KR102509622B1 - Approximate clothoid-based local route generation method and apparatus to ensure stability of automatic parking system - Google Patents

Abstract

The present invention discloses a method and apparatus for generating a local path based on an approximate clothoid that guarantees stability of an automatic parking system. According to the present invention, a processor; and a memory connected to the processor, wherein the memory sets a stability parameter of an automatic parking system, sets a parking completion point on a parking space coordinate system using a parking space image captured through a camera, and sets the set stability Generate an approximate clothoid-based local path from the initial pose of the vehicle to the parking completion point using parameters and a preset vehicle dynamics model, and control the vehicle in the longitudinal and lateral directions according to the generated local path , An approximate clausoid-based local path generating device storing program instructions executable by the processor is provided.

Description

Approximate clothoid-based local route generation method and apparatus to ensure stability of automatic parking system

The present invention relates to a method and apparatus for generating a local path based on an approximate clothoid that guarantees stability of an automatic parking system.

Traffic accidents frequently occur due to the driver's negligence, poor visibility, or violation of the obligation to look forward by a vehicle behind the vehicle while driving.

To prevent this, advanced driver assistance systems (ADAS) are being installed in recent vehicles.

The intelligent driver assistance system uses state-of-the-art detection sensors, GPS, communication, and intelligent video equipment to recognize some situations while driving, determine the situation, control the vehicle, or enable the driver to detect risk factors in advance by using sound and light. It is a driver assistance system that informs by vibration, etc.

Among driver assistance systems, a parking assistance system (SPAS, Smart Parking Assistant System) provides convenience to a driver when parking a vehicle and prevents a driver who is inexperienced in parking from a contact accident caused by leaving a parking space.

Recently, a service for supporting autonomous parking using cameras and sensors installed around the vehicle is being provided.

Conventional parking assist systems (SPAS) detect obstacles using sensors such as ultrasonic waves, which have limited sensing distance and direction, find a part of a parking space, and when a driver wants to park in a parking space, the vehicle enters the parking space. A parking path consisting of a combination of circular arcs and straight lines is created and the steering angle is directly obtained from the parking path to control the steering angle of the vehicle.

The closoid curve means a curve having a curvature change rate that continuously and gradually changes, and is generally applied to road construction for smooth driving of vehicles.

Applying the closoid curve to the parking path generation enables smooth steering and vehicle movement without discontinuous curvature, enabling very comfortable parking control for the driver.

However, the path according to the Closoid curve has a problem in that a lot of computational overhead occurs.

KR Patent Publication No. 10-2018-0119225

In order to solve the above problems of the prior art, the present invention proposes a method and apparatus for generating an approximate clothoid-based local path that guarantees the stability of an automatic parking system that can guarantee the stability of a clothoid-based local path although it is simple. do.

In order to achieve the above object, according to an embodiment of the present invention, an approximate clothoid-based local path generating device for ensuring stability of an automatic parking system, comprising: a processor; and a memory connected to the processor, wherein the memory sets a stability parameter of an automatic parking system, sets a parking completion point on a parking space coordinate system using a parking space image captured through a camera, and sets the set stability Generate an approximate clothoid-based local path from the initial pose of the vehicle to the parking completion point using parameters and a preset vehicle dynamics model, and control the vehicle in the longitudinal and lateral directions according to the generated local path , An approximate clausoid-based local path generating device storing program instructions executable by the processor is provided.

The stability parameter may be defined using a longitudinal control parameter of the vehicle and a sampling period of the vehicle dynamics model.

The longitudinal control parameter may be defined using the longitudinal speed of the vehicle and the longitudinal movement distance of the vehicle at a specific sampling time.

A steering angle for lateral control of the vehicle may be defined using the curvature of the approximate clothoid-based local path and the wheelbase of the vehicle.

The approximate clothoid-based local path is defined by the following equation,

[mathematical expression]

Here, x is the longitudinal coordinate of the vehicle in the parking space coordinate system, and c ₂ and c ₃ are time-varying coefficients defined by the following equation,

[mathematical expression]

는 상기 차량이 종방향과 이루는 각도이다. Here, k is the sampling time, y is the lateral coordinate of the vehicle in the parking space coordinate system,

Is the angle the vehicle makes with the longitudinal direction.

The vehicle dynamics model is defined as a closed-loop system below

[mathematical expression]

이고, here,

ego,

)의 곱인

정의됨에 따라 The stability parameter (p) is the sampling period (T _s ) and the longitudinal control parameter (

)

as defined

이며,

is,

는 상기 차량의 종방향과 이루는 각도에 대한 상태 의존 파라미터이다. V _x is the longitudinal speed of the vehicle,

Is a state-dependent parameter for an angle formed with the longitudinal direction of the vehicle.

인 경우 상기 수학식 3의 지수적인 안정성을 만족하도록 하는

가 존재하며, 상기

는

의 고유방정식 및 고유값에서, 상기 고유값이 복소수인 경우와 실수인 경우에 대해 다르게 결정될 수 있다. The equilibrium point of the closed loop system is

In the case of Equation 3 to satisfy the exponential stability

exists, remind

Is

In the eigenequation and eigenvalue of , the case where the eigenvalue is a complex number and the case where it is a real number may be determined differently.

는 상기 고유값이 복소수인 경우에 결정되는

와 상기 고유값이 실수인 경우에 결정되는

의 최소값으로 결정될 수 있다. remind

Is determined when the eigenvalue is a complex number

And determined when the eigenvalue is a real number

can be determined as the minimum value of

According to another aspect of the present invention, a method for generating an approximate clothoid-based local path in a device including a processor and a memory, comprising: setting a stability parameter of an automatic parking system; setting a parking completion point on a parking space coordinate system using a parking space image captured by a camera; generating an approximate clothoid-based local path from an initial pose of the vehicle to the parking completion point using the set stability parameter and a preset vehicle dynamics model; and controlling the longitudinal and lateral directions of the vehicle according to the generated local path.

According to another aspect of the present invention, a computer readable program for performing the method described above is provided.

According to the present invention, there is an advantage in that an approximate clothoid-based local path that can guarantee stability while being simple through setting stability parameters can be created.

1 is a diagram illustrating parking coordinates {xy} centered on a rear wheel axis of a vehicle and a nonholonomic model.
Figure 2 illustrates a method of virtual towing in reverse parking using approximate clothoid-based local path planning.
3 presents an approximate clothoid-based local path planning and distributed control algorithm according to this embodiment.
4 is a diagram illustrating an approximate clothoid-based local path generating apparatus according to the present embodiment.

Since the present invention can make various changes and have various embodiments, specific embodiments are illustrated in the drawings and described in detail.

However, this is not intended to limit the present invention to specific embodiments, and should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention.

Path planning, which finds a trajectory from a starting point to a target point while avoiding obstacles, is a key element of an automated parking system.

Path planning can be divided into global path planning and local path planning.

Global path planning uses probabilistic roadmaps, etc., and local path planning algorithms are assigned tasks such as path tracking or trajectory tracking to the feedback controller.

Path plans commonly used in automatic parking systems include circle-to-circle, circle-line-circle, and clothoid.

Circle-circle and circle-line-circle inevitably create a discontinuous portion of path curvature in local path planning, which differs from the human approach.

Accordingly, a clothoid-based path planning algorithm has recently been attracting attention. However, the closoid-based path planning algorithm requires a large amount of computation due to Fresnel integral calculation.

Considering that the automotive industry is generally price-sensitive, the computational performance of limited low-end ECUs must be considered.

Recently, various methods to reduce the computation time have been studied, but iterative local path planning in commercial ECUs is not suitable.

Accordingly, the present invention proposes an approximate clothoid-based local path planning to solve the problem of discontinuity and high computational load, and proposes a simple and effective distributed longitudinal and transverse control algorithm.

It is shown that the closed-loop system of the automatic parking system according to the present embodiment is expressed as a discrete linear time-varying system.

In addition, the stability of the system according to the present embodiment is verified using the Lyapunov stability theorem when the initial pose and longitudinal velocity control satisfy given conditions.

Hereinafter, a vehicle kinematic model at parking coordinates and an approximate clothoid-based local path model for an automatic parking system will be described.

1 is a diagram illustrating parking coordinates {xy} centered on a rear wheel axis of a vehicle and a nonholonomic model.

를 주차 좌표에서 후륜축 중심(Center of Rear Axle, CRA)의 차량 위치 벡터로 정의한다.

is defined as the vehicle position vector of the Center of Rear Axle (CRA) in parking coordinates.

는 CRA에서 차량의 방향(orientation)

(차량의 종방향과 이루는 각도)를 가지고 다음과 같이 정의된다. vehicle pose

is the orientation of the vehicle in the CRA

It is defined as follows with (the angle formed with the longitudinal direction of the vehicle).

In this embodiment, each variable of Equation 1 is expressed as follows in consideration of Ackerman turning geometry and the existing vehicle kinematics model.

,

및

은 각각 CRA에서 종방향 속도, 전륜 조향각 및 휠베이스이다. here,

,

and

are the longitudinal speed, front wheel steering angle and wheelbase at CRA, respectively.

The vehicle kinematics model is effective for motion control in limited low-speed driving conditions such as parking assistance systems.

In this embodiment, a discrete-time system using a first-order Euler method with a sampling period of T _s is used as follows.

Distributed control for the longitudinal motion model 3a and the transverse motion model 3b of Equation 3 will be described below.

Here, assumption 1 is as follows.

이다. Assumption 1: The range of direction of the vehicle for parking is

am.

The directional range according to Assumption 1 is sufficient for an automatic parking system based on approximate clothoid-based local path planning.

Hereinafter, the approximate clothoid-based local path model will be described in detail.

In this embodiment, an approximate clothoid based local path is generated which is efficient and has low computational complexity.

Given the arc length s of a road, it is assumed that the road is designed with the following curvature.

Here, c ₂ and c ₃ denote the road curvature and its change rate at s=0, respectively.

For small curvatures, the arc length s can be approximated by the longitudinal distance x.

Integrating Equation 4 twice gives an approximate clothoid 3rd order polynomial curve model.

Here, c ₀ and c ₁ represent the lateral offset and yaw angle offset in the parking coordinates.

The goal of parking is to move the vehicle to the parking coordinate system origin (parking completion point) so that c ₀ and c ₁ are set to 0. Therefore, the following model is used.

In local path planning, a road model such as Equation 5 is widely applied to vehicles traveling on highways, but to apply this road model to an automatic parking system, approximate clothoid-based local path planning is proposed.

Hereinafter, vehicle operation control in automatic parking will be described in detail.

Consider having a hierarchical structure that assumes no obstacles in creating local path plans, solves obstacle avoidance problems at higher control levels, and provides a set of motion targets at lower control levels.

Given a space without obstacles, a local path to the parking completion point is searched every sampling period.

It then performs distributed control of longitudinal and transverse movements.

는 벡터들의 유클리디언 norm을 나타낸다. 수식을 간단하게 하기 위해 벡터

의 2-norm을

로 정의하고, 행렬

의 유도된 norm을

으로 정의한다. Below,

denotes the Euclidean norm of the vectors. vector to simplify the formula

2-norm of

is defined as, and the matrix

the derived norm of

Defined by

Hereinafter, the vertical direction control process will be described in detail.

The purpose of longitudinal control is to move the vehicle from the parking coordinates to the parking completion point (0,0) of the parking coordinate system.

를 미리 설정된 차량의 종방향 속도로 할 때, 다음과 같이 정의한다.

Assuming that is the preset longitudinal speed of the vehicle, it is defined as follows.

이다. here,

am.

Here, we assume the following.

는 원하는 속도

, 즉

를 완벽하게 추적한다. 주차 중에는 차량 속도가 낮고 동력 전달 장치의 동역학은 주차 시스템보다 상대적으로 빠르다. 따라서 폐루프 시스템은 다음과 같은 형식으로 정의된다. Assumption 2: Longitudinal speed of vehicle

is the desired speed

, in other words

tracks perfectly. During parking, the vehicle speed is low and the dynamics of the power train are relatively faster than the parking system. Therefore, the closed-loop system is defined in the form

이다. here,

am.

를 고정된

에서

에 대한 천이(transition)이라 가정한다. 선형 상태 방정식인 수학식 8은 다음과 같은 유한 양의 상수

가 존재하는 경우에만 지수적으로 균일하게 안정하다. Theorem 1:

fixed

at

It is assumed to be a transition for Equation 8, a linear equation of state, is a finite positive constant

is exponentially uniformly stable only if

이다. for all k, j

am.

Using the result given in Theorem 1, we can show the stability of a time-varying system.

Proposal 1: Considering the longitudinal kinematics model (a in Equation 3), the equilibrium point point) is uniformly exponentially stable.

은 가정 1에 의해

의 범위로 제한된다. proof:

by assumption 1

limited to the range of

는 모든 설계된

와 함께 상수

에 의해

로 제한된다.

is all designed

constant with

by

is limited to

및 모든 시간 단계

에서

이 되도록

보장된다. initial time

and all time steps

at

so that

guaranteed

Equation 8 is therefore exponentially uniformly stable by the given Theorem 1.

Hereinafter, the lateral direction control process will be described.

It is known that in a steady state assuming a constant speed, a vehicle makes a circular motion (radius R).

where R is the radius of the desired circle tangent to the longitudinal axis of the vehicle in the CRA of FIG. 1 .

Assuming that there is no model uncertainty, the desired steering angle from Equation 10 is expressed as follows.

를 사용한다. Closoid-based local path curvature in Equation 4 for the path desired here

Use

Next, from the derivative of Equation 6, it is approximated as follows.

와

는 다음과 같이 얻어진다. Time-varying coefficient from Equation 12

and

is obtained as follows.

이다. here,

am.

는

에 대해 역(invertible)으로 될 수 있다.

Is

can be invertible for

,

는 다음과 같이 얻어진다. from Equation 13

,

is obtained as follows.

By substituting the above equation into Equation 3b, the following transverse dynamics model can be obtained.

의 함수를 아래와 같이 상태 의존 파라미터를 통해 정의한다. In order to analyze the closed-loop system of Equation 15, which is a linear time-varying system,

The function of is defined through state-dependent parameters as follows.

From Assumption 1, it is easy to see that the following exists.

The closed loop system of Equation 15 is expressed in the following form.

이다. here,

am.

은 종방향 속도

, 종방향 위치

및

의 함수가 된다. System matrix of closed-loop system

is the longitudinal speed

, longitudinal position

and

becomes a function of

가 된다. If assumption 2 is satisfied,

becomes

Then, substituting Equation 7 into Equation 16, the following can be obtained.

로 표현한다. Here, for the sake of simplicity of notation

express it as

및 모든 모든 샘플링에서의 고유치(pointwise eigenvalue)

에 대해

를 만족하는 상수

및

가 존재한다고 가정한다. Theorem 2: In Equation 16, which is a linear equation of state, all k,

and all pointwise eigenvalues at all samplings.

About

A constant that satisfies

and

Assume that exists.

경우 수학식 16이 균일하게 지수적으로 안정한 양의 상수

가 존재한다. Then for all k

If Equation 16 is a uniformly exponentially stable positive constant

exists.

로 주어진 경우,

If given as

로 정의한다.

is defined as

Then, using the result given in Theorem 2, it can be confirmed that the closed-loop system of Equation 17 is exponentially stable.

가 가정 1을 만족하는 것으로 가정한다. Proposition 2: Initial State

It is assumed that Assumption 1 is satisfied.

Also, the longitudinal speed is adjusted to satisfy assumption 2.

에 대해 지수적으로 안정하도록 하는

가 존재한다. Then the equilibrium point of the closed-loop system Equation 17 is

to be exponentially stable for

exists.

의 pointwize eigenvalue(점별 고유값)을 조사하여 항상

를 보장하는 조건이 있음을 설명할 것이다. Proof: In the following, for each k

always by examining the pointwize eigenvalues of

It will be explained that there are conditions that guarantee

의 고유방정식을 얻을 수 있다. given as

can obtain the eigen equation of

Its eigenvalue is:

가 복소수(complex conjugate)인 경우, (i)

If is a complex conjugate,

인 경우, in other words,

If

에 대해

를 보장하는

가 존재한다. From the above equation, all

About

to guarantee

exists.

가 실수인 경우, (ii)

is a real number,

인 경우, in other words,

If

로부터

에 대해

를 보장하는

가 존재한다.

from

About

to guarantee

exists.

에 대해

를 보장하는 From (i) and (ii) above

About

to guarantee

가 존재하는 것이 명백하다.

It is clear that there exists

인 양의 상수

및

가 존재하는 것을 설명한다. In the following, for all k

positive constant

and

explains the existence of

가 주어진 경우,initial value

is given,

인

및

를 선택한다.

person

and

Choose

from Equation 17

가 다음과 같이 되는 것을 알 수 있다.

It can be seen that the following

이다. here,

am.

및

는

및

에 의해 경계가 지정된다. here,

and

Is

and

bounded by

및

는 가정 1에 의해 경계가 지정된다.

and

is bounded by Assumption 1.

및

으로 경계가 지정되고, 아래의 수학식들이 항상 존재한다는 것이 분명해진다. Therefore, each norm of Equations 17 and 21 is

and

, and it becomes clear that the equations below always exist.

에서 모든

에 대해 설계된

를 갖는

가 존재한다는 것을 알 수 있다. thus,

all from

designed for

having

can be known to exist.

와

가 존재하는 것도 알 수 있다. Also in Equations 22 and 23

and

It can also be seen that there exists

는 정리 2에 주어진 것처럼 지수적으로 안정적이다. Therefore, the equilibrium point of the closed-loop system Equation 17

is exponentially stable, as given by Theorem 2.

Hereinafter, a virtual towing method for solving the problem that a small x causes a singularity will be described.

Figure 2 illustrates a method of virtual towing in reverse parking using approximate clothoid-based local path planning.

Referring to FIG. 2A , a vehicle is placed in an initial vehicle pose. The virtual towing distance is the longitudinal distance from the vehicle to the initial virtual towing point.

As shown in FIG. 2B, the vehicle enters near the parking lot entrance and the virtual towing distance decreases.

As shown in FIG. 2C, the vehicle moves to the parking space while maintaining a virtual towing distance.

As shown in Fig. 2d, it arrives at the parking place of the vehicle. At this time, the virtual towing distance maintains the final towing boundary distance.

, 횡방향 위치 및 방향은 가상 토잉 거리를 이용하여 주차 지점으로 수렴할 수 있다. Thus, state

, the lateral position and orientation can converge to the parking point using the virtual towing distance.

를 고려하고, 가상 초기 토잉 거리

를 선택한다. Virtual towing distance from vehicle to virtual towing point

Considering , the virtual initial towing distance

Choose

를 이용하여 부드러운 조향 변환을 위해

를 만족하는 초기 및 최종 토잉 경계 거리, 즉

및

를 고려한다. Also, towing coefficient

For a smooth steering transition using

The initial and final towing boundary distances satisfying , i.e.

and

Consider

Next, an approximate clothoid-based local path planning and distributed control algorithm using the virtual towing distance as Algorithm 1 of FIG. 3 is presented.

4 is a diagram illustrating an approximate clothoid-based local path generating apparatus according to the present embodiment.

As shown in FIG. 4 , the device according to this embodiment may include a processor 400 and a memory 402 .

The processor 400 may include a central processing unit (CPU) capable of executing a computer program or other virtual machines.

Memory 402 may include a non-volatile storage device such as a non-removable hard drive or a removable storage device. The removable storage device may include a compact flash unit, a USB memory stick, and the like. Memory 402 may also include volatile memory, such as various random access memories.

Program instructions executable by the processor 400 are stored in such a memory 402 .
Program instructions according to this embodiment are stored in a computer readable recording medium.

Program instructions according to an embodiment of the present invention set the stability parameter of the automatic parking system, set the parking completion point on the parking space coordinate system using the parking space image captured through the camera, and set the stability parameter and preset An approximate clothoid-based local path from the initial pose of the vehicle to the parking completion point is generated using the set vehicle dynamics model, and the vehicle is controlled in the longitudinal and lateral directions according to the generated local path.

) 및 상기 차량 동역학 모델의 샘플링 주기(T_s)의 곱인

정의될 수 있다. The stability parameter p is a longitudinal control parameter of the vehicle (

) And the product of the sampling period (T _s ) of the vehicle dynamics model

can be defined

In addition, the longitudinal control parameter may be defined using the longitudinal speed of the vehicle and the longitudinal movement distance of the vehicle at a specific sampling time.

In addition, a steering angle for lateral direction control of the vehicle may be defined using the curvature of the approximate clothoid-based local path and the wheelbase of the vehicle.

Here, the approximate clothoid-based local path is defined as in Equation 6 above, and c ₂ and c ₃ are time-varying coefficients defined as in Equation 14.

The vehicle dynamics model is defined as Equation 16.

인 경우 지수적인 안정성을 만족하도록 하는

가 존재하며, 상기

는

의 고유방정식 및 고유값에서, 상기 고유값이 복소수인 경우와 실수인 경우에 대해 다르게 결정되고, 상기

는 상기 고유값이 복소수인 경우에 결정되는

와 상기 고유값이 실수인 경우에 결정되는

의 최소값으로 결정될 수 있다. The equilibrium point of Equation 16

, which satisfies exponential stability

exists, remind

Is

In the eigenequation and eigenvalue of, the eigenvalue is determined differently for the case of a complex number and the case of a real number,

Is determined when the eigenvalue is a complex number

And determined when the eigenvalue is a real number

can be determined as the minimum value of

The embodiments of the present invention described above have been disclosed for illustrative purposes, and those skilled in the art having ordinary knowledge of the present invention will be able to make various modifications, changes, and additions within the spirit and scope of the present invention, and such modifications, changes, and additions will be considered to fall within the scope of the following claims.

Claims (10)

As an approximate clothoid-based local path generation device that guarantees the stability of an automatic parking system,
processor; and
Including a memory coupled to the processor,
the memory,
Set the stability parameters of the automatic parking system,
Using the parking space image captured by the camera, a parking completion point is set on the parking space coordinate system,
generating an approximate clothoid-based local path from the initial pose of the vehicle to the parking completion point using the set stability parameter and a preset vehicle dynamics model;
To control the longitudinal and transverse directions of the vehicle according to the generated local path,
storing program instructions executable by the processor;
Wherein the stability parameter is defined using a longitudinal control parameter of the vehicle and a sampling period of the vehicle dynamics model. delete According to claim 1,
The longitudinal control parameter is defined using the longitudinal speed of the vehicle and the longitudinal movement distance of the vehicle at a specific sampling time. According to claim 1,
A steering angle for lateral control of the vehicle is defined using a curvature of the approximate clothoid-based local path and a wheelbase of the vehicle. According to claim 1,
The approximate clothoid-based local path is defined by the following equation,
[mathematical expression]

Here, x is the longitudinal coordinate of the vehicle in the parking space coordinate system, and c ₂ and c ₃ are time-varying coefficients defined by the following equation.
[mathematical expression]

Here, k is the sampling time, y is the lateral coordinate of the vehicle in the parking space coordinate system,

Is the angle the vehicle makes with the longitudinal direction According to claim 1,
The vehicle dynamics model is an approximate clothoid-based local path generation device defined as the following closed-loop system.
[mathematical expression]

here,

ego,
The stability parameter p is a longitudinal control parameter of the vehicle (

) And the product of the sampling period (T _s ) of the vehicle dynamics model

as defined
Sampling period of the longitudinal control parameter of the vehicle and the vehicle dynamics model

is,
V _x is the longitudinal speed of the vehicle,

Is a state-dependent parameter for an angle formed with the longitudinal direction of the vehicle According to claim 6,
The equilibrium point of the closed loop system is

In the case of Equation 3 to satisfy the exponential stability

exists,
remind

Is

In the eigenequation and eigenvalue of, the eigenvalue is determined differently for the case where the eigenvalue is a complex number and the case where it is a real number. According to claim 7,
remind

Is determined when the eigenvalue is a complex number

And determined when the eigenvalue is a real number

An approximate clothoid-based local path generator determined by the minimum value of As an approximate clothoid-based local path generation method in a device including a processor and a memory,
Setting stability parameters of the automatic parking system;
setting a parking completion point on a parking space coordinate system using a parking space image captured by a camera;
generating an approximate clothoid-based local path from an initial pose of the vehicle to the parking completion point using the set stability parameter and a preset vehicle dynamics model; and
Controlling the vehicle in longitudinal and lateral directions according to the generated local path,
Wherein the stability parameter is defined using a longitudinal control parameter of the vehicle and a sampling period of the vehicle dynamics model. A program stored in a computer readable recording medium for performing the method according to claim 9.

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