CN115202349A - Multi-mobile-robot cooperative formation control method, device, equipment and storage medium based on communication interference - Google Patents

Multi-mobile-robot cooperative formation control method, device, equipment and storage medium based on communication interference Download PDF

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CN115202349A
CN115202349A CN202210827675.8A CN202210827675A CN115202349A CN 115202349 A CN115202349 A CN 115202349A CN 202210827675 A CN202210827675 A CN 202210827675A CN 115202349 A CN115202349 A CN 115202349A
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robot
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formation
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CN115202349B (en
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王建晖
李咏华
张立
吴宇深
刘嘉睿
杨平
岳夏
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Guangzhou University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0287—Control of position or course in two dimensions specially adapted to land vehicles involving a plurality of land vehicles, e.g. fleet or convoy travelling
    • G05D1/0291—Fleet control
    • G05D1/0295—Fleet control by at least one leading vehicle of the fleet
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Abstract

The invention discloses a communication interference-based multi-mobile-robot cooperative formation control method, a device, equipment and a storage medium, wherein the control method comprises the following steps: a kinematic model of the incomplete constraint wheeled mobile robot is defined through coordinate transformation, a sliding mode variable structure is adopted for control, and a formation controller is designed by utilizing the tracking error of each trolley so as to adjust the linear velocity and the angular velocity of the robot in real time, so that the rapid convergence of the tracking error is realized. The formation control method provided by the invention can be effectively applied to formation control and formation change control of the multiple mobile robots, has better anti-interference performance, enables the multiple mobile robot system to keep an expected formation and move according to an expected track, and is beneficial to solving complex operation tasks of formation, cooperative transportation and the like of the multiple mobile robot system.

Description

Multi-mobile-robot cooperative formation control method, device, equipment and storage medium based on communication interference
Technical Field
The invention relates to the field of multi-mobile-robot control, in particular to a multi-mobile-robot cooperative formation control method, device, equipment and storage medium based on communication interference.
Background
With the rapid development of the intelligent manufacturing industry, the application requirements of multiple mobile robots are gradually increased. Inspired by the group behaviors in nature, in practical engineering application, people also realize the group behaviors of a plurality of unmanned systems through communication connection, such as cooperative work of a plurality of unmanned aerial vehicles, a plurality of underwater vehicles, a plurality of autonomous mobile robots and the like.
For a plurality of unmanned aerial vehicles, the reconnaissance and attack tasks are executed through cooperative formation, so that the reconnaissance or attack range can be increased, the robustness of the whole system is improved, and the whole task cannot be influenced due to failure or failure of a single system; in space, a plurality of small satellites can obtain a better observation effect by being formed in a team in a coordinated mode, and the requirement on the observation capacity of a single satellite is lowered; under water, the multiple unmanned underwater vehicles can improve detection precision or enlarge the whole search range through cooperation, so that the information collection capability of the whole system is improved, and the search efficiency is improved; on the land, a plurality of autonomous mobile robots can monitor the dangerous environment through cooperation, even search and rescue work of wounded personnel is completed on a battlefield, each mobile robot only needs to be responsible for a part of areas, and then the whole area monitoring or search and rescue task is efficiently completed through the whole team formation cooperation.
In addition, each mobile robot carries out parameter and sharing of system information through a wireless network, compared with a limited communication network, the bandwidth resource of the wireless communication network is limited, and the transmission of the information is interfered arbitrarily. Therefore, the problem of communication interference between robots needs to be emphasized in the design of the multi-mobile robot cooperative formation controller. Most of the existing formation control researches aim at the situation that the formation form of the formation is unchanged, but in the actual situation, the relative position of the random robot and the pilot robot needs to be changed according to specific tasks.
Disclosure of Invention
Aiming at the problems of formation control and formation change control of multiple mobile robots, the invention provides a communication interference-based multi-mobile-robot cooperative formation control method, a device, equipment and a storage medium, and the problems are solved by adopting a pilot-following-based multi-mobile-robot formation control method.
The invention is realized by the following technical scheme:
in a first aspect, the invention provides a cooperative formation control method for multiple mobile robots based on communication interference, which includes: establishing a kinematic model of the wheeled mobile robot and a kinematic model of formation control through coordinate transformation;
for a piloting robot, a kinematic model of the robot is established, a pose error is obtained by analyzing a current actual pose and an expected pose and is input into a formation controller, and a linear velocity and an angular velocity for controlling the robot to track an expected track are obtained through calculation;
for the following robot, calculating according to the current actual pose and the relative position of the piloting robot by establishing a kinematic model of the robot to obtain an expected pose of the following robot, and analyzing to obtain a pose error;
and a sliding mode variable structure is adopted for control, and a formation controller is designed by utilizing the tracking error of each trolley so as to adjust the linear velocity and the angular velocity of the robot in real time, thereby realizing the rapid convergence of the tracking error.
Further, the wheeled mobile robot kinematics model is established as follows:
in a pilot-follow type formation system composed of n wheeled mobile robots, the i-th mobile robot is represented by i = {1, 2.. Multidot., n }, the first of which is a pilot robot. Assuming that the speed of the mobile robot is low, neglecting the transverse sliding of wheels and the transverse force applied in the driving process, establishing a global coordinate system XOY taking the ground as a reference and a robot coordinate system XOY taking the mobile robot as a reference, wherein theta i For moving the robotThe included angle between the horizontal direction and the vertical direction;
the actual pose coordinate of the mobile robot is (x) i ,y i ,θ i ) When moving forward, the linear velocity and the angular velocity are respectively v i 、ω i The robot kinematics model is as follows:
Figure BDA0003747120680000021
wherein
Figure BDA0003747120680000022
A kinematic model representing the robot;
the given expected track pose coordinate of the piloting robot under the XOY coordinate is (x) r ,y r ,θ r ) The actual pose coordinate is (x) 1 ,y 1 ,θ 1 ) The linear and angular velocities of the desired trajectory are v, respectively r And omega r And the linear velocity and angular velocity of the actual track are respectively v 1 And omega 1 And by utilizing the plane coordinate transformation, the pose error equation of the piloting robot is as follows:
Figure BDA0003747120680000023
differentiating the formula (2), and obtaining a pose error differential equation of the piloting robot by combining the formula (1):
Figure BDA0003747120680000024
further, the formation control kinematic model establishment process is as follows:
R 1 to pilot the robot, R i (i = {2,3,. Eta., n }) is a following robot, R vi Is R i Mapping robot in desired formation, linear and angular velocities v respectively vi And omega vi During movement, R 1 And R vi Relative position therebetweenΔ i ＝[Δ ix ,Δ iy ]∈R 2 Described therein of ix To follow the deviation, delta, of the expected pose of the robot from the current actual pose of the piloting robot in the x direction iy Is the deviation of the expected pose of the following robot and the pose of the pilot robot in the y direction; and obtaining an expected pose of the following robot by using plane coordinate transformation:
Figure BDA0003747120680000031
(x 1 ,y 1 ,θ 1 ) T is the pose of the piloting robot (x) vi ,y vi ,θ vi ) T For following robot R i (i = {2,3,.., n }) then the pose error equation for the following robot is:
Figure BDA0003747120680000032
and (3) differentiating the formula (5) and substituting the formula (1) for continuous sorting to obtain a following robot attitude error differential equation:
Figure BDA0003747120680000033
further, the formation controller is designed by utilizing the tracking error of each trolley to adjust the linear velocity and the angular velocity of the robot in real time, and the method comprises the following specific steps:
and (3) describing a formation task of the multiple mobile robots: in a piloting-following formation system consisting of n wheeled mobile robots, the formation control aims at adjusting the position of each robot to move in a specific geometric figure, i.e. the linear and angular velocities of the following and piloting robots are kept the same, i.e. v vi ＝v 1 ，ω vi ＝ω 1 And the relative position and orientation satisfy desired topological and physical constraints:
Figure BDA0003747120680000034
Figure BDA0003747120680000035
Figure BDA0003747120680000036
in order to realize formation control and formation transformation control of multiple mobile robots, a formation control strategy based on a finite time approach law is provided, and the formation control strategy comprises the following steps:
for the piloted robot, firstly, a kinematic model of the robot is established according to the formula (1), the current actual pose and the expected pose are analyzed according to the formula (2) to obtain pose errors, the pose errors are input into a formation controller, and the linear velocity and the angular velocity for controlling the piloted robot to track the expected track are obtained through calculation;
for the following robot, a kinematic model of the robot is established according to the formula (1), and then the current actual pose and the relative position delta of the piloting robot are determined i ＝[Δ ix ,Δ iy ]∈R 2 Calculating to obtain an expected pose of the following robot, and analyzing according to the formula (5) to obtain a pose error;
designing a sliding mode switching function:
Figure BDA0003747120680000041
by designing the formation controller of the mobile robot, s 1 And s 2 Towards 0, i.e. so that
Figure BDA0003747120680000042
Converge to 0, and
Figure BDA0003747120680000043
converge to
Figure BDA0003747120680000044
Thereby ensuring that
Figure BDA0003747120680000045
And
Figure BDA0003747120680000046
the track tracking and formation control of the mobile robot are realized;
designing a finite time approaching law:
Figure BDA0003747120680000047
wherein k is 1 ，k 2 ，ε 1 ，ε 2 ，η 1 ，η 2 Are all adjustable parameters, delta 1 And delta 2 Are individually fal(s) 1 ,η 1 ,δ 1 )、fal(s 2 ,η 2 ,δ 2 ) Interval length of positive and negative symmetrical linear segments near origin, and fal(s) 1 ,η 1 ,δ 1 ) And fal(s) 2 ,η 2 ,δ 2 ) Are all non-continuous functions of the function,
Figure BDA0003747120680000048
Figure BDA0003747120680000049
order to
Figure BDA00037471206800000410
Deriving formula (12) and combining formula (5) and formula (13):
Figure BDA00037471206800000411
the control law can be obtained by arranging the formula:
Figure BDA00037471206800000412
wherein
Figure BDA00037471206800000413
In particular, when i =1, v in the above formulae v1 ＝v r ，ω v1 ＝ω r ；
When the temperature is higher than the set temperature
Figure BDA00037471206800000414
Then, choose the lyapunov function:
Figure BDA0003747120680000051
order to
Figure BDA0003747120680000052
Derivation of the above equation yields:
Figure BDA0003747120680000053
if and only if
Figure BDA0003747120680000054
If the time equal sign is true, then:
Figure BDA0003747120680000055
guarantee
Figure BDA0003747120680000056
Converge to
Figure BDA0003747120680000057
And is
Figure BDA0003747120680000058
Converge to 0, then
Figure BDA0003747120680000059
Converging to 0.
In a second aspect, the present invention provides a cooperative formation control apparatus for multiple mobile robots based on communication interference, the apparatus including:
the acquisition module is used for establishing a kinematic model of the wheeled mobile robot and a kinematic model for formation control through coordinate transformation;
the first analysis module is used for analyzing the current actual pose and the expected pose to obtain pose errors and inputting the pose errors into the formation controller by establishing a kinematic model of the robot for the piloting robot, and calculating to obtain the linear velocity and the angular velocity for controlling the robot to track the expected track;
the second analysis module is used for calculating the expected pose of the following robot according to the current actual pose and the relative position of the piloting robot by establishing a kinematic model of the robot for the following robot and then analyzing the expected pose to obtain a pose error;
and the control module is controlled by adopting a sliding mode variable structure, and a formation controller is designed by utilizing the tracking error of each trolley so as to adjust the linear velocity and the angular velocity of the robot in real time and realize the rapid convergence of the tracking error.
In a third aspect, the present invention provides an electronic device, comprising: a processor and a memory, the processor being configured to execute a computer program stored in the memory to cause the electronic device to execute any one of the robot cooperative formation control methods described above.
In a fourth aspect, the present invention provides a computer-readable storage medium, where the storage medium stores one or more programs, and the one or more programs are executable by one or more processors to implement the robot cooperative formation control method according to any one of the foregoing aspects.
The invention has the advantages that:
(1) The multi-mobile-robot cooperative formation control method can realize the finite time convergence of formation errors and weaken the buffeting phenomenon of the system, thereby accelerating the corresponding speed of a cooperative formation system;
(2) The multi-mobile-robot cooperative formation control method is based on communication interference among multiple mobile robots, and experimental results show that the multi-mobile-robot formation control method also has better anti-interference performance during formation change control;
(3) The multi-mobile-robot cooperative formation control method can realize formation control and formation change control of the multi-mobile robots and can meet practical application scenes.
Drawings
FIG. 1 is a communication topology between mobile robots in an embodiment of the present invention;
FIG. 2 is a mobile robot pose model according to an embodiment of the present invention;
FIG. 3 is a model of the formation control kinematics of a mobile robot according to an embodiment of the present invention;
FIG. 4 is a diagram of a formation control structure for mobile robots according to an embodiment of the present invention;
FIG. 5 is a diagram of a desired formation of an embodiment of the present invention;
FIG. 6 shows a formation motion trajectory 1 of a mobile robot in the formation control simulation according to the embodiment of the present invention;
FIG. 7 is a schematic diagram of a tracking robot course angle error 1 in the formation control simulation according to the embodiment of the present invention;
FIG. 8 shows a distance 1 between a tracking random robot and a piloting robot in the formation control simulation according to the embodiment of the present invention in the X-axis direction;
FIG. 9 is a Y-axis direction distance 1 between the following random robot and the piloting robot in the formation control simulation according to the embodiment of the present invention;
FIG. 10 is a diagram illustrating a formation motion trajectory 1 of a mobile robot under interference in a formation control simulation according to an embodiment of the present invention;
FIG. 11 shows a following robot course angle error 1 under interference in the formation control simulation according to the embodiment of the present invention;
FIG. 12 shows the distance 1 between the following robot and the piloting robot in the X-axis direction under the interference in the formation control simulation according to the embodiment of the present invention;
FIG. 13 shows a distance 1 between a following robot and a piloting robot in the Y-axis direction under interference in the formation control simulation according to the embodiment of the present invention;
FIG. 14 is a diagram of a moving trajectory 2 of a formation of mobile robots in a formation transformation control simulation according to an embodiment of the present invention;
FIG. 15 is a diagram of a tracking robot heading angle error 2 in the formation transform control simulation in accordance with an embodiment of the present invention;
FIG. 16 is a diagram illustrating the distance 2 between the tracking random robot and the piloting robot in the formation transformation control simulation according to the embodiment of the present invention in the X-axis direction;
FIG. 17 is a view showing a distance 2 in the Y-axis direction between the following robot and the piloting robot in the formation change control simulation according to the embodiment of the present invention;
FIG. 18 is a diagram illustrating a formation motion trajectory 2 of mobile robots under interference in formation transformation control simulation according to an embodiment of the present invention;
FIG. 19 is a schematic diagram of a following robot course angle error 2 under interference in formation transformation control simulation according to an embodiment of the present invention;
FIG. 20 shows the distance 2 between the following robot and the piloting robot in the X-axis direction under the interference in the formation transformation control simulation according to the embodiment of the present invention;
fig. 21 shows a distance 2 between the following robot and the piloting robot in the Y axis direction under interference in the formation transformation control simulation according to the embodiment of the present invention.
Detailed Description
The following embodiments are described in detail with reference to the accompanying drawings, and the following embodiments are implemented on the premise of the technical solution of the present invention, and give detailed embodiments and specific operation procedures, but the scope of the present invention is not limited to the following embodiments.
The embodiment is as follows:
referring to fig. 1-21, in order to solve the problems of formation control and formation change control of multiple mobile robots, embodiments of the present invention provide a method, an apparatus, a device, and a storage medium for cooperative formation control of multiple mobile robots based on communication interference, where the method employs a pilot-following based formation control method for multiple mobile robots. The specific technical scheme is as follows:
in a first aspect, the invention provides a method for controlling cooperative formation of multiple mobile robots based on communication interference, which comprises the following steps: establishing a kinematic model of the wheeled mobile robot and a kinematic model of formation control through coordinate transformation;
for the piloted robot, by establishing a kinematic model of the robot, analyzing the current actual pose and the expected pose to obtain pose errors, inputting the pose errors into a formation controller, and calculating to obtain linear velocity and angular velocity for controlling the robot to track an expected track;
for the following robot, calculating according to the current actual pose and the relative position of the piloting robot by establishing a kinematic model of the robot to obtain an expected pose of the following robot, and analyzing to obtain a pose error;
and a sliding mode variable structure is adopted for control, and a formation controller is designed by utilizing the tracking error of each trolley so as to adjust the linear velocity and the angular velocity of the robot in real time, thereby realizing the rapid convergence of the tracking error.
Further, the wheeled mobile robot kinematics model is established as follows:
in a pilot-follow type formation system composed of n wheeled mobile robots, the i-th mobile robot is represented by i = {1, 2.. Multidot., n }, the first of which is a pilot robot. Assuming that the speed of the mobile robot is low, neglecting the transverse sliding of wheels and the transverse force applied in the driving process, establishing a global coordinate system XOY taking the ground as a reference and a robot coordinate system XOY taking the mobile robot as a reference, wherein theta i Is the included angle between the moving direction of the mobile robot and the horizontal direction;
the actual pose coordinate of the mobile robot is (x) i ,y i ,θ i ) Linear and angular velocities, v respectively, during forward movement i 、ω i The robot kinematics model is as follows:
Figure BDA0003747120680000071
wherein
Figure BDA0003747120680000072
A kinematic model representing the robot;
the given expected track pose coordinate of the piloting robot under the XOY coordinate is (x) r ,y r ,θ r ) The actual pose coordinate is (x) 1 ,y 1 ,θ 1 ) The linear and angular velocities of the desired trajectory are v, respectively r And ω r The linear velocity and angular velocity of the actual track are respectively v 1 And omega 1 And by using the plane coordinate transformation, the pose error equation of the piloting robot is as follows:
Figure BDA0003747120680000073
differentiating the formula (2), and obtaining a pose error differential equation of the piloting robot by combining the formula (1):
Figure BDA0003747120680000074
further, the formation control kinematic model establishment process is as follows:
R 1 to pilot the robot, R i (i = {2, 3.. Multidot., n }) is a following robot, R vi Is R i Mapping robot in desired formation, linear and angular velocities v respectively vi And ω vi During movement, R 1 And R vi Relative position therebetween by Δ i ＝[Δ ix ,Δ iy ]∈R 2 Described therein of ix To follow the deviation, Δ, of the expected pose of the robot from the pose of the lead robot in the x-direction iy Is the deviation of the expected pose of the following robot and the pose of the navigation robot in the y direction; and obtaining an expected pose of the following robot by using plane coordinate transformation:
Figure BDA0003747120680000081
(x 1 ,y 1 ,θ 1 ) T is the pose of the piloting robot (x) vi ,y vi ,θ vi ) T For following the robot R i (i = {2,3,.. N }), the pose error equation of the following robot is:
Figure BDA0003747120680000082
and (3) differentiating the formula (5) and substituting the formula (1) for continuous sorting to obtain a following robot attitude error differential equation:
Figure BDA0003747120680000083
further, the formation controller is designed by utilizing the tracking error of each trolley to adjust the linear velocity and the angular velocity of the robot in real time, and the method comprises the following specific steps:
and (3) describing a formation task of the multiple mobile robots: in a piloting-following formation system consisting of n wheeled mobile robots, the formation control aims at adjusting the position of each robot to move in a specific geometric figure, i.e. the linear and angular velocities of the following and piloting robots are kept the same, i.e. v vi ＝v 1 ，ω vi ＝ω 1 And the relative position and orientation satisfy desired topological and physical constraints:
Figure BDA0003747120680000084
Figure BDA0003747120680000085
Figure BDA0003747120680000086
in order to realize formation control and formation transformation control of multiple mobile robots, a formation control strategy based on a finite time approach law is provided, and the formation control strategy comprises the following steps:
for a piloting robot, firstly, a kinematic model of the robot is established according to formula (1), a current actual pose and an expected pose are analyzed according to formula (2) to obtain pose errors, the pose errors are input into a formation controller, and linear velocity and angular velocity for controlling the piloting robot to track an expected track are obtained through calculation;
for the following robot, a kinematic model of the robot is established according to the formula (1), and then the current actual pose and the relative position delta of the robot are navigated i ＝[Δ ix ,Δ iy ]∈R 2 Calculating to obtain an expected pose of the following robot, and analyzing according to the formula (5) to obtain a pose error;
designing a sliding mode switching function:
Figure BDA0003747120680000091
by designing the formation controller of the mobile robot, s 1 And s 2 To 0, i.e. to
Figure BDA0003747120680000092
Converge to 0, and
Figure BDA0003747120680000093
converge to
Figure BDA0003747120680000094
Thereby ensuring
Figure BDA0003747120680000095
And
Figure BDA0003747120680000096
track tracking and formation control of the mobile robot are realized;
designing a finite time approaching law:
Figure BDA0003747120680000097
wherein k is 1 ，k 2 ，ε 1 ，ε 2 ，η 1 ，η 2 Are all adjustable parameters, delta 1 And delta 2 Are fal(s) respectively 1 ,η 1 ,δ 1 )、fal(s 2 ,η 2 ,δ 2 ) Interval length of positive and negative symmetrical linear segments near origin, and fal(s) 1 ,η 1 ,δ 1 ) And fal(s) 2 ,η 2 ,δ 2 ) Are all non-continuous functions of the function,
Figure BDA0003747120680000098
Figure BDA0003747120680000099
order to
Figure BDA00037471206800000910
Deriving formula (12) and combining formula (5) and formula (13):
Figure BDA00037471206800000911
the control law can be obtained by arranging the formula:
Figure BDA00037471206800000912
wherein
Figure BDA0003747120680000101
In particular, when i =1, v in the above formulae v1 ＝v r ，ω v1 ＝ω r ；
When in use
Figure BDA0003747120680000102
Then, the lyapunov function is selected:
Figure BDA0003747120680000103
order to
Figure BDA0003747120680000104
Derivation of the above equation can be found:
Figure BDA0003747120680000105
if and only if
Figure BDA0003747120680000106
If the time equal sign is true, then:
Figure BDA0003747120680000107
guarantee
Figure BDA0003747120680000108
Converge to
Figure BDA0003747120680000109
And is
Figure BDA00037471206800001010
Converge to 0, then
Figure BDA00037471206800001011
Converging to 0.
In a second aspect, the present invention provides a cooperative formation control apparatus for multiple mobile robots based on communication interference, comprising:
the acquisition module is used for establishing a kinematic model of the wheeled mobile robot and a kinematic model for formation control through coordinate transformation;
the first analysis module is used for analyzing the current actual pose and the expected pose to obtain pose errors and inputting the pose errors into the formation controller by establishing a kinematic model of the robot for the piloting robot, and calculating to obtain the linear velocity and the angular velocity for controlling the robot to track the expected track;
the second analysis module is used for calculating the expected pose of the following robot according to the current actual pose and the relative position of the piloting robot by establishing a kinematic model of the robot for the following robot and then analyzing the expected pose to obtain a pose error;
and the control module is controlled by adopting a sliding mode variable structure, and a formation controller is designed by utilizing the tracking error of each trolley so as to adjust the linear velocity and the angular velocity of the robot in real time and realize the rapid convergence of the tracking error.
In a third aspect, the present invention provides an electronic device, comprising: a processor and a memory, the processor being configured to execute a computer program stored in the memory to cause the electronic device to execute the robot cooperative formation control method of any one of the above.
In a fourth aspect, the present invention provides a computer-readable storage medium, wherein the storage medium stores one or more programs, and the one or more programs are executable by one or more processors to implement any one of the robot collaborative formation control methods described above.
In order to verify the effectiveness of the piloting follow-up type formation control method provided by the invention, formation control and formation transformation numerical simulation experiments are respectively carried out on a formation formed by five mobile robots, and three expected formation formations are provided, as shown in fig. 8. In the formula (13), the finite time approximation law sliding mode control parameter is set as k 1 ＝k 2 ＝3，δ 1 ＝δ 2 ＝0.2，η 1 ＝η 2 ＝0.5，ε 1 ＝ε 2 ＝0.01。
In the desired formation shown in FIG. 5, R 1 And R vi A relative position matrix of
Figure BDA0003747120680000111
Further, the multi-mobile robot formation control simulation steps are as follows:
firstly, a multi-mobile robot system consisting of 4 following robots and 1 pilot robot is adopted to carry out formation control numerical simulation under MATLAB/Simulink.
Initial conditions of the mobile robot are shown in table 1
TABLE 1 initial conditions of a mobile robot
Figure BDA0003747120680000112
The piloting-following formation control task is divided into three stages: i) 0 to 9.4s is the first stage, the desired formation is (1) of fig. 5, the desired trajectory of the pilot is a straight line, and the desired linear velocity is v r =4.8m/s, desired angular velocity ω r =0rad/s; II) 9.4s to 25.1s is the second stage, the formation is expected to be unchanged, the expected track of the pilot is a circular arc with the radius of 24 meters, and the expected linear speed is v r =4.8m/s, desired angular velocity ω r =0.2rad/s; III) 25.1s to 34.6s is a third stage, the expected formation form is not changed, the expected track of a pilot is a straight line, and the expected linear speed is v r =4.8m/s, desired angular velocity ω r =0rad/s. The simulation results are shown in fig. 6 to 9.
Fig. 7 to 9 show the heading angle, the X-axis direction and the Y-axis direction error of the following robot and the piloting robot, and since the robot is in a static state at the beginning and there is a certain error between each robot position and heading angle and the expected value, it takes longer to converge to the expected formation, which is 2.61s.
In order to verify the anti-interference performance of the multi-mobile-robot formation control method, based on the influence of terrain, electronic signals and other factors on the communication of the mobile robot in the actual motion process, the following robot and the pilot robot are assumed to have short-time communication interference between 12.5s and 13.5s, and state variables x and x are sety is added as a time varying function
Figure BDA0003747120680000113
And
Figure BDA0003747120680000114
to simulate external disturbances. The simulation results are shown in fig. 10 to 13.
Further, the formation transformation control simulation steps of the multiple mobile robots are as follows:
and a multi-mobile robot system consisting of 4 following robots and 1 pilot robot is also adopted to carry out formation control and formation transformation control numerical simulation under MATLAB/Simulink.
Initial conditions of the mobile robot are shown in table 2
TABLE 2 initial conditions of the Mobile robot
Figure BDA0003747120680000121
The piloting-following formation task is divided into three stages:
i) 0 to 15.7s is the first stage, the desired formation is (1) of fig. 5, and the desired trajectory of the pilot is a circular arc with a radius of 24 meters:
Figure BDA0003747120680000122
desired linear velocity v r 4.8m/s, angular velocity ω r ＝0.2rad/s；
II) 15.7s to 30s is the second stage, the desired formation is (2) of fig. 5, and the desired trajectory of the pilot is a circular arc with a radius of 32 meters:
Figure BDA0003747120680000123
the desired linear and angular velocities are v, respectively r =4.8m/s and ω r ＝0.15rad/s；
III) 30s to 50s is the third stage, the desired formation is (3) of fig. 5, and the desired trajectory of the pilot is unchanged.
The simulation results are shown in fig. 14 to 17.
Fig. 14 is a formation of 5 mobile robot systems at each movement time, each robot is represented by a circle of a different color, and an arrow in the circle represents a movement direction of each mobile robot. Starting the formation transformation at 0s, 15.7s and 30s, 5 robots can converge to the desired formation and move along the desired trajectory in all three phases.
FIGS. 15 to 17 are schematic diagrams showing the errors of the heading angles, the X-axis direction and the Y-axis direction of the following robot and the piloting robot, and the first stage converges to the desired formation Δ due to the initial standstill of the robots and the large deviation of the position and heading angle of each robot from the desired value Ⅰ It is used for a long time of 2.00s. The second stage formation is adjusted to delta Ⅱ The formation is still square, and the distances between the following robot and the pilot robot in the X-axis direction and the Y-axis direction are increased, so that the adjustment time is shorter and is 1.79s. Adjusting formation of the third stage to delta Ⅲ The formation is changed from a square shape to a rhombus shape, the errors of course angles of the following robots 1 and 4 and the piloting robot are large in the formation adjusting process due to large formation change, and the length of the adjusting time side is 1.82s.
Similarly, in order to verify the anti-interference performance of the multi-mobile-robot formation control method in formation change control, based on the fact that the mobile robot is influenced by terrain, electronic signals and the like in the actual motion process, the following robot and the pilot robot are assumed to have short-time communication interference between 20s and 21s, and the change function is added into the state variables x and y
Figure BDA0003747120680000131
And
Figure BDA0003747120680000132
to simulate external disturbances. The simulation results are shown in fig. 18 to 21.
As can be seen from fig. 18 to 21, the positions and directions of the following robots after the disturbance is added in 20s to 21s are also affected, the maximum value of the heading angle error is 0.3259rad, and the distance errors from the piloting robot in the directions of the X axis and the Y axis are 1.4525m and 0.5829m. After disturbance is finished, the expected formation is recovered 1.59s after the following robot uses the method, and the formation control method of the multiple mobile robots has good anti-interference performance when the formation is changed and controlled.
As can be seen from the experimental results of fig. 6 to 21, the formation control strategy designed herein can be effectively applied to the formation control and formation change control of multiple mobile robots.
The control method is a piloting-following type multi-mobile-robot formation control method, and is characterized in that a kinematic model of a non-complete constraint wheeled mobile robot is defined through coordinate transformation, sliding mode variable structure control is adopted, and a formation controller is designed by utilizing the tracking error of each trolley to adjust the linear velocity and the angular velocity of the robot in real time, so that the rapid convergence of the tracking error is realized. The formation control method can be effectively applied to formation control and formation change control of the multiple mobile robots, has better anti-interference performance, enables the multiple mobile robot system to keep an expected formation and move according to an expected track, and is beneficial to solving complex operation tasks of formation, cooperative transportation and the like of the multiple mobile robot system.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the prior art according to the concepts of the present invention should be within the scope of protection determined by the claims.

Claims (7)

1. A multi-mobile-robot cooperative formation control method based on communication interference is characterized by comprising the following steps: the method comprises the following steps:
establishing a kinematic model of the wheeled mobile robot and a kinematic model for formation control through coordinate transformation;
for a piloting robot, a kinematic model of the robot is established, a pose error is obtained by analyzing a current actual pose and an expected pose and is input into a formation controller, and a linear velocity and an angular velocity for controlling the robot to track an expected track are obtained through calculation;
for the following robot, calculating according to the current actual pose and the relative position of the piloting robot by establishing a kinematic model of the robot to obtain an expected pose of the following robot, and analyzing to obtain a pose error;
and a sliding mode variable structure is adopted for control, and a formation controller is designed by utilizing the tracking error of each trolley so as to adjust the linear velocity and the angular velocity of the robot in real time and realize the rapid convergence of the tracking error.
2. The cooperative formation control method for multiple mobile robots based on communication interference of claim 1, wherein: the wheeled mobile robot kinematic model is established by the following steps:
in a pilot-following formation system composed of n wheeled mobile robots, i = {1, 2.. Multidot.n } represents the ith mobile robot, wherein the first mobile robot is a pilot robot, a global coordinate system XOY taking the ground as a reference and a robot coordinate system XOY taking the mobile robot as a reference are established, wherein theta is theta i Is an included angle between the moving direction of the mobile robot and the horizontal direction;
the actual pose coordinate of the mobile robot is (x) i ,y i ,θ i ) When moving forward, the linear velocity and the angular velocity are respectively v i 、ω i The robot kinematics model is as follows:
Figure FDA0003747120670000011
wherein
Figure FDA0003747120670000012
A kinematic model representing the robot;
the given expected track pose coordinate of the piloting robot under the XOY coordinate is (x) r ,y r ,θ r ) The actual pose coordinate is (x) 1 ,y 1 ,θ 1 ) The linear and angular velocities of the desired trajectory are v, respectively r And ω r The linear velocity and angular velocity of the actual track are respectively v 1 And omega 1 And by using the plane coordinate transformation, the pose error equation of the piloting robot is as follows:
Figure FDA0003747120670000013
differentiating the formula (2), and obtaining a pose error differential equation of the piloting robot by combining the formula (1):
Figure FDA0003747120670000021
3. the cooperative formation control method for multiple mobile robots based on communication interference according to claim 2, wherein: the kinematic model building process of the wheeled mobile robot is as follows:
R 1 to pilot the robot, R i (i = {2,3,. Eta., n }) is a following robot, R vi Is R i Mapping robot in desired formation, linear and angular velocities v respectively vi And ω vi During movement, R 1 And R vi Relative position therebetween by Δ i ＝[Δ ix ,Δ iy ]∈R 2 Description of wherein Δ ix To follow the deviation, Δ, of the expected pose of the robot from the current actual pose of the piloting robot in the x direction iy Is the deviation of the expected pose of the following robot and the pose of the navigation robot in the y direction; and obtaining an expected pose of the following robot by using plane coordinate transformation:
Figure FDA0003747120670000022
(x 1 ,y 1 ,θ 1 ) T to pilot the pose of the robot, (x) vi ,y vi ,θ vi ) T For following robot R i (i = {2,3,.. N }), the pose error equation of the following robot is:
Figure FDA0003747120670000023
and (3) differentiating the formula (5) and substituting the formula (1) for continuous sorting to obtain a following robot attitude error differential equation:
Figure FDA0003747120670000024
4. the cooperative formation control method for multiple mobile robots based on communication interference according to claim 3, wherein: in the kinematic model for formation control, a formation controller is designed by utilizing the tracking error of each trolley to adjust the linear velocity and the angular velocity of the robot in real time, and the method comprises the following specific steps:
describing a multi-mobile robot formation task: in a piloting-following formation system consisting of n wheeled mobile robots, the formation control aims at adjusting the position of each robot to move in a specific geometric figure, i.e. the linear and angular velocities of the following and piloting robots are kept the same, i.e. v vi ＝v 1 ，ω vi ＝ω 1 And the relative position and orientation satisfy desired topological and physical constraints:
Figure FDA0003747120670000025
Figure FDA0003747120670000031
Figure FDA0003747120670000032
in order to realize formation control and formation transformation control of multiple mobile robots, a formation control strategy based on a finite time approach law is provided, and the formation control strategy comprises the following steps:
for a piloting robot, firstly, a kinematic model of the robot is established according to formula (1), a current actual pose and an expected pose are analyzed according to formula (2) to obtain pose errors, the pose errors are input into a formation controller, and linear velocity and angular velocity for controlling the piloting robot to track an expected track are obtained through calculation;
for the following robot, a kinematic model of the robot is established according to the formula (1), and then the current actual pose and the relative position delta of the piloting robot are determined i ＝[Δ ix ,Δ iy ]∈R 2 Calculating to obtain an expected pose of the following robot, and analyzing according to the formula (5) to obtain a pose error;
designing a sliding mode switching function:
Figure FDA0003747120670000033
by designing the formation controller of the mobile robot, s 1 And s 2 To 0, i.e. to
Figure FDA0003747120670000034
Converge to 0, and
Figure FDA0003747120670000035
converge to
Figure FDA0003747120670000036
Thereby, the deviceGuarantee
Figure FDA0003747120670000037
Converging to 0, and realizing the track tracking and formation control of the mobile robot;
designing a finite time approaching law:
Figure FDA0003747120670000038
wherein k is 1 ，k 2 ，ε 1 ，ε 2 ，η 1 ，η 2 Are all adjustable parameters, delta 1 And delta 2 Are individually fal(s) 1 ,η 1 ,δ 1 )、fal(s 2 ,η 2 ,δ 2 ) Interval length of positive and negative symmetrical linear segments near origin, and fal(s) 1 ,η 1 ,δ 1 ) And fal(s) 2 ,η 2 ,δ 2 ) Are all non-continuous functions of the function,
Figure FDA0003747120670000039
Figure FDA00037471206700000310
order to
Figure FDA00037471206700000311
Deriving formula (12) and combining formula (5) and formula (13):
Figure FDA0003747120670000041
the control law can be obtained by arranging the formula:
Figure FDA0003747120670000042
wherein
Figure FDA0003747120670000043
When i =1, v in the above formulae v1 ＝v r ，ω v1 ＝ω r ；
When the temperature is higher than the set temperature
Figure FDA0003747120670000044
Then, the lyapunov function is selected:
Figure FDA0003747120670000045
order to
Figure FDA0003747120670000046
Derivation of the above equation yields:
Figure FDA0003747120670000047
if and only if
Figure FDA0003747120670000048
If the time equal sign is true, then:
Figure FDA0003747120670000049
guarantee
Figure FDA00037471206700000410
Converge to
Figure FDA00037471206700000411
And is provided with
Figure FDA00037471206700000412
Converge to 0, then
Figure FDA00037471206700000413
Converging to 0.
5. A multi-mobile-robot cooperative formation control device based on communication interference is characterized by comprising the following modules:
the acquisition module is used for establishing a kinematic model of the wheeled mobile robot and a kinematic model for formation control through coordinate transformation;
the first analysis module is used for analyzing the current actual pose and the expected pose to obtain pose errors for the piloting robot by establishing a kinematic model of the robot, inputting the pose errors into the formation controller, and calculating to obtain the linear velocity and the angular velocity for controlling the robot to track the expected track;
the second analysis module is used for calculating the expected pose of the following robot according to the current actual pose and the relative position of the piloting robot by establishing a kinematic model of the following robot and obtaining a pose error through analysis;
and the control module is controlled by adopting a sliding mode variable structure, and a formation controller is designed by utilizing the tracking error of each trolley so as to adjust the linear velocity and the angular velocity of the robot in real time, thereby realizing the rapid convergence of the tracking error.
6. An electronic device, comprising: a processor and a memory, the processor being configured to execute a computer program stored in the memory to cause the electronic device to perform the robot cooperative formation control method of any one of claims 1 to 4.
7. A computer-readable storage medium, wherein the storage medium stores one or more programs, the one or more programs being executable by one or more processors to implement the robot cooperative formation control method according to any one of claims 1 to 4.
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