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

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.

는 노드 또는 정점(vertices)(

)을 포함하는 그래프이다. 여기서,

는 에지 또는 아크의 집합이다. 임의의 노드

은 에이전트 i(추종 로봇i)가 에이전트 j(추종 로봇 j)로부터 정보를 획득할 수 있다는 것을 의미하며, 그 역은 성립하지 않는다. 여기서, 에이전트 j(추종 로봇 j)와 에이전트 i(추종 로봇i)는 각각 부모 노드와 자식 노드일 수 있다.

Is a node or vertices (

). ≪ / RTI > here,

Is a set of edges or arcs. Any node

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.

로, 이는 노드 i로 들어오는 에지를 가지는 노드의 집합이다. 노드

으로부터 노드

로의 직접 패스는

형태의 에지 시퀀스이다. 직접 트리는 루트를 제외하고 모든 노드가 하나의 부모를 가지는 직접 그래프이다. The neighbor set of node i

, Which is the set of nodes with edges coming into node i. Node

Gt;

The direct pass to

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).

이고,

는 i번째 이동 로봇의 두 구동 휠간의 중심점 좌표를 나타내고,

는 i번째 이동 로봇의 진행 각도이며,

이되,

와

는 i번째 이동 로봇의 forward linear와 각 속도를 나타낸다.

이고,

는 i번째 이동 로봇의 종방향 슬립 속도를 나타내고,

는 i번째 로봇의 휠 미끄러짐에 따른 요 레이트 변화(perturbation)를 나타낸다. 또한,

이고,

는 i번째 이동 로봇의 스키딩 속도를 나타내고,

는 i번째 이동 로봇의 휠에 적용되는 제어 토크를 나타내며,

이다.here,

ego,

Represents the center-point coordinates between the two driving wheels of the i-th mobile robot,

Is the traveling angle of the i-th mobile robot,

However,

Wow

Represents the forward linear and angular velocity of the i-th mobile robot.

ego,

Represents the longitudinal slip velocity of the i-th mobile robot,

Represents the yaw rate change (perturbation) due to the wheel slip of the i-th robot. Also,

ego,

Represents the skidding speed of the i-th mobile robot,

Represents the control torque applied to the wheel of the i-th mobile robot,

to be.

,

,

및

는 ?oo and Park 논문에 공지되어 있으며, 이는 당업자에게는 자명한 사항이므로 별도의 정의는 생략하기로 한다.
Also, in the kinematic equation,

,

,

And

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.

와

는

로 인해,

,

및

로 유계될 수 있다. 여기서,

는 미지의 상수이다. 첫번째 변량은

,

,

를 포함하는

로 유계될 수 있다. 여기서,

는 미지의 상수이다.
Assumption 1: Skimming and sleeping change

Wow

The

Due to,

,

And

. ≪ / RTI > here,

Is an unknown constant. The first variable

,

,

Containing

. ≪ / RTI > here,

Is an unknown constant.

과

은 모르는 것을 가정하기로 한다. 여기서,

이다.Assumption 2: System matrix for dynamics

and

Assume that you do not know. here,

to be.

)로 설명될 수 있다. 여기서,

이다. 추종 로봇 사이의 통신을 설명하기 위해, 서브 그래프를

로 정의하기로 한다. 여기서,

이다. 서브 그래프(

)의 인접 행렬(

)는

이다. 만일

이면

이고, 그렇지 않다면,

이다. 또한, 그래프(

)의 라플라시안 행렬(

)은

로 정의될 수 있다. 여기서,

은 선도 로봇으로부터 추종 로봇까지의 통신 가중치를 나타내며, 리더 로봇(

)이면,

이고, 아니면

이다. 또한,

이고,

는 추종 로봇들 사이의 통신을 나타내는 서브 그래프의 라플라시안 행렬이다. 여기서,

이고,

는 차수 행렬(degree matrix D)의 대각 요소를 나타낸다.
The communication topology for the (M + 1) mobile robot is shown in graph (

). here,

to be. In order to explain the communication between the following robot,

. here,

to be. Subgraph (

) Adjacent matrix (

)

to be. if

If

If not,

to be. Also,

) Laplacian matrix (

)silver

. ≪ / RTI > here,

Represents the communication weight from the leading robot to the following robot, and the leader robot

),

, Or

to be. Also,

ego,

Is a Laplacian matrix of subgraphs indicating communication between following robots. here,

ego,

Represents the diagonal element of the degree matrix D.

)가 확장 트리(spanning tree)를 가지면,

이다.

로부터

이다. 여기서,

은 모두 1인 M-벡터이다.
Remark 1. Graph (

) Has a spanning tree,

to be.

from

to be. here,

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).

이고,

이며,

이고,

는 i번째 이동 로봇과 h번째 이동 로봇간의 거리를 나타낸다. 또한,

이고,

과

는 각각 i번째 이동 로봇의 검출 영역(detection region)의 반경과 h번째 이동 로봇의 검출 영역의 반경을 나타낸다.

는 로봇들간의 최소 안전 거리를 나타내는 회피 영역(avoidance region)이고,

이다.here,

ego,

Lt;

ego,

Represents the distance between the i-th mobile robot and the h-th mobile robot. Also,

ego,

and

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.

Is an avoidance region indicating the minimum safety distance between the robots,

to be.

와

좌표에 대한

의 부분 변량은 수학식 4 및 수학식 5와 같이 정의될 수 있다.

Wow

About Coordinates

Can be defined as shown in Equation (4) and Equation (5).

이다.
here,

to be.

을 설계하기 위한 것이다.The control objective is the approximation based adaptive cluster control law

.

외부에서,

과

, 여기서,

,

,

는 충분히 작은 상수이다.

는 i번째 추종 로봇과 리더 로봇 사이의 희망하는 오프셋을 나타낸다. 그리고,

는 위치

와 방향(

), 선속도(

)와 각속도(

)인 경우,

,

,

에 의해 생성되는 리더 로봇의 위치이다.
(I) detection area

Outside,

and

, here,

,

,

Is a sufficiently small constant.

Represents the desired offset between the ith following robot and the leader robot. And,

Location

And direction (

), Linear velocity

) And angular velocity

),

,

,

Is the position of the leader robot generated by the robot.

내부에서, i번째 추종 로봇은 위치

와

의 영향하에 있는 검출된 로봇의 충돌을 피한다. 여기서,

이고,

이고,

에 대해

이다. 여기서,

는 상수이다. 또한,

이고,

과

는 i번째 로봇과 j번째 로봇 사이의 희망하는 오프셋 벡터(

)의 각 요소를 나타낸다. 여기서,

만족한다.
(II) detection region

Inside, the i-th following robot is located

Wow

Avoiding the collision of the detected robots under the influence of the robot. here,

ego,

ego,

About

to be. here,

Is a constant. Also,

ego,

and

Is the desired offset vector between the i-th robot and the j-th robot

). ≪ / RTI > here,

Satisfies.

을 만족하는 i번째 추종 로봇에서 이용 가능하다.
Assumption 2: The position and velocity information of the leader robot is related,

Of the i-th following robot satisfying the following equation.

로 간주될 수 있다. 그르므로, 에러(

와

)는 추종 에러 항

과 충돌 회피 항

의 조합으로 정의될 수 있다.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

. ≪ / RTI > So, error (

Wow

) Is a tracking error term

And collision avoidance port

. ≪ / RTI >

이므로,

과

의 영향은

과

이다. 여기서,

과

은 내부 검출 영역에 가까운 로봇들 사이의 거리에 따라 증가되고,

이고,

로, 충돌 회피를 이룰 수 있다. 제어기(

) 설계에 따라

과

는 시간이 증가함에 따라 "0"으로 접근한다.

를 가지므로, i번째 추종 로봇은 내부 검출 영역에서 검출된 로봇을 회피할 수 있다.In the inner detection area

Because of,

and

The effect of

and

to be. here,

and

Is increased in accordance with the distance between robots close to the internal detection area,

ego,

, Collision avoidance can be achieved. Controller (

Depending on the design

and

Approaches "0" as time increases.

The ith following robot can avoid the robot detected in the internal detection region.

은 이동 로봇의 그룹이 원하는 군집 추종을 수행하는 동안 로봇들간의 어떠한 충돌도 발생하지 않는다는 것을 의미한다.
(ii) conditions

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.

이다.here,

to be.

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

)과 경계층 에러(

)를 수학식 9 내지 수학식 14와 같이 정의한다.For distributed controller design, the distributed error surface (

) And boundary layer error (

) Is defined as the following Equations (9) to (14).

,

,

,

,

과

는 각각 가상 제어와 필터링된 가상 제어를 나타낸다.here,

,

,

,

,

and

Respectively represent virtual control and filtered virtual control.

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

과

를 위해 가상 제어기

,

를 설계하고, 1차 저역 통과 필터를 사용하여 필터링된 가상 신호

과

를 도출한다.(i) Dynamics In equation (6), the state variable

and

For the virtual controller

,

And outputs the filtered virtual signal < RTI ID = 0.0 >

and

.

)를 위한 가성 제어기(

)를 설계하고, 1차 저역 통과 필터를 사용하여 필터링된 가상 신호(

)를 유도한다.(ii) Dynamic Equation The state variable of equation (7)

A pseudo controller (

) Are designed, and the filtered virtual signal (

).

)를 설계한다.
(iii) the dynamic controller of equation (8)

).

,

)을 설계하기 위한 분산된 에러 표면을 고려한다. 수학식 6을 적용한 수학식 9와 수학식 10 내지 13의 시간 변량은 수학식 15와 같다.Step 1: First virtual control law (

,

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).

이고,here,

ego,

이며,

Lt;

이다.

to be.

)은 수학식 16과 같이 정리될 수 있다.Local virtual control term (

) Can be rearranged as shown in Equation (16).

은 양의 설계 파라미터이고,

는 스몰 설계 파라미터이며, here,

Is a positive design parameter,

Is a small design parameter,

이고,

이며,

는

의 예측치로 수학식 17의 적응적 학습 법칙에 따라 조정될 수 있다.

ego,

Lt;

The

Lt; RTI ID = 0.0 > (17) < / RTI >

는 튜닝 이득이고,

는

조정을 위한 상수이다.here,

Is a tuning gain,

The

It is a constant for adjustment.

의 정의를 사용하여 가상 제어 법칙(

,

)은 수학식 18 및 수학식 19와 같이 획득될 수 있다.In Equation (16)

Using the definition of virtual control law (

,

) Can be obtained as shown in Equations (18) and (19).

,

는

의 지속성(continuity)과 식별 가능성(differentiability)를 보증하기 위한 정수이다. 우선,

를 "0"으로 설정하고,

이 불연속적일때마다

씩 증가시켜 가변한다.

은 필터링된 신호(

)를 획득하기 위해 1차 저역 통과 필터를 통과한다. 예를 들어,

이다. 여기서,

는 시간 상수이다.
here,

,

The

Is an integer for ensuring continuity and differentiability of the data. first,

Is set to "0 &

Whenever this is discontinuous

Respectively.

Lt; RTI ID = 0.0 >

Lt; / RTI > pass through the first-order low-pass filter. E.g,

to be. here,

Is a time constant.

를 설명하기 위해 수학식 10을 고려하자. 수학식 11과 14를 사용하여

의 시간 변량은 수학식 20과 같이 나타낼 수 있다.Step2:

Let us consider Equation 10 to illustrate. Using Equations 11 and 14,

Can be expressed as shown in Equation (20).

)는 수학식 21과 같다.Local virtual control (

) ≪ / RTI >

는 설계 파라미터이고,

는

의 예측치로 적응 법칙에 의해 수학식 22와 같이 조정될 수 있다.here,

Is a design parameter,

The

As shown in Equation (22) by the adaptive rule.

는 튜닝 이득이고,

는 상수이다. 수학식 21에서

항은 smooth 함수(smooth function)

,

에 의해 정의될 수 있다.here,

Is a tuning gain,

Is a constant. In Equation 21,

The term " smooth function "

,

Lt; / RTI >

는 1차 저역 통과 필터(

)를 통과시킨다. 여기서,

는 상수이다.

Is a first-order low-pass filter (

). here,

Is a constant.

의 설계를 위해 에러 표면을 고려하자. 수학식 7을 시간 변량으로 나타내면 수학식 23과 같다.Step 3:

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

과

는 상수 행렬이다.here,

and

Is a constant matrix.

)는 적응적 함수 근사화 기술에 의해 예측되는 안정성 분석 과정으로부터 유도될 수 있다.Unknown smooth nonlinear function vector (

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

)는 수학식 24의 컴팩트 집합(

)상의

의 예측치이다.Function operator

) Is a compact set of equation (24)

)top

.

는 복원 에러 벡터이고,

는

로 정의되는 최적 가중치 행렬(

)의 예측된 가중치 행렬이다.

는

로 유계된다. 여기서,

는 미지의 상수이고,

는 Frobenius 놈을 나타낸다.here,

Is a reconstruction error vector,

The

The optimal weighting matrix (

) ≪ / RTI >

The

Respectively. here,

Is an unknown constant,

Represents the Frobenius bomb.

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

이고,

은 고차원 항이다. 수학식 24를 수학식 25로 대체하면, 수학식 16과 같다.here,

ego,

Is a higher order term. Substituting equation (25) into equation (24) yields equation (16).

이고,

는 상수이다.here,

ego,

Is a constant.

)는 수학식 28과 같다.Actual controller (

) ≪ / RTI >

는 설계 파라미터이고,

는 미지의 비선형 항(

)의 근사화한 것이다.here,

Is a design parameter,

The unknown nonlinear term (

).

The unknown nonlinear terms are as follows.

,

,

,

,

,

,

는 양의 상수이고,

이다.here,

,

,

,

,

,

,

Is a positive constant,

to be.

)는 적응법칙에 따라 수학식 29와 같이 튜닝될 수 있다.Forecast (

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

이고,

는 양의 설계 파라미터이고,

는

의 j번째 요소를 나타낸다.here,

ego,

Is a positive design parameter,

The

J < / RTI >

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

,

, here,

,

,

,

,

은 가상 제어기의 시간 변량을 정의하는 연속 함수이다.

Is a continuous function that defines the time variance of the virtual controller.

Considering Lyapunov function, Equation 31 is obtained.

이고,

,

,

,

,

,

는 하나의 행렬의 추적을 나타낸다.
here,

ego,

,

,

,

,

,

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.

)와 방향각은 전체 폐루프 시스템의 모든 신호가 유계되는 동안

과

을 각각 만족한다. 또한,

이면, 방향 에러(

)는 원점 근처로 수렴될 수 있다.(i) Outside the detection area, a distributed position tracking error (

) And the direction angle are the same for all signals in the entire closed loop system

and

Respectively. Also,

, The direction error (

) Can be converged near the origin.

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

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.

이면

이고, 아니면

이다. 또한,

이면

이고, 아니면

이다.

If

, Or

to be. Also,

If

, Or

to be.

,

로 각각 채택될 수 있다. 여기서,

이며,

이다.

에 따른 방향 에러의 수렴을 체크하기 위해, 2가지의 스키딩과 슬리핑을 가정하기로 한다.The avoidance area and the collision area

,

Respectively. here,

Lt;

to be.

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:

Case 2:

는 추종 로봇의 위치 추종 에러로 정의될 수 있다. 4개의 모 웨이블릿을 포함하는 웨이블릿 신경망과 하나의 노드가 미지의 비선형 함수(

)을 위해 이용된다.

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

Lt; / RTI >

,

,

,

,

,

,

,

,

,

,

,

,

로 설정하기로 한다. 여기서, i=1,2,3이다. The design parameters for the simulation are

,

,

,

,

,

,

,

,

,

,

,

,

. Here, i = 1, 2, 3.

과

속도에 의해 생성된 경로를 움직이는 것을 가정하기로 한다.Further, the reader robot

and

It is assumed that the path generated by velocity is moving.

,

,

,

로 설정될 수 있다.The initial posture for the robot is

,

,

,

Lt; / RTI >

)보다 큰 거리에서는 검출 영역에 있는 로봇이 빠르게 다른 로봇을 피하기 때문에, 충돌이 발생하지 않는다.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 (

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

로 수렴될 수 있다.
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

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)

And avoids collision with other mobile robots based on the partial variance of the mobile robot.

&Quot; (4) "

&Quot; (5) "

here,

ego,

Lt;

ego,

Lt;

ego,

Represents the distance between the i-th mobile robot and the h-th mobile robot. Also,

ego,

and

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.

Is an avoidance region indicating the minimum safety distance between the robots,

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)

Based on the partial variance of the mobile robot, the collision with other mobile robots is avoided.
&Quot; (4) "

&Quot; (5) "

here,

ego,

Lt;

ego,

Lt;

ego,

Represents the distance between the i-th mobile robot and the h-th mobile robot. Also,

ego,

and

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.

Is an avoidance region indicating the minimum safety distance between the robots,

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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