KR101813610B1 - Three-dimensional nonlinear path-following guidance system and method based on differential geometry - Google Patents

Abstract

A three-dimensional nonlinear path following derivation system and method based on the derivative of a curve is disclosed. A three-dimensional nonlinear path following guidance system according to an embodiment of the present invention is a system for deriving a path following guidance that guides a moving object to follow a target path. The system includes a control for acquiring the position and velocity of the moving object to be controlled as control target information A target information obtaining unit; A closest point calculating unit for calculating a closest point corresponding to a position of the moving object with respect to the target path; A target path characteristic calculation unit for calculating a differential geometry characteristic with respect to the target path; An induction command generator for obtaining a forward look-up vector calculated as a front main time and a radial distance based on the control subject information, the nearest point information, and the differential geometric characteristics of the target path and generating an induction command given by acceleration, ; And a movement controller for controlling the movement of the moving object according to the guidance command.

Description

[0001] The present invention relates to a three-dimensional nonlinear path following guidance system and method based on differential geometry of a curve,

The present invention relates to a three-dimensional nonlinear path following induction system and method based on the derivative of a curve.

The path-following problem can be defined as designing an induction command such that a vehicle such as a gas and / or a vehicle follows a target path. This path following is one of the important problems for autonomous operation of UAV. Recently, the tasks related to autonomous flight of UAV are increasingly complicated, and accurate and effective three-dimensional path follow-up technology is required.

Various induction techniques have been developed for path tracking, but most of them are related to two-dimensional path tracing. They are largely based on error kinematics / dynamics based approach, vector field based approach, And the virtual target following approach.

In the error kinematics / mechanics - based approach, error parameters were defined and applied to account for path - following problems. Kinematic / dynamic models of error variables are derived, and linear or nonlinear control models are applied for error control. This approach has the advantage of ensuring stability and reliable tracking performance from direct error feedback. However, the instruction is somewhat complicated and model dependent. In addition, a singularity problem may limit the set of feasible initial conditions.

In the vector field based method, when a vector field for specifying the desired course angle or speed is established at each point, the moving object converges to the target path along the vector field. The advantage of this approach is that it is global convergence in the case of straight and circular paths. However, it has a disadvantage that it can not be applied to general space curves.

In a virtual target tracking or a look-ahead point based approach, the inductive command is designed to track the virtual target on the target path. This approach, derived from traditional gaze induction techniques, has a simplicity of induction command, model independence, and a front-sight effect that enables good tracking and wind effect compensation. It also provides robustness against disturbances. However, if the initial position of the moving object should be within a specific forward viewing distance from the target path, and the target path is formed by combining complex curves of three-dimensional general curves, it is difficult to determine the forward main point.

The above-described background technology is technical information that the inventor holds for the derivation of the present invention or acquired in the process of deriving the present invention, and can not necessarily be a known technology disclosed to the general public prior to the filing of the present invention.

As a prior art related to the path following, Korean Patent Laid-open Publication No. 10-2011-0138090 discloses a vehicle steering control method and apparatus for following a target parking path. According to the present invention, the current vehicle attitude is calculated using the vehicle internal information, the target attitude of the vehicle is derived from the current attitude using the target parking path, the control attitude angle is calculated using the current attitude and the target attitude . It is developed only for the parallel parking situation of the vehicle. There is a limit that the steering angle is given as command and only one axial tracking error is fed back.

Korean Patent Publication No. 10-2011-0138090

The present invention eliminates the path-following error generated in a conventional forward-point-of-view-based tracking algorithm for a three-dimensional general path following a moving object such as a UAV and restricts the initial position and speed Dimensional nonlinear path follow-up guidance system based on the differential geometry of the curvilinear curves.

In contrast to the conventional technique of tracking a virtual target on a target path, the present invention uses a forward look-up vector calculated by directly utilizing the differential geometry of a target path, Dimensional nonlinear path following induction system based on the differential geometry of the three-dimensional nonlinear path following induction system.

The present invention can be applied to various tasks of the UAV based on the route follow-up. Especially, when a complicated route is required due to obstacles or the like, or when the 3D elevation of the UAV is required, the UAV is safer and more precise Dimensional nonlinear path follow-induction system based on the derivative of a curve that can be performed by the user.

Other objects of the present invention will become readily apparent from the following description.

According to an aspect of the present invention, there is provided a route follow-up guidance system for guiding a mobile object to follow a target route, comprising: a control object information obtaining unit for obtaining a position and a speed of the mobile object to be controlled as control object information; A closest point calculating unit for calculating a closest point corresponding to a position of the moving object with respect to the target path; A target path characteristic calculation unit for calculating a differential geometry characteristic with respect to the target path; An induction command generator for obtaining a forward look-up vector calculated as a front main time and a radial distance based on the control subject information, the nearest point information, and the differential geometric characteristics of the target path, ; And a movement control unit for controlling the movement of the moving object in accordance with the instruction to guide the 3D nonlinear path following guidance system.

The target path may be a mediated curve, and the target path characteristic calculating unit may calculate a unit tangent vector, an unit vector, and a curvature of the target path at the nearest point.

The values of the inductive gain and the boundary layer thickness, which are design variables, can be selected prior to the generation of the inductive command.

The induction command may make the moving body above the target path and make the velocity direction of the moving body coincide with the tangential direction of the target path.

When it is desired to follow the constant speed airspeed path, the induction command generator may generate a side induction command that is orthogonal to the relative speed vector of the moving object in which the wind speed is reflected.

According to another aspect of the present invention, there is provided a path-following induction method performed in a path-following induction system for inducing a mobile body to follow a target path, and a recording medium on which a program for performing the method is recorded.

According to an embodiment of the present invention, there is provided a three-dimensional nonlinear path following induction method, comprising: obtaining position and speed of a moving object to be controlled as control target information; Calculating a closest point corresponding to a position of the moving object with respect to the target path; Calculating a differential geometry characteristic for the target path; Obtaining a forward look-up vector calculated as a front main time and a radial distance based on the control subject information, the nearest point information, and the differential geometric characteristics of the target path; Generating an induction command given by an acceleration using the forward look-up vector; And controlling the movement of the moving object according to the guidance command.

The target path may be a mediated curve, and the target path characteristic calculating step may calculate a unit tangent vector, an unit vector, and a curvature of the target path at the nearest point.

And selecting a value of the inductive gain and the boundary layer thickness, which are design variables, before the generation of the inductive command.

The induction command may make the moving body above the target path and make the velocity direction of the moving body coincide with the tangential direction of the target path.

When it is desired to follow the constant speed airspeed path, the induction command generation step may generate a side induction command that is orthogonal to the relative speed vector of the moving object in which the wind speed is reflected.

,

,

)를 획득하는 단계; 설계 변수인 유도이득 k 및 경계층 두께

의 값을 선택하는 단계; 상기 이동체의 위치에 해당하는 상기 목표 경로 상의 최근접점 P을 계산하는 단계; 오차 벡터

를 계산하는 단계; 상기 최근접점에서의 단위 접벡터

, 단위 법벡터

, 곡률

을 계산하는 단계; 상기 유도이득, 상기 경계층 두께, 상기 곡률을 이용하여 방사상 이격거리

를 계산하는 단계; 이동된 오차 벡터

를 계산하는 단계; 상기 경계층 두께에 대한 상기 이동된 오차 벡터의 크기의 비의 함수로 주어지는 전방주시각

을 계산하는 단계; 상기 방사상 이격거리 및 상기 전방주시각을 이용하여 전방주시 벡터

를 계산하는 단계; 상기 전방주시 벡터를 이용하여 수직 가속도 명령

을 생성하는 단계를 포함할 수 있다.According to another aspect of the present invention, there is provided a 3D nonlinear path following induction method, comprising: a step of giving the target path as an intermediate curve; The position and velocity information of the moving object

,

,

); The design variables k and the thickness of the boundary layer

Selecting a value of < RTI ID = 0.0 > Calculating a nearest point P on the target path corresponding to the position of the moving object; Error vector

; The unit vector at the last contact

, Unit vector

, Curvature

; Using the induction gain, the thickness of the boundary layer, and the curvature,

; The shifted error vector

; And a ratio of the magnitude of the shifted error vector to the thickness of the boundary layer,

; Using the radial spacing distance and the front main clock,

; Using the forward look-up vector,

For example,

인 경우

로 계산될 수 있다.The radial spacing is determined by the following equation:

If

Lt; / RTI >

인 경우

로 계산될 수 있다.Or the radial spacing is such that the forward principal visual function

If

Lt; / RTI >

가 반영된 상대속도

를 계산하는 단계; 상기 수직 가속도 명령 및 상기 상대속도를 이용하여 상기 상대속도 벡터에 직교하는 측면 유도 명령을 생성하는 단계를 더 포함할 수 있다. 상기 측면 유도 명령은 다음 수학식과 같이 주어질 수 있다.If you want to follow the constant-speed airspeed path,

Relative speed

; Generating the lateral guidance command orthogonal to the relative velocity vector using the vertical acceleration command and the relative velocity. The side guidance command can be given by the following equation.

Other aspects, features, and advantages will become apparent from the following drawings, claims, and detailed description of the invention.

According to the embodiment of the present invention, it is possible to eliminate a path following error generated in a conventional front viewpoint-based path follow-up technique at the time of a three-dimensional general path following of a moving object such as UAV, There is an effect of alleviating the restriction on the speed.

In addition, unlike the existing technique of tracking the virtual target assumed on the target path, the use of the forward look-up vector calculated by directly utilizing the differential geometry of the target path makes numerical calculation easier and real- have.

In addition, it can be applied to various missions of UAV based on path following. Especially, when a complicated route is required due to obstacles or the like, or when a 3-dimensional high-speed operation of UAV is required, the UAV is safer and more precise There is an effect to be able to do.

1 is a block diagram of a 3D nonlinear path following guidance system based on a derivative of a curve according to an embodiment of the present invention;
FIG. 2 is a flowchart of a three-dimensional nonlinear path following induction method based on a differential geometry of a curve according to an embodiment of the present invention;
3 is a diagram showing a geometric concept of a three-dimensional path following problem and a Frenet-Serret frame of a target path,
4 is a diagram showing a geometric concept of a three-dimensional nonlinear path following induction method based on a differential geometry of a curve,
5 is a diagram showing the direction of an instruction instruction,
FIG. 6 is a diagram showing a forward principal time function used in the derivation instruction designing process,
FIG. 7 is a flowchart of a three-dimensional nonlinear path following induction method,
8 is a view showing a three-dimensional trajectory when a three-dimensional helical path is used as a target path,
9 is a graph showing acceleration components for each axis in comparison with a conventional induction method,
10 is a diagram showing a time trajectory with respect to a magnitude of an error vector with respect to a conventional induction technique;

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. 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.

It is to be understood that when an element is referred to as being "connected" or "connected" to another element, it may be directly connected or connected to the other element, . On the other hand, when an element is referred to as being "directly connected" or "directly connected" to another element, it should be understood that there are no other elements in between.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The singular expressions include plural expressions unless the context clearly dictates otherwise. In this specification, the terms "comprises" or "having" and the like refer to the presence of stated features, integers, steps, operations, elements, components, or combinations thereof, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

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.

Also, the terms " part, "" module," and the like, which are described in the specification, mean a unit for processing at least one function or operation, and may be implemented by hardware or software or a combination of hardware and software.

It is to be understood that the components of the embodiments described with reference to the drawings are not limited to the embodiments and may be embodied in other embodiments without departing from the spirit of the invention. It is to be understood that although the description is omitted, multiple embodiments may be implemented again in one integrated embodiment.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the like elements throughout. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail.

FIG. 1 is a block diagram of a three-dimensional nonlinear path following guidance system based on a differential geometry of a curve according to an embodiment of the present invention. FIG. 2 is a block diagram of a three-dimensional nonlinear And FIG.

The 3D nonlinear path following guidance system 100 based on the differential geometry of the curved line according to an embodiment of the present invention can be applied to a system that uses a differential unit geometry characteristic of a curve, unit vector, curvature, And generating a vertical acceleration command for designating the forward viewing vector as a tracking direction vector.

Referring to FIG. 1, a 3D nonlinear path following system 100 according to the present embodiment includes a control object information obtaining unit 110, a closest point calculating unit 120, a target path characteristic calculating unit 130, A generation unit 140, and a movement control unit 150.

The control object information obtaining unit 110 obtains the position and speed of the moving object to be controlled as control object information (step S210).

The position, speed, acceleration, etc. of the moving object can be obtained through a sensor installed on the moving object or through a control center (not shown) for remotely controlling the moving object.

The nearest point calculation unit 120 calculates a nearest point corresponding to the position of the moving object at every moment with respect to the target path given by the mediated curve (step S220). Here, the closest point means a point on the target path closest to the controlled object.

The target path characteristic calculation unit 130 calculates a differential geometry characteristic with respect to the target path (step S230).

The target path computes the unit tangent vector, the unit vector, and the curvature at the nearest point, which is the differential geometry of the bar, the bar being the median curve.

The induction command generator 140 obtains a forward look-up vector calculated by the front main time and the radial distance based on the control object information, the closest contact information, and the differential geometry of the target path (step S240). Finally, an induction command given by the acceleration is generated (step S250).

Here, the values of the inductive gain and the boundary layer thickness, which are design variables, can be selected prior to generation of the induction command.

The generation of the forward viewing vector and the generation of the induction command will be described in detail later with reference to the related drawings.

The movement control unit 150 controls the movement of the moving object by controlling the acceleration of the moving object to be controlled according to the induction command generated by the induction command generating unit 140 (step S260).

Hereinafter, the 3D nonlinear path following induction method performed in the 3D nonlinear path following inducing system according to the present embodiment will be described in detail.

In applying the 3D nonlinear path following induction method according to the present embodiment, the following assumption is made.

Assumptions 1. The smoothness condition of the desired path

The target path can be parameterized and is a twice differentiable space curve.

Assumption 2. Uniqueness of reference path

The closest projection point on the target path can be uniquely determined as a reference point.

Assumption 3. Direction of unit tangent vector

The direction of the unit tangent vector of the target path is determined by the target path following direction.

FIG. 3 shows a geometric concept of a three-dimensional path-following problem, and a Frenet-Serret frame of the target path is shown.

는 각각 프레넷-세렛 프레임을 구성하는 단위 접벡터(unit tangent vector), 단위 법벡터(unit normal vector) 및 단위 종법벡터(unit binormal vector),

은

로 매개화된 목표 경로, s 및

는 각각 목표 경로 및 이동체 경로(vehicle path)에 따른 거리를 나타낸다. In Fig. 3, P is a nearest point of a desired path, M is a moving object to be controlled, r is a position vector defined in an inertial frame, v is a velocity vector,

A unit tangent vector, a unit normal vector, and a unit binormal vector, which constitute a frame of a prefetch-let frame,

silver

The target path, s, and

Represents the distance along the target path and the vehicle path, respectively.

에서, 최근접점 P는 다음과 같이 정의된다.Set Goal Path

, The nearest point P is defined as follows.

(One)

이다. Here,

to be.

At the nearest point defined by equation (1), the condition that the error vector and the unit tangent vector are orthogonal is satisfied as follows.

(2)

이라는 유도기법에 따라 명령되어지는 것에 똑같은 가속도를 만들어내는 내부 루프 컨트롤러(inner-loop controller)를 구비하고 있는 것으로 가정한다. 여기서, 내부 루프 컨트롤러는 앞서 설명한 이동 제어부(150)에 해당한다.The moving body

It is assumed that it has an inner-loop controller that produces the same acceleration as that commanded by the induction technique of < RTI ID = 0.0 > Here, the inner loop controller corresponds to the movement controller 150 described above.

As can be deduced from the conceptual diagram shown in FIG. 3, the precision path tracking is intended to satisfy the following two conditions.

First, it is on-track that the mobile is on the target path, which is about the convergence of the position error that the distance between M and P converges to zero.

로 표기되는 이동체의 속도 벡터와

사이의 각도가 0에 수렴한다는 속도 방향 오차의 수렴성에 대한 것이다. Second, the velocity direction of the moving object coincides with the tangential direction of the target path,

The velocity vector of the moving object

The convergence of the velocity direction error that the angle between the two angles converges to zero.

되면 다음 조건을 만족하도록 유도 명령

이 설계됨으로써 해결 가능하게 된다.In other words, the path-following problem is mathematically

The instruction to satisfy the following condition

So that it can be solved.

(3)

(4)

If Equation (3) is satisfied, the mobile will be on the target path, which means position convergence.

If Equation (4) is satisfied, the moving object will follow the direction of the target path, which means velocity direction convergence.

인 경우 이동체는 온-트랙(on-track) 상태에 있고,

인 경우 이동체는 정렬(aligned) 상태에 있는 것으로 정의할 수 있다.
Also,

The moving object is in an on-track state,

The moving object can be defined as being in an aligned state.

In the present embodiment, a modified Fretnet-Setlet frame is used to describe motion along the target path curve.

From the differential geometry perspective, the velocity and acceleration of the particle can be expressed as:

(5)

(6)

는 곡률(curvature)이다. here,

Is a curvature.

가 곡선의 형상을 결정한다. The shape of the spatial curve depends only on the curvature. The speed along the curve does not affect the shape of the curve. Therefore, in Expression (6), the vertical acceleration component

Determines the shape of the curve.

And (6), the acceleration along the spatial curve does not have a normal normal component.

The acceleration command of the moving object generated by the path following induction method according to the present embodiment satisfies the following condition.

In order to keep the on-track state and the alignment state of the mobile body in order to follow the precise path, it is necessary to satisfy the following command condition.

(7)

(8)

는 수직 가속도에 대한 명령이다. here,

Is a command for vertical acceleration.

Equation (7) indicates that the curvature of the moving object path should be the same as the curvature of the target path, and Equation (8) means that the acceleration of the object should not have the normal normal component to the target path.

In applying the 3D nonlinear path following induction method, the induction geometry concept as shown in FIG. 4 can be considered.

4 is a diagram showing a geometric concept of a three-dimensional nonlinear path following induction method based on a differential geometry of a curve, FIG. 5 is a diagram showing a direction of an induction instruction, Fig.

The induction command in the 3D nonlinear path following induction method according to the present embodiment can be expressed as follows.

(9)

는 수직 유도 명령,

는 유도 이득,

는 이동체의 관성 속도,

은 전방주시 벡터(look-ahead vector)이다. here,

A vertical induction command,

Is the induction gain,

Is the inertia velocity of the moving body,

Is a look-ahead vector.

은 d의 방향에서

의 방향으로

의 각도만큼 회전한 단위 벡터이다. The vertical guidance command is an induction command for vertical acceleration, which is an acceleration component perpendicular to the inertia velocity. As shown in FIG. 4,

In the direction of d

In the direction of

Of the unit vector.

은 벡터 삼중적(vector triple product)에 의해 다음과 같이 표현될 수 있다. Vertical acceleration

Can be expressed by a vector triple product as follows.

(10)

은 임의의 값이다. here,

Is an arbitrary value.

이고, 수학식 (6)에서

이므로, 다음과 같은 수학식을 얻을 수 있다.In equation (5)

(6)

, The following equation can be obtained.

(11)

Equation (11) can be rewritten as follows.

(12)

을 만족하는 몇몇 T에 대해서

라는 사실을 이용하면, 수학식 (12)는 다음과 같이 다시 쓸 수 있다.

For some Ts that satisfy

, The equation (12) can be rewritten as follows.

(13)

과

에 상응하는 벡터 q의 삼중적으로 생성될 수 있다. 그러므로, 유도 기법은 적절한 q의 선택에 의해 구성될 수 있다. 본 실시예에서 q가 후술할 전방주시 효과(look-ahead effect)를 실현하도록

이 제시된다. The vertical acceleration command in equation (10)

and

Lt; RTI ID = 0.0 > q. ≪ / RTI > Therefore, the derivation technique can be constructed by choosing an appropriate q. In this embodiment, q is set so as to realize a look-ahead effect to be described later

.

이라면, 유도 명령의 방향은 다음과 같이 표현될 수 있다.

, The direction of the induction command can be expressed as follows.

(14)

이고, b에 수직한 벡터 성분이다(도 5 참조). here,

And is a vector component perpendicular to b (see Fig. 5).

의 방향 벡터는 다음과 같이 쓸 수 있다.According to equations (9) and (10)

Can be written as follows.

(15)

을 전방주시 벡터

에 정렬되도록 한다. 전방주시 효과라 칭해지는 이러한 특징은 추적 유도의 속성에서 기인한다.
The moving object according to the induction command such as the equation (9)

Forward vector

. This feature, referred to as the front-viewing effect, is attributed to the trait-inducing nature.

는 전방주시각(look-ahead angle)

과 방사상 이격거리(radially shifted distance)

에 의해 만들어진다. 도 4에서 C는 최근접점 P에서 곡률 중심이고, W는 P에서 C로의 직선 상에 정의되는 지점이다. Referring to FIG. 4,

Is a look-ahead angle.

And a radially shifted distance

Lt; / RTI > 4, C is the center of curvature at the nearest point P, and W is a point defined on a straight line from P to C.

는 다음과 같이 표현될 수 있다.

Can be expressed as follows.

(16)

이므로, M에서 W로의 거리 벡터는 다음과 같이 표현될 수 있다.Error vector

, The distance vector from M to W can be expressed as follows.

(17)

라 하면, 전방주시 벡터

는 다음과 같이 만들어질 수 있다.

, The front view vector

Can be created as follows.

(18)

의 값은 수학식 (7) 및 (8)을 이용하여 설명한 바 있는 정밀 경로 추종 조건을 만족시키도록 결정될 수 있다. Radial spacing

Can be determined so as to satisfy the precise path following condition described using equations (7) and (8).

이고,

이다. 따라서, 다음과 같은 수학식을 얻을 수 있다.If the mobile is in the on-track state,

ego,

to be. Therefore, the following equation can be obtained.

(19)

은

의 함수로서 지정된다. here,

silver

. ≪ / RTI >

이고, 따라서 다음과 같은 수학식을 얻을 수 있다.In addition to the on-track state, if the moving object is in an aligned state,

Thus, the following equation can be obtained.

(20)

If the equations (19) and (20) are substituted into the equation (9), the command generated in the on-track state and the alignment state can be expressed as follows.

(21)

It can be seen that equation (8) is satisfied by equation (21).

In addition, the induction command of Equation (21) must satisfy Equation (7) as follows.

(22)

는 정밀 경로 추종을 위해 다음 조건을 만족해야 한다.Therefore,

The following conditions must be met for precise path following.

(23)

은 몇가지 조건을 만족시킬 필요가 있다. In order to realize the effect of forward gaze on pathfinding,

It is necessary to satisfy several conditions.

에 평행한 축 주위에서 반경

을 가지는 가상의 실린더를 가정한다. 이 실린더는 경계층(boundary layer)이라 칭하고,

은 경계층 두께라 한다. As shown in Fig. 4,

Lt; RTI ID = 0.0 >

Lt; RTI ID = 0.0 > a < / RTI > This cylinder is referred to as a boundary layer,

Is the boundary layer thickness.

은 경계층 두께

에 대한 d 벡터(이동된 오차 벡터)의 크기의 비의 함수로 주어지며, 전방주시각 함수로 다음의 두 가지 중 한 가지를 선택하여 사용하면 된다. In the induction command design process,

Boundary Layer Thickness

And the size of the d vector (the shifted error vector). The following two functions can be selected as the forward principal visual function.

(24)

(25)

FIG. 6 shows the forward main visual functions used in the inductive command design process, and shows the BL function (equation (24)) and the acos function (equation (25)), respectively.

The radial distance depends on which frontal view is taken. If the first BL function (Equation (24)) is selected as the forward principal visual function, then it is calculated as follows.

(26)

And the second acos function (equation (25)) is selected as the forward principal visual function, it is calculated as follows.

(27)

에 의해 한계를 가진다(bounded). The size of the induction command is

And is bounded by.

이다. In the 3D nonlinear path following induction method according to the present embodiment, there are two design variables, which are the induction gain k and the boundary layer thickness

to be.

The derivative gain k affects the amount of instruction. If the initial position of the moving body is outside the boundary layer, the thickness of the boundary layer determines the position at which the moving body starts to steer the velocity vector in the direction of the target path. Therefore, the 3D nonlinear path following induction method according to the present embodiment can apply the autonomous flight mode irrespective of the initial position of the moving object.

In addition, the 3D nonlinear path following induction method according to the present embodiment does not cause a problem of singularity.

The main difference between the induction method according to the present embodiment and the conventional forward main point-based induction method is that the induction method according to the present embodiment realizes the forward-looking effect by the front main point, not the forward point of view.

The path follow-up method based on the forward viewpoint is given as follows.

(28)

은 이동체에 대해 특정 거리

만큼 전방에 위치하고 있는, 목표 경로 상의 전방주시점의 상대적인 위치 벡터에 의해 정의되는 전방주시 벡터이다. 이 유도 방법은 목표 경로가 일정한 곡률을 가지는 2차원 곡선이 아닌 경우에는 정밀 경로 추종 조건을 만족할 수 없게 된다.

Lt; RTI ID = 0.0 >

And is a forward-looking vector defined by the relative position vector of the forward main view on the target path. This derivation method can not satisfy the precise path following condition if the target path is not a two-dimensional curve having a constant curvature.

This is because even if the moving object is in an on-track state and an alignment state, the following result is obtained.

In accordance with another embodiment of the present invention, some modifications may be made to the induction command generation process for constant airspeed path tracking.

가 0(zero)이 아닐 때, 관성 속도

는 바람의 영향으로 상대속도

와 동일하지 않게 된다. 그러므로, 수직 유도 명령

은

에 접하는 성분을 가지며, 실제 대기속도(airspeed)를 변경하는 것은 쉽지 않기 때문에 이상적이지 않게 된다. 따라서 실제 비행 상황에서 정속 대기속도를 유지하는 것이 정속 대지속도(constant ground speed)를 유지하는 것보다 우수한 성능을 나타낸다. Wind speed

Is not zero, the inertial velocity < RTI ID = 0.0 >

The relative speed

. ≪ / RTI > Therefore,

silver

And it is not ideal to change the actual airspeed because it is not easy to change the airspeed. Therefore, maintaining the constant airspeed in real flight conditions is superior to maintaining the constant ground speed.

에서 다음의 명령 수정 로직에 따라 수정된

를 측면 유도 명령(side guidance command)이라 하기로 한다. Vertical induction command

Modified according to the following command modification logic

Is referred to as a side guidance command.

에 직교(orthogonal)해야 한다. In order to maintain the constant speed, the acceleration of the moving object must satisfy the following condition,

To be orthogonal.

(29)

As described above, the shape of the curve depends not only on the inertia velocity along the curve but also on the vertical acceleration. Therefore, whatever the tangential acceleration, the vertical acceleration must be equal to Equation (9) in order to preserve the path following ability, so the following condition must be satisfied.

(30)

Equation (30) can be rewritten as follows.

(31)

및

에 의해 정의된 평면에 놓여져야 하므로, 다음과 같다.Side-guided commands are used to avoid generating

And

As shown in the following table.

(32)

The equations (29), (31), and (32) can be rewritten as matrix equations as follows.

(33)

As a result, the modified side derivation command can be given as follows.

(34)

A flowchart of the three-dimensional nonlinear path following induction method described so far is shown in Fig. 7 may be performed by each component of the 3D nonlinear path following guidance system 100 shown in FIG.

가 주어진다. 그리고 제어대상 정보획득부(110)는 이동체의 위치 및 속도 정보(

,

,

)를 획득하고, 설계변수인 유도이득 k, 경계층 두께

의 값을 선택한다(단계 S310). The control target information obtaining section 110 is provided with a target curve

Is given. The control object information obtaining unit 110 obtains the position and velocity information of the moving object

,

,

), And the design variable k, the boundary layer thickness

(Step S310).

도 계산할 수 있다. The nearest point calculation unit 120 determines the nearest point P corresponding to the position of the mobile at every moment by using the equation (1) (step S320). The error vector

Can also be calculated.

, 단위 법벡터

, 곡률

를 계산한다(단계 S330). The target path characteristic calculation unit 130 calculates the target path characteristic

, Unit vector

, Curvature

(Step S330).

를 계산한다(단계 S340).The induction command generation unit 140 generates the induction command by using the equation (27) (or the equation (26)

(Step S340).

, 수학식 (17)에 의해 이동체(M)에서 W로의 거리벡터, 즉 이동된 오차 벡터(shifted error vector) d, 수학식 (25)(혹은 수학식 (24))에 의해 전방주시각

을 계산한다(단계 S350). Then, the distance vector of the center point W of the boundary layer is calculated by the equation (16)

, A distance vector from the moving object M to W, that is, a shifted error vector d, and Equation (25) (or Equation (24)) by Equation (17)

(Step S350).

을 계산한다(단계 S360). Then, according to the equation (18)

(Step S360).

을 계산하고(단계 S370), 이를 출력한다(단계 S380). Thereafter, the vertical induction command < RTI ID = 0.0 >

(Step S370), and outputs it (step S380).

를 계산하고, 이를 출력할 수도 있다. Although it is not shown in the drawing, when the constant-speed-of-air-speed-path following is required before step S380,

And output it.

The three-dimensional nonlinear path following induction method based on the curved differential shown in FIG. 2 and / or FIG. 7 can be implemented by a time series sequential automation by a program built in or installed in a digital processing apparatus (three- dimensional nonlinear path following system 100) It is of course also possible to carry out this procedure. The codes and code segments that make up the program can be easily deduced by a computer programmer in the field. In addition, the program is stored in a computer readable medium readable by the digital processing apparatus, and is read and executed by the digital processing apparatus to implement the method. The information storage medium includes a magnetic recording medium and an optical recording medium.

The results of the numerical simulation showing the performance of the 3D nonlinear path following induction method according to the present embodiment will be described with reference to the related drawings. Numerical simulations of the conventional induction method were also performed for comparison of the path following performance.

FIG. 8 is a view showing a three-dimensional trajectory when a three-dimensional spiral path is used as a target path, FIG. 9 is a diagram showing acceleration components for each axis with respect to a conventional induction technique, Of FIG.

Referring to FIG. 8, a three-dimensional trajectory is shown, a red line 410 is a given target path, a blue line 420 is a result of the induction technique according to the present embodiment, a black line 430 is a result of a conventional induction technique .

As can be seen from the figure, the result of the induction technique according to the present embodiment almost coincides with the target path. This shows that the path tracking error is smaller than the conventional induction method.

Referring to Fig. 9, acceleration components for each axis are shown. It can be seen that the size of the induction command corresponding to the amount of input is not greatly different in both the induction technique and the conventional induction technique according to the present embodiment. Considering the fact that the larger the size of the input / command is, the smaller the error, the induction technique according to the present embodiment is advantageous in that the induction technique and the command size are similar to each other but a smaller path following error is exhibited.

Referring to FIG. 10, a visual trajectory for the magnitude of the error vector is shown. It can be seen that the induction method according to the present embodiment shows a smaller path following error than the conventional induction method as previously predicted from the three-dimensional trajectory. In the case of the conventional induction method, the path following error It can be seen that it does not decrease.

8 to 10, it can be seen that the induction method according to the present embodiment shows superior path following performance as compared with the conventional induction technique.

The route follow-induction technique according to the present embodiment generates an instruction to follow a designated route, so that it can be used for various tasks that must be performed while following a fixed route, such as a fixed wing or a rotary wing aircraft, Do. Accordingly, the present invention can be applied to precise automatic operation of various systems. For example, it can be used to avoid collision of an aircraft or an automobile when there is an appropriate path generation method, and to prevent an accident.

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 following claims And changes may be made without departing from the spirit and scope of the invention.

100: 3D nonlinear path following guidance system
110: Control target information acquisition unit 120: Nearest point calculation unit
130: Target path characteristic calculation unit 140: Induction command generation unit
150:

Claims (16)

A path following guidance system for guiding a mobile body to follow a target path,
A control object information obtaining unit that obtains the position and speed of the moving object to be controlled as control object information;
A nearest point calculating unit for calculating a nearest point corresponding to a position of the moving object with respect to the target path given by a mediated curve;
A target path characteristic calculation unit for calculating a differential geometry characteristic with respect to the target path;
An induction command generator for obtaining a forward look-up vector calculated as a front main time and a radial distance based on the control subject information, the nearest point information, and the differential geometric characteristics of the target path and generating an induction command given by acceleration, ; And
And a movement controller for controlling the movement of the moving object according to the induction command.
The method according to claim 1,
Wherein the target path characteristic calculation unit calculates a unit tangent vector, a unit normal vector, and a curvature of the target path at the nearest point, .
The method according to claim 1,
Wherein a value of the inductive gain and the boundary layer thickness, which are design variables, is selected prior to the generation of the induction command.
The method according to claim 1,
Wherein the induction command causes the moving body to be on the target path so that the velocity direction of the moving body coincides with the tangential direction of the target path.
The method according to claim 1,
If you want to follow a constant airspeed path,
Wherein the induction command generator generates a side induction command that is orthogonal to a relative speed vector of the moving object in which the wind speed is reflected.
A path following induction method performed in a path following guidance system for inducing a mobile body to follow a target path,
Obtaining position and speed of the moving object to be controlled as control object information;
Calculating a closest point corresponding to the position of the mobile object with respect to the target path given by the mediated curve;
Calculating a differential geometry characteristic for the target path;
Obtaining a forward look-up vector calculated as a front main time and a radial distance based on the control subject information, the nearest point information, and the differential geometric characteristics of the target path;
Generating an induction command given by an acceleration using the forward look-up vector; And
And controlling the movement of the moving object according to the induction command.
The method according to claim 6,
Wherein the target path characteristic calculation step calculates a unit tangent vector, a unit normal vector, and a curvature of the target path at the nearest point, Way.
The method according to claim 6,
Further comprising the step of selecting values of the inductive gain and the boundary layer thickness which are design variables before the generation of the inductive command.
The method according to claim 6,
Wherein the induction command causes the moving body to be on the target path so that the velocity direction of the moving body coincides with the tangential direction of the target path.
The method according to claim 6,
If you want to follow a constant airspeed path,
Wherein the induction command generation step generates a side induction command that is orthogonal to a relative speed vector of the moving object in which the wind speed is reflected.
A path following induction method performed in a path following guidance system for inducing a mobile body to follow a target path,
The target path being given as a mediated curve;
The position and velocity information of the moving object

,

,

);
The design variables k and the thickness of the boundary layer

Selecting a value of < RTI ID = 0.0 >
Calculating a nearest point P on the target path corresponding to the position of the moving object;
Error vector

;
The unit vector at the last contact

, Unit vector

, Curvature

;
Using the induction gain, the thickness of the boundary layer, and the curvature,

;
The shifted error vector

;
And a ratio of the magnitude of the shifted error vector to the thickness of the boundary layer,

;
Using the radial spacing distance and the front main clock,

;
Using the forward look-up vector,

Dimensional nonlinear path following induction method.
12. The method of claim 11,
The radial spacing is determined by the following equation:

If

Dimensional nonlinear path following induction method.
12. The method of claim 11,
The radial spacing is determined by the following equation:

If

Dimensional nonlinear path following induction method.
12. The method of claim 11,
If you want to follow a constant airspeed path,
Wind speed

Relative speed

;
Generating a lateral induction command orthogonal to the relative velocity vector using the vertical acceleration command and the relative velocity.
15. The method of claim 14,
Wherein the side guidance command is given by the following equation: < EMI ID = 1.0 >

A recording medium on which a program that can be read by a digital processing apparatus is recorded for performing the three-dimensional nonlinear path following guidance method according to any one of claims 6 to 15.

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