that the system satisfies
,/>
Then
At the position of
Under the condition of (2) tracking errory e Converging to zero;
step S44, designing a global Lyapunov function, and adding a subsystem Lyapunov function meeting the condition of step S23 in the global Lyapunov function design, wherein the global Lyapunov function is designed as follows
(9) Deriving and obtaining
wherein 
Deriving from formula (7), obtaining +.>
Bringing the formulae (7), (8), (11) into (10) to obtain
Step S45, designing a controller,
stabilize the system, i.e. meet
Thus, the system controller is designed to be
wherein ,k 1 >0, k 2 >0，k 1 、k 2 to control the gain, ifw L , v L , 
Is bounded, thenv F , w F Is bounded;
bringing formula (14) into formula (12), and finishing to obtain
2. The Backstepping-based multi-robot formation control method according to claim 1, wherein step S1 is specifically as follows:
selecting one robot as a pilot of a robot group, wherein the other robots move along with the pilot robot, the pilot robot is equivalent to a brain and is responsible for a pilot, namely, the azimuth trend of a formation, and the other robots are responsible for keeping the relative distance and the relative angle between the robot and the pilot;
setting a virtual pilot for the following robot, and setting the deflection angle, the angular speed, the angular acceleration and the linear speed of the virtual pilot and the pilot robot to be consistent; in addition, the motion trail of the virtual navigator is determined by the relative distance and angle between the virtual navigator and the navigator robot, and the motion trail of the following robot is determined by a set motion control strategy;
order the
Representing coordinates of the piloting robot in the global coordinate system XOY,/for>
Coordinates for virtual navigator, +.>
To follow the coordinates of the robot, < > a->
The angle of the robot movement direction to the X-axis is indicated. />
3. The Backstepping-based multi-robot formation control method of claim 1, further comprising a step of checking as follows:
step S61, controller parametersk 1 ,k 2 The values are obtained through a plurality of experiments, and different values are setk 1 , k 2 Value, comparisonXA shaft(s),YThe convergence speed of the axis and the motion angle tracking error is used for obtaining a relative optimal parameter value;
and step S62, setting different speeds to realize trilateral formation, and carrying out simulation experiments on the system based on the parameter settings.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211594765.3A CN115657686B (en) | 2022-12-13 | 2022-12-13 | Multi-robot formation control method based on Backstepping |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211594765.3A CN115657686B (en) | 2022-12-13 | 2022-12-13 | Multi-robot formation control method based on Backstepping |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN115657686A CN115657686A (en) | 2023-01-31 |
| CN115657686B true CN115657686B (en) | 2023-05-16 |
Family
ID=85019101
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211594765.3A Active CN115657686B (en) | 2022-12-13 | 2022-12-13 | Multi-robot formation control method based on Backstepping |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115657686B (en) |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102215260A (en) * | 2011-06-02 | 2011-10-12 | 北京理工大学 | Multi-agent system cooperative control method capable of maintaining connectivity |
| CN105182734A (en) * | 2015-09-17 | 2015-12-23 | 哈尔滨工程大学 | Air cushion ship formation control device and method based on virtual navigator and navigation strategy |
| CN106994969A (en) * | 2017-03-24 | 2017-08-01 | 奇瑞汽车股份有限公司 | A kind of fleet's formation control loop and method |
| CN108549394A (en) * | 2018-04-12 | 2018-09-18 | 哈尔滨工程大学 | A kind of more AUV straight lines formation control methods based on pilotage people and virtual pilotage people |
| CN110262247A (en) * | 2019-07-05 | 2019-09-20 | 青岛大学 | The distributed command filtered blurry control method of multi-robot system |
| CN113110593A (en) * | 2021-05-06 | 2021-07-13 | 西北工业大学 | Flight formation cooperative self-adaptive control method based on virtual structure and estimation information transmission |
| CN113220021A (en) * | 2021-05-06 | 2021-08-06 | 西北工业大学 | Flight formation cooperative self-adaptive tracking control method based on virtual leader |
| CN115032999A (en) * | 2022-06-24 | 2022-09-09 | 中国安全生产科学研究院 | Dynamic optimization formation transformation method for multi-robot formation |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2018035252A1 (en) * | 2016-08-17 | 2018-02-22 | Kennesaw State University Research And Services Foundation, Inc. | Vehicle with non-physically coupled sections |
-
2022
- 2022-12-13 CN CN202211594765.3A patent/CN115657686B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102215260A (en) * | 2011-06-02 | 2011-10-12 | 北京理工大学 | Multi-agent system cooperative control method capable of maintaining connectivity |
| CN105182734A (en) * | 2015-09-17 | 2015-12-23 | 哈尔滨工程大学 | Air cushion ship formation control device and method based on virtual navigator and navigation strategy |
| CN106994969A (en) * | 2017-03-24 | 2017-08-01 | 奇瑞汽车股份有限公司 | A kind of fleet's formation control loop and method |
| CN108549394A (en) * | 2018-04-12 | 2018-09-18 | 哈尔滨工程大学 | A kind of more AUV straight lines formation control methods based on pilotage people and virtual pilotage people |
| CN110262247A (en) * | 2019-07-05 | 2019-09-20 | 青岛大学 | The distributed command filtered blurry control method of multi-robot system |
| CN113110593A (en) * | 2021-05-06 | 2021-07-13 | 西北工业大学 | Flight formation cooperative self-adaptive control method based on virtual structure and estimation information transmission |
| CN113220021A (en) * | 2021-05-06 | 2021-08-06 | 西北工业大学 | Flight formation cooperative self-adaptive tracking control method based on virtual leader |
| CN115032999A (en) * | 2022-06-24 | 2022-09-09 | 中国安全生产科学研究院 | Dynamic optimization formation transformation method for multi-robot formation |
Non-Patent Citations (3)
| Title |
|---|
| Li Juan etal..Multi-AUV Fixed-point and Positioning Control Based on Virtual Leader.《2019 IEEE International Conference on Mechatronics and Automation (ICMA)》.2019,第560-565页. * |
| 于美妍等.基于backstepping的三轮机器人编队控制.《复杂系统与复杂性科学》.2021,第28-34页. * |
| 彭云根.未知扰动下水下机器人预设性能跟踪与编队控制研究.《中国优秀硕士学位论文全文数据库基础科学辑》.2020,第A010-41页. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN115657686A (en) | 2023-01-31 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Cheng et al. | Fixed-time fault-tolerant formation control for heterogeneous multi-agent systems with parameter uncertainties and disturbances | |
| CN109343345B (en) | Mechanical arm polynomial interpolation track planning method based on QPSO algorithm | |
| CN108415425B (en) | Distributed swarm robot cooperative clustering algorithm based on improved gene regulation and control network | |
| CN106502250B (en) | The path planning algorithm of multi-robot formation in three-dimensional space | |
| CN109240091B (en) | Underwater robot control method based on reinforcement learning and tracking control method thereof | |
| Kapnopoulos et al. | A cooperative particle swarm optimization approach for tuning an MPC-based quadrotor trajectory tracking scheme | |
| CN108748160A (en) | Manipulator motion planning method based on particle cluster algorithm on multiple populations | |
| CN110850719A (en) | Spatial non-cooperative target parameter self-tuning tracking method based on reinforcement learning | |
| CN110722533B (en) | External parameter calibration-free visual servo tracking of wheeled mobile robot | |
| CN110543727A (en) | Improved particle swarm algorithm-based omnidirectional mobile intelligent wheelchair robot parameter identification method | |
| CN115509251A (en) | Multi-unmanned aerial vehicle multi-target cooperative tracking control method based on MAPPO algorithm | |
| CN112947575A (en) | Unmanned aerial vehicle cluster multi-target searching method and system based on deep reinforcement learning | |
| Chen et al. | Multi-AUV cooperative hunting control with improved Glasius bio-inspired neural network | |
| Cao et al. | Dynamic task assignment for multi-AUV cooperative hunting | |
| Ugurlu et al. | Reinforcement learning versus conventional control for controlling a planar bi-rotor platform with tail appendage | |
| CN115657686B (en) | Multi-robot formation control method based on Backstepping | |
| Yang et al. | Game-theoretic utility tree for multi-robot cooperative pursuit strategy | |
| CN112684709B (en) | Cluster tracking kinematics modeling method, device and storage medium | |
| CN113759935A (en) | Intelligent group formation mobile control method based on fuzzy logic | |
| Dong et al. | Robot visual servo control based on fuzzy adaptive PID | |
| CN110162084A (en) | Cruising missile group system formation control method based on congruity theory | |
| CN113031643B (en) | Unmanned aerial vehicle formation and obstacle avoidance method | |
| CN115202206A (en) | Automatic design method for controller of cluster aircraft system | |
| Ciupan et al. | ANN Method for Control of Robots to Avoid Obstacles | |
| CN111580550A (en) | Unmanned aerial vehicle human-simulated intelligent control method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |