KR101641022B1 - Mobile robot and control method thereof under unknown slippage effects - Google Patents

Mobile robot and control method thereof under unknown slippage effects Download PDF

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Publication number
KR101641022B1
KR101641022B1 KR1020150091963A KR20150091963A KR101641022B1 KR 101641022 B1 KR101641022 B1 KR 101641022B1 KR 1020150091963 A KR1020150091963 A KR 1020150091963A KR 20150091963 A KR20150091963 A KR 20150091963A KR 101641022 B1 KR101641022 B1 KR 101641022B1
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South Korea
Prior art keywords
mobile robot
robot
detection area
mobile
area
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KR1020150091963A
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Korean (ko)
Inventor
김태형
유성진
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중앙대학교 산학협력단
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B25J9/1666—Avoiding collision or forbidden zones
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J13/00—Controls for manipulators
    • B25J13/08—Controls for manipulators by means of sensing devices, e.g. viewing or touching devices
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1674—Programme controls characterised by safety, monitoring, diagnostic
    • B25J9/1676—Avoiding collision or forbidden zones
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/42—Recording and playback systems, i.e. in which the programme is recorded from a cycle of operations, e.g. the cycle of operations being manually controlled, after which this record is played back on the same machine

Abstract

Disclosed are a mobile robot and a control method of the mobile robot under unknown slip effects. Each mobile robot of a leading and following group control system comprises: a detection unit detecting whether another mobile robot is placed within a predetermined detection region of the mobile robot; and a controller controlling movement of the mobile robot in consideration of an unknown slip variable for the other mobile robot to be placed out of the detection region when the other mobile robot is placed within the detection region. The detection region is a predetermined imaginary region to avoid a collision between the mobile robot and the other mobile robot.

Description

[0001] The present invention relates to a mobile robot and a control method for the mobile robot having an unknown slip,

The present invention relates to a mobile robot and a control method in a mobile robot having an unknown slip.

Backstepping and dynamic surface design are mainly used to design the control system of the mobile robot at the dynamics level. Studies on the control of these conventional mobile robots have not taken into account the slip phenomenon of the mobile robot considered in actual environments.

In order to overcome such a problem, a control technique of a mobile robot having a wheel skidding and a sleeping has been developed. However, this has been proposed for a single robot at a kinematic level and does not consider a multi-robot. .

The present invention is to provide a control method in a mobile robot and a mobile robot having an unknown slip.

Another object of the present invention is to provide a control method in a mobile robot capable of avoiding other mobile robots so as to be out of the detection area when a mobile robot enters another detection area of the mobile robot and a mobile robot having an unknown slip.

In addition, the present invention is characterized in that the mobile robots positioned outside the detection area are provided with a mobile robot capable of maintaining a certain distance from the leading robot in a restricted communication relationship between the mobile robots, And a control method of the mobile robot.

According to an aspect of the present invention, there is provided a mobile robot capable of avoiding another mobile robot to depart from a detection region when another mobile robot enters the detection region of the mobile robot.

According to the first embodiment, in each mobile robot of the lead-tracking group control system, a detection unit detects whether another mobile robot is located within the set detection area of the mobile robot; And a controller for controlling the movement of the mobile robot in consideration of an unknown slip parameter so that the other mobile robot is positioned outside the detection area when the other mobile robot is positioned within the detection area, And the mobile robot is a virtual region set for collision avoidance between the mobile robot and the other mobile robot.

The detection area radius of the mobile robot is a virtual area set on the basis of the center position of the mobile robot.

The controller can control the movement of the mobile robot so that the other mobile robot is positioned outside the detection area of the mobile robot using the repulsive force of the mobile robot.

Wherein the detector detects whether the other mobile robot is located in the collision avoiding area of the mobile robot, and the controller is configured to increase the repulsive force of the mobile robot as the other mobile robot is located closer to the collision avoiding area of the mobile robot So that the movement of the mobile robot can be controlled such that the other mobile robot is located outside the detection area of the mobile robot.

Wherein the collision avoiding area is a virtual area set smaller than the detection area with respect to the center position of the mobile robot.

A communication unit for acquiring the position of the other mobile robot through communication with the other mobile robot; And a sensor for measuring the distance of the other mobile robot when the calculated distance is within a predetermined distance.

 According to another aspect of the present invention, there is provided a control method of a mobile robot capable of avoiding another mobile robot to depart from a detection area when another mobile robot enters the detection area of the mobile robot.

According to the first embodiment, there is provided a control method of each mobile robot in a lead-tracking cluster control system, comprising: detecting whether another mobile robot is located within a set detection area of the mobile robot; And controlling movement of the mobile robot in consideration of an unknown slip parameter so that the other mobile robot is positioned outside the detection area when the other mobile robot is positioned within the detection area, And a virtual area set for avoiding collision between the mobile robot and the other mobile robot.

The step of controlling to avoid the other mobile robot may control the mobile robot such that the other mobile robot deviates from the detection area of the mobile robot using the repulsive force of the mobile robot.

The step of controlling the mobile robot to avoid the other mobile robot may include increasing the repelling force of the mobile robot as the other mobile robot approaches the collision avoiding area of the mobile robot using the calculated distance, It is possible to control the mobile robot to deviate from the detection area of the mobile robot.

Estimating a position of the leading robot in consideration of an unknown slip parameter when the other mobile robot is located outside the detection area and controlling the movement of the mobile robot to maintain a predetermined distance from the estimated leading robot .

When a different mobile robot enters the detection area of the mobile robot, it is possible to prevent other mobile robots from moving out of the detection area by providing the control method in the mobile robot according to the embodiment of the present invention and the mobile robot having an unknown slip There is an advantage to be able to do.

Accordingly, the present invention has an advantage that damage due to collision between mobile robots can be prevented in advance.

In addition, the present invention allows the mobile robots located outside the detection area to maintain a certain distance from the leading robot in a restricted communication relationship between the mobile robots, and to control the path through which the leader robot moves.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a view schematically showing a configuration of a mobile robot in a lead-tracking community control system according to a first embodiment; Fig.
2 is a view for explaining a detection region according to an embodiment of the present invention;
3 is a flowchart showing a collision avoidance method of a mobile robot in a lead-tracking cluster control system according to an embodiment of the present invention.
4 is a graph showing simulation results of collision avoidance and cluster control according to an embodiment of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS The present invention is capable of various modifications and various embodiments, and specific embodiments are illustrated in the drawings and described in detail in the detailed description. It is to be understood, however, that the invention is not to be limited to the specific embodiments, but includes all modifications, equivalents, and alternatives falling within the spirit and scope of the invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail with reference to the accompanying drawings.

The terms first, second, etc. may be used to describe various components, but the components should not be limited by the terms. The terms are used only for the purpose of distinguishing one component from another.

The terminology used in this application is used only to describe a specific embodiment and is not intended to limit the invention. The singular expressions include plural expressions unless the context clearly dictates otherwise. In the present application, the terms "comprises" or "having" and the like are used to specify that there is a feature, a number, a step, an operation, an element, a component or a combination thereof described in the specification, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

The present invention is for controlling a mobile robot to avoid collision with another mobile robot in a lead-following cluster system. To this end, according to the present invention, a virtual detection area and a collision avoidance area are set based on the center position of the mobile robot, respectively, and when another mobile robot enters the detection area, it can be avoided. Here, the other mobile robot may be a leading robot or another following robot following the leading robot.

Hereinafter, it should be understood that collision with a leading robot or another following robot is avoided in each following robot in a cluster control system in which a plurality of (M) following robots follow one leading robot.

Such collision avoidance is limited to the case where different moving regions are located in the detection region and the collision avoidance region of the mobile robot, and the mobile robots located outside the detection region maintain a certain distance from the leading robot in the restricted communication relation between the mobile robots And can control the movement path of the leader robot.

In addition, the position of the leading robot is time-varying, and not all tracking robots can acquire the position information of the leading robot. Only some following robots can acquire the position information of the leading robot through communication or sensing through the sensor .

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

FIG. 1 is a view schematically showing the configuration of a mobile robot in a lead-tracking cluster control system according to a first embodiment, and FIG. 2 is a view for explaining a detection region according to an embodiment of the present invention .

1, the mobile robot includes a communication unit 110, a sensor 115, a calculation unit 120, a memory 125, and a controller 125.

The communication unit 110 is a means for transmitting and receiving data with other mobile robots.

For example, the communication unit 110 can transmit and receive position information with other mobile robots.

The sensor 115 is a means for measuring the distance of another mobile robot. The sensor 115 can measure distances of other mobile robots located within a predetermined distance.

The calculation unit 120 is a means for calculating the distance between the mobile robot and another mobile robot.

And may further include a detection unit (not shown) as one configuration of the calculation unit 120. The detecting unit detects whether another mobile robot is located within the detection area of the mobile robot based on the calculated distance.

The memory 125 stores various algorithms, applications, and various data derived from this process, which are necessary to control the mobile robot in the lead-following cluster control system to avoid collision with other mobile robots.

The controller 125 controls the movement of the mobile robot in consideration of an unknown slip parameter so that another mobile robot is positioned outside the detection area when another mobile robot is positioned within the detection area.

In addition, the controller 125 can control the other mobile robots to avoid other mobile robots using the repulsive force as soon as another mobile robot enters the detection area of the mobile robot. At this time, the controller 125 can control the other mobile robots to be avoided by increasing the repulsive force as the other mobile robots enter the detection area of the mobile robot deeply (i.e., closer to the collision avoiding area).

The controller 125 may control the mobile robot to follow a path along which the leading robot is moving while maintaining a certain distance from the leading robot when another mobile robot is not located within the detection area. At this time, the controller 125 may control the mobile robot to follow a predetermined distance from the leading robot in consideration of slip parameters of the leading robot and the moving robot, as will be described in detail below.

2 is a view for explaining a detection area of the mobile robot.

The detection area of the mobile robot is a virtual area set based on the center position of the mobile robot. When another mobile robot enters the detection area of the mobile robot, the mobile robot can avoid using the repulsive force so that another mobile robot deviates from the detection area. 2, the detection area of the mobile robot is set so as to avoid collision with other mobile robots based on the detection area. Thus, in the lead-following cluster control system according to the embodiment of the present invention, There is an advantage that it is possible to prevent breakage in advance.

FIG. 3 is a flowchart illustrating a collision avoidance method of a mobile robot in a lead-tracking cluster control system according to an embodiment of the present invention. FIG. 4 is a graph illustrating simulation results of collision avoidance according to an embodiment of the present invention. to be.

In step 310, the mobile robot detects whether another mobile robot is located within the detection area of the mobile robot.

For example, the mobile robot may acquire the position of another mobile robot or acquire the distance to another mobile robot through the sensor, and then detect whether or not another mobile robot is located within the detection area of the mobile robot have.

If another mobile robot is located outside the detection area in step 315, the mobile robot maintains a certain distance from the leading robot in consideration of an unknown slip parameter and controls the movement of the mobile robot so as to follow the leading robot.

At this time, the mobile robot estimates the position of the leading robot in consideration of an unknown slip parameter, and controls the movement of the mobile robot to maintain a constant distance from the position of the estimated leading robot. This will be more clearly understood from the following description.

In step 320, when the mobile robot has another mobile robot in the detection area, the mobile robot controls the movement of the mobile robot in consideration of an unknown slip parameter so that the other mobile robot is positioned outside the detection area.

For example, the mobile robot can control the mobile robot such that another mobile robot deviates from the detection area of the mobile robot using the repulsive force of the mobile robot. Further, as the mobile robot moves closer to the collision avoiding region of the mobile robot of the other mobile robot (i.e., as it is deeply in the detection area), the repulsive force of the mobile robot is increased so that the other mobile robot quickly deviates from the detection area of the mobile robot. Can be controlled.

This will be understood more clearly and in detail through the following description.

In one embodiment of the present invention, a lead-tracking cluster control will be described on a graph-based basis in order to explain a collision avoiding method of a mobile robot (i.e., following robot). In addition, collision avoidance of the mobile robot described below will be collectively referred to as a follower robot, in which a following robot following the leading robot avoids collision with a leading robot or another following robot.

Therefore, the concept of the graph theory will be described first.

Figure 112015062628857-pat00001
Is a node or vertices (
Figure 112015062628857-pat00002
). ≪ / RTI > here,
Figure 112015062628857-pat00003
Is a set of edges or arcs. Any node
Figure 112015062628857-pat00004
Means that agent i (follower robot i) can acquire information from agent j (follower robot j), and vice versa. Here, the agent j (follower robot j) and the agent i (follower robot i) may be a parent node and a child node, respectively.

The neighbor set of node i

Figure 112015062628857-pat00005
, Which is the set of nodes with edges coming into node i. Node
Figure 112015062628857-pat00006
Gt;
Figure 112015062628857-pat00007
The direct pass to
Figure 112015062628857-pat00008
It is the edge sequence of the form. A direct tree is a direct graph in which all nodes except a root have one parent.

The concept of graph theory is briefly described.

Hereinafter, a description will be made of a method in which a following robot assumes a lead-following cluster control system in which one leading robot and M following robots are present, and the following robot avoids collision with the leading robot or the following robot.

In the following description, the following robot may also be referred to as an agent 1 to an agent M. [ Also, the leading robot may be named agent 0.

Therefore, the representations of the agents 1 to M should be understood as follower robot 1 to follower robot M, and agent 0 should be understood as a lead robot.

Expressing the following robot as a graph theory, it can be composed of M mobile robots that have a skidding and a sleeping phenomenon on a wheel.

This can be represented by equations (1) and (2).

Figure 112015062628857-pat00009

Figure 112015062628857-pat00010

here,

Figure 112015062628857-pat00011
ego,
Figure 112015062628857-pat00012
Represents the center-point coordinates between the two driving wheels of the i-th mobile robot,
Figure 112015062628857-pat00013
Is the traveling angle of the i-th mobile robot,
Figure 112015062628857-pat00014
However,
Figure 112015062628857-pat00015
Wow
Figure 112015062628857-pat00016
Represents the forward linear and angular velocity of the i-th mobile robot.
Figure 112015062628857-pat00017
ego,
Figure 112015062628857-pat00018
Represents the longitudinal slip velocity of the i-th mobile robot,
Figure 112015062628857-pat00019
Represents the yaw rate change (perturbation) due to the wheel slip of the i-th robot. Also,
Figure 112015062628857-pat00020
ego,
Figure 112015062628857-pat00021
Represents the skidding speed of the i-th mobile robot,
Figure 112015062628857-pat00022
Represents the control torque applied to the wheel of the i-th mobile robot,
Figure 112015062628857-pat00023
to be.

Also, in the kinematic equation,

Figure 112015062628857-pat00024
,
Figure 112015062628857-pat00025
,
Figure 112015062628857-pat00026
And
Figure 112015062628857-pat00027
Is known from the paper of O.O. and Park, which will be obvious to those skilled in the art and will not be further described.

Assumption 1: Skimming and sleeping change

Figure 112015062628857-pat00028
Wow
Figure 112015062628857-pat00029
The
Figure 112015062628857-pat00030
Due to,
Figure 112015062628857-pat00031
,
Figure 112015062628857-pat00032
And
Figure 112015062628857-pat00033
. ≪ / RTI > here,
Figure 112015062628857-pat00034
Is an unknown constant. The first variable
Figure 112015062628857-pat00035
Figure 112015062628857-pat00036
,
Figure 112015062628857-pat00037
,
Figure 112015062628857-pat00038
Containing
Figure 112015062628857-pat00039
. ≪ / RTI > here,
Figure 112015062628857-pat00040
Is an unknown constant.

Assumption 2: System matrix for dynamics

Figure 112015062628857-pat00041
Figure 112015062628857-pat00042
and
Figure 112015062628857-pat00043
Assume that you do not know. here,
Figure 112015062628857-pat00044
to be.

The communication topology for the (M + 1) mobile robot is shown in graph (

Figure 112015062628857-pat00045
). here,
Figure 112015062628857-pat00046
to be. In order to explain the communication between the following robot,
Figure 112015062628857-pat00047
. here,
Figure 112015062628857-pat00048
to be. Subgraph (
Figure 112015062628857-pat00049
) Adjacent matrix (
Figure 112015062628857-pat00050
)
Figure 112015062628857-pat00051
to be. if
Figure 112015062628857-pat00052
If
Figure 112015062628857-pat00053
If not,
Figure 112015062628857-pat00054
to be. Also,
Figure 112015062628857-pat00055
) Laplacian matrix (
Figure 112015062628857-pat00056
)silver
Figure 112015062628857-pat00057
. ≪ / RTI > here,
Figure 112015062628857-pat00058
Represents the communication weight from the leading robot to the following robot, and the leader robot
Figure 112015062628857-pat00059
),
Figure 112015062628857-pat00060
, Or
Figure 112015062628857-pat00061
to be. Also,
Figure 112015062628857-pat00062
ego,
Figure 112015062628857-pat00063
Is a Laplacian matrix of subgraphs indicating communication between following robots. here,
Figure 112015062628857-pat00064
ego,
Figure 112015062628857-pat00065
Represents the diagonal element of the degree matrix D.

Remark 1. Graph (

Figure 112015062628857-pat00066
) Has a spanning tree,
Figure 112015062628857-pat00067
Figure 112015062628857-pat00068
to be.
Figure 112015062628857-pat00069
from
Figure 112015062628857-pat00070
to be. here,
Figure 112015062628857-pat00071
Is an M-vector with all 1's.

The potential function for collision avoidance between the following robot and the following robot or between the leading robot and the following robot can be expressed by Equation (3).

Figure 112015062628857-pat00072

here,

Figure 112015062628857-pat00073
ego,
Figure 112015062628857-pat00074
Lt;
Figure 112015062628857-pat00075
ego,
Figure 112015062628857-pat00076
Figure 112015062628857-pat00077
Represents the distance between the i-th mobile robot and the h-th mobile robot. Also,
Figure 112015062628857-pat00078
ego,
Figure 112015062628857-pat00079
and
Figure 112015062628857-pat00080
Represents the radius of the detection region of the i-th mobile robot and the radius of the detection region of the h-th mobile robot, respectively.
Figure 112015062628857-pat00081
Is an avoidance region indicating the minimum safety distance between the robots,
Figure 112015062628857-pat00082
to be.

Figure 112015062628857-pat00083
Wow
Figure 112015062628857-pat00084
About Coordinates
Figure 112015062628857-pat00085
Can be defined as shown in Equation (4) and Equation (5).

Figure 112015062628857-pat00086

Figure 112015062628857-pat00087

here,

Figure 112015062628857-pat00088
to be.

The control objective is the approximation based adaptive cluster control law

Figure 112015062628857-pat00089
.

(I) detection area

Figure 112015062628857-pat00090
Outside,
Figure 112015062628857-pat00091
Figure 112015062628857-pat00092
and
Figure 112015062628857-pat00093
, here,
Figure 112015062628857-pat00094
,
Figure 112015062628857-pat00095
,
Figure 112015062628857-pat00096
Is a sufficiently small constant.
Figure 112015062628857-pat00097
Represents the desired offset between the ith following robot and the leader robot. And,
Figure 112015062628857-pat00098
Location
Figure 112015062628857-pat00099
Figure 112015062628857-pat00100
And direction (
Figure 112015062628857-pat00101
), Linear velocity
Figure 112015062628857-pat00102
) And angular velocity
Figure 112015062628857-pat00103
),
Figure 112015062628857-pat00104
,
Figure 112015062628857-pat00105
,
Figure 112015062628857-pat00106
Is the position of the leader robot generated by the robot.

(II) detection region

Figure 112015062628857-pat00107
Inside, the i-th following robot is located
Figure 112015062628857-pat00108
Wow
Figure 112015062628857-pat00109
Avoiding the collision of the detected robots under the influence of the robot. here,
Figure 112015062628857-pat00110
ego,
Figure 112015062628857-pat00111
Figure 112015062628857-pat00112
ego,
Figure 112015062628857-pat00113
About
Figure 112015062628857-pat00114
Figure 112015062628857-pat00115
to be. here,
Figure 112015062628857-pat00116
Is a constant. Also,
Figure 112015062628857-pat00117
ego,
Figure 112015062628857-pat00118
Figure 112015062628857-pat00119
and
Figure 112015062628857-pat00120
Is the desired offset vector between the i-th robot and the j-th robot
Figure 112015062628857-pat00121
). ≪ / RTI > here,
Figure 112015062628857-pat00122
Satisfies.

Assumption 2: The position and velocity information of the leader robot is related,

Figure 112015062628857-pat00123
Of the i-th following robot satisfying the following equation.

Remark 2. (i) Collision avoidance has higher priority than cluster follow-up because collision between robots can lead to more deadly system damage than temporary deterioration of cluster follow-up performance. Therefore, in the control objective (II), the position of the neighbor for the controller design of the ith following robot is considered to be fixed in the detection area. Furthermore, the direction of the neighbor is determined by the direction of motion of the ith following robot in the distributed control scheme. The direction of the neighbor is

Figure 112015062628857-pat00124
. ≪ / RTI > So, error (
Figure 112015062628857-pat00125
Wow
Figure 112015062628857-pat00126
) Is a tracking error term
Figure 112015062628857-pat00127
And collision avoidance port
Figure 112015062628857-pat00128
. ≪ / RTI >

In the inner detection area

Figure 112015062628857-pat00129
Because of,
Figure 112015062628857-pat00130
and
Figure 112015062628857-pat00131
The effect of
Figure 112015062628857-pat00132
and
Figure 112015062628857-pat00133
to be. here,
Figure 112015062628857-pat00134
and
Figure 112015062628857-pat00135
Is increased in accordance with the distance between robots close to the internal detection area,
Figure 112015062628857-pat00136
ego,
Figure 112015062628857-pat00137
, Collision avoidance can be achieved. Controller (
Figure 112015062628857-pat00138
Depending on the design
Figure 112015062628857-pat00139
and
Figure 112015062628857-pat00140
Approaches "0" as time increases.
Figure 112015062628857-pat00141
Figure 112015062628857-pat00142
The ith following robot can avoid the robot detected in the internal detection region.

(ii) conditions

Figure 112015062628857-pat00143
Means that no collision between the robots occurs while the group of mobile robots performs the desired cluster follow-up.

The position, angle and velocity (linear velocity and angular velocity) for the design of the circulation controller by applying kinematics and dynamics can be expressed by Equations 6 to 8.

Figure 112015062628857-pat00144

Figure 112015062628857-pat00145

Figure 112015062628857-pat00146

Figure 112015062628857-pat00147

here,

Figure 112015062628857-pat00148
to be.

The controller design based on the dynamic surface design technique consists of three steps.

For distributed controller design, the distributed error surface (

Figure 112015062628857-pat00149
Figure 112015062628857-pat00150
) And boundary layer error (
Figure 112015062628857-pat00151
Figure 112015062628857-pat00152
) Is defined as the following Equations (9) to (14).

Figure 112015062628857-pat00153

Figure 112015062628857-pat00154

Figure 112015062628857-pat00155

Figure 112015062628857-pat00156

Figure 112015062628857-pat00157

Figure 112015062628857-pat00158

here,

Figure 112015062628857-pat00159
,
Figure 112015062628857-pat00160
,
Figure 112015062628857-pat00161
,
Figure 112015062628857-pat00162
,
Figure 112015062628857-pat00163
and
Figure 112015062628857-pat00164
Respectively represent virtual control and filtered virtual control.

The three-step design steps based on such an error surface are as follows.

(i) Dynamics In equation (6), the state variable

Figure 112015062628857-pat00165
and
Figure 112015062628857-pat00166
For the virtual controller
Figure 112015062628857-pat00167
,
Figure 112015062628857-pat00168
And outputs the filtered virtual signal < RTI ID = 0.0 >
Figure 112015062628857-pat00169
and
Figure 112015062628857-pat00170
.

(ii) Dynamic Equation The state variable of equation (7)

Figure 112015062628857-pat00171
A pseudo controller (
Figure 112015062628857-pat00172
) Are designed, and the filtered virtual signal (
Figure 112015062628857-pat00173
).

(iii) the dynamic controller of equation (8)

Figure 112015062628857-pat00174
).

Step 1: First virtual control law (

Figure 112015062628857-pat00175
,
Figure 112015062628857-pat00176
Consider a distributed error surface for the design of an error surface. The time variances of Equations (9) and (10) to (13) using Equation (6) are as shown in Equation (15).

Figure 112015062628857-pat00177

here,

Figure 112015062628857-pat00178
Figure 112015062628857-pat00179
ego,

Figure 112015062628857-pat00180
Lt;

Figure 112015062628857-pat00181
to be.

Local virtual control term (

Figure 112015062628857-pat00182
) Can be rearranged as shown in Equation (16).

Figure 112015062628857-pat00183

here,

Figure 112015062628857-pat00184
Is a positive design parameter,
Figure 112015062628857-pat00185
Is a small design parameter,

Figure 112015062628857-pat00186
ego,
Figure 112015062628857-pat00187
Lt;
Figure 112015062628857-pat00188
The
Figure 112015062628857-pat00189
Figure 112015062628857-pat00190
Lt; RTI ID = 0.0 > (17) < / RTI >

Figure 112015062628857-pat00191

here,

Figure 112015062628857-pat00192
Is a tuning gain,
Figure 112015062628857-pat00193
The
Figure 112015062628857-pat00194
It is a constant for adjustment.

In Equation (16)

Figure 112015062628857-pat00195
Using the definition of virtual control law (
Figure 112015062628857-pat00196
,
Figure 112015062628857-pat00197
) Can be obtained as shown in Equations (18) and (19).

Figure 112015062628857-pat00198

Figure 112015062628857-pat00199

here,

Figure 112015062628857-pat00200
Figure 112015062628857-pat00201
Figure 112015062628857-pat00202
,
Figure 112015062628857-pat00203
The
Figure 112015062628857-pat00204
Is an integer for ensuring continuity and differentiability of the data. first,
Figure 112015062628857-pat00205
Is set to "0 &
Figure 112015062628857-pat00206
Whenever this is discontinuous
Figure 112015062628857-pat00207
Respectively.
Figure 112015062628857-pat00208
Lt; RTI ID = 0.0 >
Figure 112015062628857-pat00209
Lt; / RTI > pass through the first-order low-pass filter. E.g,
Figure 112015062628857-pat00210
to be. here,
Figure 112015062628857-pat00211
Is a time constant.

Step2:

Figure 112015062628857-pat00212
Let us consider Equation 10 to illustrate. Using Equations 11 and 14,
Figure 112015062628857-pat00213
Can be expressed as shown in Equation (20).

Figure 112015062628857-pat00214

Local virtual control (

Figure 112015062628857-pat00215
) ≪ / RTI >

Figure 112015062628857-pat00216

here,

Figure 112015062628857-pat00217
Is a design parameter,
Figure 112015062628857-pat00218
The
Figure 112015062628857-pat00219
As shown in Equation (22) by the adaptive rule.

Figure 112015062628857-pat00220

here,

Figure 112015062628857-pat00221
Is a tuning gain,
Figure 112015062628857-pat00222
Is a constant. In Equation 21,
Figure 112015062628857-pat00223
The term " smooth function "
Figure 112015062628857-pat00224
Figure 112015062628857-pat00225
,
Figure 112015062628857-pat00226
Lt; / RTI >

Figure 112015062628857-pat00227
Is a first-order low-pass filter (
Figure 112015062628857-pat00228
). here,
Figure 112015062628857-pat00229
Is a constant.

Step 3:

Figure 112015062628857-pat00230
Consider an error surface for the design of. Equation (7) can be expressed by the time variance as shown in Equation (23).

Figure 112015062628857-pat00231

here,

Figure 112015062628857-pat00232
and
Figure 112015062628857-pat00233
Is a constant matrix.

Unknown smooth nonlinear function vector (

Figure 112015062628857-pat00234
) Can be derived from the stability analysis process predicted by the adaptive function approximation technique.

Function operator

Figure 112015062628857-pat00235
) Is a compact set of equation (24)
Figure 112015062628857-pat00236
)top
Figure 112015062628857-pat00237
.

Figure 112015062628857-pat00238

here,

Figure 112015062628857-pat00239
Is a reconstruction error vector,
Figure 112015062628857-pat00240
The
Figure 112015062628857-pat00241
Figure 112015062628857-pat00242
The optimal weighting matrix (
Figure 112015062628857-pat00243
) ≪ / RTI >
Figure 112015062628857-pat00244
The
Figure 112015062628857-pat00245
Respectively. here,
Figure 112015062628857-pat00246
Is an unknown constant,
Figure 112015062628857-pat00247
Represents the Frobenius bomb.

In order to adjust all the weights of the function approximator, Taylor series expansion is expressed by Equation (25).

Figure 112015062628857-pat00248

here,

Figure 112015062628857-pat00249
ego,
Figure 112015062628857-pat00250
Is a higher order term. Substituting equation (25) into equation (24) yields equation (16).

Figure 112015062628857-pat00251

Figure 112015062628857-pat00252

here,

Figure 112015062628857-pat00253
ego,
Figure 112015062628857-pat00254
Is a constant.

Actual controller (

Figure 112015062628857-pat00255
) ≪ / RTI >

Figure 112015062628857-pat00256

here,

Figure 112015062628857-pat00257
Is a design parameter,
Figure 112015062628857-pat00258
The unknown nonlinear term (
Figure 112015062628857-pat00259
).

The unknown nonlinear terms are as follows.

Figure 112015062628857-pat00260
Figure 112015062628857-pat00261
Figure 112015062628857-pat00262
Figure 112015062628857-pat00263
Figure 112015062628857-pat00264

here,

Figure 112015062628857-pat00265
,
Figure 112015062628857-pat00266
,
Figure 112015062628857-pat00267
,
Figure 112015062628857-pat00268
,
Figure 112015062628857-pat00269
,
Figure 112015062628857-pat00270
,
Figure 112015062628857-pat00271
Is a positive constant,
Figure 112015062628857-pat00272
Figure 112015062628857-pat00273
to be.

Forecast (

Figure 112015062628857-pat00274
Can be tuned as shown in equation (29) according to the adaptive law.

Figure 112015062628857-pat00275

here,

Figure 112015062628857-pat00276
ego,
Figure 112015062628857-pat00277
Is a positive design parameter,
Figure 112015062628857-pat00278
The
Figure 112015062628857-pat00279
J < / RTI >

The time variance of the boundary error in Equations (12) to (14) is defined as Equation (30).

Figure 112015062628857-pat00280

here,

Figure 112015062628857-pat00281
,
Figure 112015062628857-pat00282
,

Figure 112015062628857-pat00283
,

Figure 112015062628857-pat00284
Figure 112015062628857-pat00285
Figure 112015062628857-pat00286
Is a continuous function that defines the time variance of the virtual controller.

Considering Lyapunov function, Equation 31 is obtained.

Figure 112015062628857-pat00287

here,

Figure 112015062628857-pat00288
ego,
Figure 112015062628857-pat00289
Figure 112015062628857-pat00290
,
Figure 112015062628857-pat00291
,
Figure 112015062628857-pat00292
,
Figure 112015062628857-pat00293
,
Figure 112015062628857-pat00294
,
Figure 112015062628857-pat00295
Represents the tracking of one matrix.

Theory 1: Considering a number of mobile robots including unknown skidding and sleeping, it is assumed that the leading robot has a direct path with all following robots. The cluster control system can perform the cluster control purpose in a direct communication environment during collision avoidance between the robots.

(i) Outside the detection area, a distributed position tracking error (

Figure 112015062628857-pat00296
) And the direction angle are the same for all signals in the entire closed loop system
Figure 112015062628857-pat00297
Figure 112015062628857-pat00298
and
Figure 112015062628857-pat00299
Respectively. Also,
Figure 112015062628857-pat00300
, The direction error (
Figure 112015062628857-pat00301
) Can be converged near the origin.

(ii) Inside the detection area, collision avoidance between robots is guaranteed. E.g,

Figure 112015062628857-pat00302
to be.

Remark 3. Handles unknown slip phenomenon under limited communication link environment between robots. The adaptive control method for compensating the unknown slip phenomenon of Equation (17) can be derived by taking into account the potential function and the rate of change of the distributed cluster control.

The same skidding and sleeping phenomenon can be considered in a group consisting of one leader robot and three following robots.

Figure 112015062628857-pat00303
If
Figure 112015062628857-pat00304
, Or
Figure 112015062628857-pat00305
to be. Also,
Figure 112015062628857-pat00306
If
Figure 112015062628857-pat00307
, Or
Figure 112015062628857-pat00308
to be.

The avoidance area and the collision area

Figure 112015062628857-pat00309
,
Figure 112015062628857-pat00310
Respectively. here,
Figure 112015062628857-pat00311
Lt;
Figure 112015062628857-pat00312
to be.
Figure 112015062628857-pat00313
In order to check the convergence of the directional error according to the above-mentioned equation, two kinds of skipping and sleeping are assumed.

Case 1:

Figure 112015062628857-pat00314

Case 2:

Figure 112015062628857-pat00315

Figure 112015062628857-pat00316
Figure 112015062628857-pat00317
Can be defined as a position tracking error of the following robot. Wavelet neural network with four parent wavelets and one unknown node nonlinear function
Figure 112015062628857-pat00318
Lt; / RTI >

The design parameters for the simulation are

Figure 112015062628857-pat00319
,
Figure 112015062628857-pat00320
,
Figure 112015062628857-pat00321
,
Figure 112015062628857-pat00322
,
Figure 112015062628857-pat00323
,
Figure 112015062628857-pat00324
,
Figure 112015062628857-pat00325
,
Figure 112015062628857-pat00326
,
Figure 112015062628857-pat00327
,
Figure 112015062628857-pat00328
Figure 112015062628857-pat00329
,
Figure 112015062628857-pat00330
,
Figure 112015062628857-pat00331
,
Figure 112015062628857-pat00332
. Here, i = 1, 2, 3.

Further, the reader robot

Figure 112015062628857-pat00333
and
Figure 112015062628857-pat00334
It is assumed that the path generated by velocity is moving.

The initial posture for the robot is

Figure 112015062628857-pat00335
,
Figure 112015062628857-pat00336
,
Figure 112015062628857-pat00337
,
Figure 112015062628857-pat00338
Lt; / RTI >

For Case 1, the distributed cluster tracking error is shown in Figs. 4 (a) and 4 (b) showing the distance between the robots and the avoidance area. Distance is avoided (

Figure 112015062628857-pat00339
), The collision does not occur because the robot in the detection area quickly avoids another robot.

Distributed cluster tracking can be performed with guaranteed collision avoidance, despite unknown slip and model nonlinearity. The direction error of Case 1 can be converged to "0 ". The direction error for Case 2 (Figure 4 (c)) is

Figure 112015062628857-pat00340
Lt; / RTI >

It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the invention as defined in the appended claims. It will be understood that the invention may be varied and varied without departing from the scope of the invention.

110:
115: Sensor
120:
125: Memory
130:

Claims (13)

In each mobile robot of the lead-follower cluster control system,
A detecting unit that detects whether another mobile robot is located within a set detection area of the mobile robot or a predetermined collision avoidance area of the mobile robot; And
Controls the movement of the mobile robot in consideration of an unknown slip parameter so that the other mobile robot is positioned outside the detection area using the repulsive force of the mobile robot when the other mobile robot is positioned within the detection area, And a controller for controlling the movement of the mobile robot such that the other mobile robot is located outside the detection area of the mobile robot by increasing the repulsive force of the mobile robot as the mobile robot is positioned closer to the collision avoiding area of the mobile robot,
The controller estimates the position of the leading robot in a state where there is communication restriction with the leading robot in consideration of an unknown slip parameter when the other moving robots are located outside the detection area, The movement of the mobile robot is controlled so as to maintain the movement of the mobile robot,
Wherein the detection region is a virtual region set for collision avoidance between the mobile robot and the other mobile robot,
Wherein the collision avoiding area is a virtual area set smaller than the detection area with respect to the center position of the mobile robot,
The controller comprising:
Equations (4) and (5)
Figure 112016039009619-pat00345
And avoids collision with other mobile robots based on the partial variance of the mobile robot.

&Quot; (4) "
Figure 112016039009619-pat00346


&Quot; (5) "
Figure 112016039009619-pat00347

here,
Figure 112016039009619-pat00348
ego,
Figure 112016039009619-pat00349
Lt;
Figure 112016039009619-pat00350
ego,
Figure 112016039009619-pat00351
Lt;
Figure 112016039009619-pat00352
ego,
Figure 112016039009619-pat00353
Figure 112016039009619-pat00354
Represents the distance between the i-th mobile robot and the h-th mobile robot. Also,
Figure 112016039009619-pat00355
ego,
Figure 112016039009619-pat00356
and
Figure 112016039009619-pat00357
Represents the radius of the detection region of the i-th mobile robot and the radius of the detection region of the h-th mobile robot, respectively.
Figure 112016039009619-pat00358
Is an avoidance region indicating the minimum safety distance between the robots,
Figure 112016039009619-pat00359
being.

The method according to claim 1,
Wherein the detection area radius of the mobile robot is a virtual area set based on a center position of the mobile robot.
delete delete delete The method according to claim 1,
A communication unit for acquiring the position of the other mobile robot through communication with the other mobile robot; And
Further comprising a sensor for measuring a distance of the other mobile robot when the distance from the other mobile robot is within a predetermined distance.
delete A control method for each mobile robot in a lead-follower cluster control system,
Detecting whether another mobile robot is located within the set detection area of the mobile robot or the set collision avoidance area of the mobile robot;
Controlling movement of the mobile robot in consideration of an unknown slip parameter so that the other mobile robot is positioned outside the detection area when the other mobile robot is positioned within the detection area;
Controlling the movement of the mobile robot such that the other mobile robot is positioned outside the detection area of the mobile robot by increasing the repulsive force of the mobile robot as the other mobile robot is located closer to the collision avoiding area of the mobile robot; And
When the other mobile robots are located outside the detection area, the position of the leading robot is estimated in a state of communication restriction with the leading robot in consideration of an unknown sliding parameter, and a predetermined distance is maintained with the estimated leading robot And controlling movement of the mobile robot,
Wherein the detection region is a virtual region set for collision avoidance between the mobile robot and the other mobile robot,
Wherein the collision avoiding area is a virtual area set smaller than the detection area with respect to the center position of the mobile robot,
Wherein the step of controlling movement of the mobile robot includes:
Equations (4) and (5)
Figure 112016039009619-pat00360
Based on the partial variance of the mobile robot, the collision with other mobile robots is avoided.
&Quot; (4) "
Figure 112016039009619-pat00361


&Quot; (5) "
Figure 112016039009619-pat00362

here,
Figure 112016039009619-pat00363
ego,
Figure 112016039009619-pat00364
Lt;
Figure 112016039009619-pat00365
ego,
Figure 112016039009619-pat00366
Lt;
Figure 112016039009619-pat00367
ego,
Figure 112016039009619-pat00368
Figure 112016039009619-pat00369
Represents the distance between the i-th mobile robot and the h-th mobile robot. Also,
Figure 112016039009619-pat00370
ego,
Figure 112016039009619-pat00371
and
Figure 112016039009619-pat00372
Represents the radius of the detection region of the i-th mobile robot and the radius of the detection region of the h-th mobile robot, respectively.
Figure 112016039009619-pat00373
Is an avoidance region indicating the minimum safety distance between the robots,
Figure 112016039009619-pat00374
being.
9. The method of claim 8,
Wherein the detection area radius of the mobile robot is a virtual area set based on a center position of the mobile robot.
delete delete delete delete
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WO2019212239A1 (en) * 2018-05-04 2019-11-07 Lg Electronics Inc. A plurality of robot cleaner and a controlling method for the same
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Title
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Journal of Institute of Control, Robotics and Systems Vol. 16 No. 1 (2010.1.)* *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR101937269B1 (en) 2017-05-15 2019-01-14 한국생산기술연구원 Planning method for robot motion
US11707175B2 (en) 2018-01-03 2023-07-25 Samsung Electronics Co., Ltd. Moving apparatus for cleaning, collaborative cleaning system, and method of controlling the same
WO2019212239A1 (en) * 2018-05-04 2019-11-07 Lg Electronics Inc. A plurality of robot cleaner and a controlling method for the same
US11148290B2 (en) 2018-05-04 2021-10-19 Lg Electronics Inc. Plurality of robot cleaner and a controlling method for the same

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