KR20220071988A - 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 an approximate closoid-based local route that guarantees automatic parking system stability. According to the present invention, a processor; and a memory connected to the processor, wherein the memory sets a stability parameter of the automatic parking system, sets a parking completion point on a parking space coordinate system using a parking space image captured by a camera, and sets the set stability To generate an approximate clothoid-based local path from the initial pose of the vehicle to the parking completion point using the parameters and a preset vehicle dynamics model, and to control the vehicle in the longitudinal and lateral directions according to the generated local path , an approximate clothoid-based local path generation apparatus for 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 an approximate closoid-based local route that guarantees automatic parking system stability.

Accidents occur frequently due to driver's negligence, poor visibility, or violation of the duty to keep an eye on the vehicle behind.

To prevent this, an advanced driver assistance system (ADAS) is being installed in a vehicle recently.

The intelligent driver assistance system uses state-of-the-art sensors, GPS, communication, and intelligent video equipment to recognize some situations while driving and judge the situation, control the vehicle, or use sound and light so that the driver can detect dangers in advance. It is a driver assistance system that notifies you with , vibration, etc.

Among the driver assistance systems, the Smart Parking Assistant System (SPAS) provides convenience to the driver when the vehicle is parked, and prevents an inexperienced driver from contacting an accident due to departure from a parking space in advance.

Recently, a service that supports autonomous parking using cameras and sensors installed around the vehicle has also been provided.

The conventional parking assistance system (SPAS) detects obstacles using sensors such as ultrasonic waves with limited sensing distance and direction to find a part of a parking space that can be parked. To control the vehicle's steering angle, it creates a parking path consisting of a combination of arcs and straight lines and obtains steering directly from the parking path.

Closoid curve refers to a curve having a continuous and gradually changing rate of change of curvature, and is generally applied to road construction for smooth driving of vehicles.

If the closeoid curve is applied to the creation of the parking path, smooth steering and vehicle movement can be obtained without discontinuous curvature, enabling very comfortable parking control for the driver.

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

KR Patent Publication No. 10-2018-0119225

In order to solve the problems of the prior art, the present invention is to propose a method and apparatus for generating an approximate closoid-based local path that guarantees the stability of the automatic parking system that can ensure the stability of the simple but stable closoid-based local path. do.

In order to achieve the above object, according to an embodiment of the present invention, there is provided an approximate clothoid-based local route generating apparatus for ensuring automatic parking system stability, comprising: a processor; and a memory connected to the processor, wherein the memory sets a stability parameter of the automatic parking system, sets a parking completion point on a parking space coordinate system using a parking space image captured by a camera, and sets the set stability To generate an approximate clothoid-based local path from the initial pose of the vehicle to the parking completion point using the parameters and a preset vehicle dynamics model, and to control the vehicle in the longitudinal and lateral directions according to the generated local path , an approximate clothoid-based local path generation apparatus for 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 a curvature of the approximate clothoid-based local path and a wheelbase of the vehicle.

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

[Equation]

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 and are defined by the following equation,

[Equation]

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 the following closed-loop system

[Equation]

이고, here,

ego,

)의 곱인

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

) is the product of

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 with respect to 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

to satisfy the exponential stability of Equation 3 above

exists, remind

Is

In the eigen equation and eigenvalue of , the eigenvalue may be determined differently from a case where the eigenvalue is a complex number and a case where the eigenvalue is a real number.

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 if the eigenvalues are real

It can be determined as the minimum value of

According to another aspect of the present invention, there is provided a method for generating an approximate clothoid-based local path in a device including a processor and a memory, the method 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 the 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.

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

According to the present invention, there is an advantage in that it is possible to generate an approximate clothoid-based local path that is simple and can guarantee stability through the setting of the stability parameter.

1 is a view illustrating parking coordinates {xy} of the center of a rear wheel axle of a vehicle and a nonholonomic model.
2 shows a virtual towing method 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 the present embodiment.
4 is a diagram illustrating an apparatus for generating an approximate clothoid-based local path according to the present embodiment.

Since the present invention can have various changes and can 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, it should be understood to include all modifications, equivalents and substitutes included in the spirit and scope of the present invention.

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

Route planning can be divided into global route planning and local route planning.

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

There are circle-to-circle, circle-line-circle, and closoid in route planning commonly used in automatic parking systems.

Circle-circle and circle-line-circle inevitably produce discrete portions of path curvature in local path planning, which differs from human approaches.

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

In general, considering that the automotive industry is price-sensitive, computational performance in limited low-cost 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 lateral control algorithm.

It is shown that the closed-loop system of the automatic parking system according to this 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 the given conditions.

Hereinafter, a kinematic model of a vehicle in 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} of the center of a rear wheel axle 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 the rear axle (CRA) in the 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

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

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 steering angle and wheelbase in 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 the 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 lateral motion model 3b in Equation 3 will be described below.

Here, assumption 1 is as follows.

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

to be.

The direction range according to assumption 1 is sufficient for an autonomous parking system of approximate clothoid-based local route planning.

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

In this embodiment, we generate an approximate clothoid-based local path that is efficient and has low computational complexity.

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

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

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

If Equation 4 is integrated twice, an approximate clothoid cubic polynomial curve model is obtained.

Here, c ₀ and c ₁ denote a lateral offset and a yaw angle offset in 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, so the following model is used.

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

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

In generating the local path plan, it is assumed that there are no obstacles, and it is considered to have a hierarchical structure that solves the obstacle avoidance problem at the upper control level and provides a set of motion targets at the lower control level.

Given an obstacle-free space, a local path to the parking completion point is searched for every sampling cycle.

Then, distributed control of longitudinal and lateral movements is performed.

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 vectors. vector to simplify the formula

2-norm of

is defined as, and the matrix

The derived norm of

to be defined as

Hereinafter, the longitudinal 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.

When α is the preset longitudinal speed of the vehicle, it is defined as follows.

이다. here,

to be.

Here, the following is assumed.

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 the vehicle

is the desired speed

, In other words

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

이다. here,

to be.

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

Assume that it is a transition to . Equation 8, which is a linear equation of state, is a finite positive constant

is exponentially uniformly stable only in the presence of

이다. for all k and j

to be.

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

Proposition 1: Considering the longitudinal kinematics model (a in Equation 3), the equilibrium point of Equation 8, which is a closed-loop system, for all initial x with the initial direction of the vehicle satisfying assumption 1 point) is uniformly exponentially stable.

은 가정 1에 의해

의 범위로 제한된다. proof:

is by assumption 1

limited to the scope 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

to be

Guaranteed.

Therefore, Equation 8 is exponentially uniformly stable according to the given Theorem 1.

Hereinafter, the transverse control process will be described.

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

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. Here, in Equation 4 for the desired path, the clothoid-based local path curvature

use

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

와

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

Wow

is obtained as

이다. here,

to be.

는

에 대해 역(invertible)으로 될 수 있다.

Is

can be inverted with respect to .

,

는 다음과 같이 얻어진다. from Equation 13

,

is obtained as

By substituting Equation 3b using the above equation, the following lateral 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 the state-dependent parameter as shown below.

From assumption 1, it can be easily seen that the following contents exist.

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

이다. here,

to be.

은 종방향 속도

, 종방향 위치

및

의 함수가 된다. System Matrix in Closed-Loop System

is the longitudinal speed

, longitudinal position

and

becomes a function of

가 된다. If assumption 2 is satisfied, then

becomes

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

로 표현한다. Here, for simplicity of notation,

expressed 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, every k,

and pointwise eigenvalues at all samplings.

About

a constant that satisfies

and

is assumed to exist.

경우 수학식 16이 균일하게 지수적으로 안정한 양의 상수

가 존재한다. Then for every 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 velocity is adjusted to satisfy assumption 2.

에 대해 지수적으로 안정하도록 하는

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

to be exponentially stable with respect to

exists

의 pointwize eigenvalue(점별 고유값)을 조사하여 항상

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

always by examining the pointwize eigenvalue of

It will be explained that there are conditions that guarantee

의 고유방정식을 얻을 수 있다. given as

We can get the eigen equation of

Its eigenvalues are as follows.

가 복소수(complex conjugate)인 경우, (i)

If is a complex number (complex conjugate),

인 경우, in other words,

If ,

에 대해

를 보장하는

가 존재한다. From the above equation, all

About

to ensure

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 ensure

exists

에 대해

를 보장하는 From (i) and (ii) above

About

to ensure

가 존재하는 것이 명백하다.

It is clear that there is

인 양의 상수

및

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

a positive constant

and

explains the existence of

가 주어진 경우,initial value

If is given,

인

및

를 선택한다.

sign

and

select

from Equation 17

가 다음과 같이 되는 것을 알 수 있다.

It can be seen that the following

이다. here,

to be.

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 in Equations 17 and 21 is

and

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

에서 모든

에 대해 설계된

를 갖는

가 존재한다는 것을 알 수 있다. therefore,

all from

designed for

having

It can be seen that there is

와

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

Wow

is also known to exist.

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

is exponentially stable as given in Theorem 2.

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

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

Referring to FIG. 2A , the 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 entrance to the parking lot, and the virtual towing distance decreases.

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

As shown in Fig. 2d, the vehicle arrives at a parking place. In this case, the virtual towing distance maintains the final towing boundary distance.

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

, lateral position and orientation may 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

taking into account the virtual initial towing distance

select

를 이용하여 부드러운 조향 변환을 위해

를 만족하는 초기 및 최종 토잉 경계 거리, 즉

및

를 고려한다. Also, the toe coefficient

for a smooth steering transition using

The initial and final towing boundary distances that satisfy , i.e.

and

consider

The following presents an approximate clothoid-based local path planning and distributed control algorithm using the virtual toe distance as Algorithm 1 of FIG. 3 .

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

As shown in FIG. 4 , the device according to the present 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 fixed 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.

The memory 402 stores program instructions executable by the processor 00 .

The program commands 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 by 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 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, the 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.

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

The vehicle dynamics model is defined as in 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

to satisfy exponential stability in the case of

exists, remind

Is

In the eigen equation and eigenvalue of , it is determined differently for a case in which the eigenvalue is a complex number and a case where the eigenvalue is a real number,

is determined when the eigenvalue is a complex number

and determined if the eigenvalues are real

It can be determined as the minimum value of

The above-described embodiments of the present invention have been disclosed for purposes of illustration, and various modifications, changes, and additions will be possible within the spirit and scope of the present invention by those skilled in the art having ordinary knowledge of the present invention, and such modifications, changes and additions should be regarded as belonging to the following claims.

Claims (10)

An approximate closoid-based local path generator that guarantees automatic parking system stability,
processor; and
a memory coupled to the processor;
The memory is
Set the stability parameters of the automatic parking system,
Set the parking completion point on the parking space coordinate system using the parking space image captured by the camera,
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 longitudinal and transverse directions of the vehicle according to the generated local path;
Approximate closoid-based local path generation apparatus for storing program instructions executable by the processor. According to claim 1,
The apparatus for generating an approximate clothoid-based 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. 3. The method of claim 2,
The longitudinal control parameter is an approximate clothoid-based local path generating apparatus defined using a longitudinal speed of the vehicle and a 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,
[Equation]

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, which are approximated clothoid-based local path generating apparatus defined by the following equation.
[Equation]

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 defined as the following closed-loop system
[Equation]

here,

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

) and the sampling period (T _s ) of the vehicle dynamics model.

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

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

is a state-dependent parameter with respect to the angle formed with the longitudinal direction of the vehicle. 7. The method of claim 6,
The equilibrium point of the closed loop system

to satisfy the exponential stability of Equation 3 above

exists,
remind

Is

Approximate clothoid-based local path generation apparatus in which the eigenvalue is determined differently for a case where the eigenvalue is a complex number and a case where the eigenvalue is a real number in the eigen equation and eigenvalue of . 8. The method of claim 7,
remind

is determined when the eigenvalue is a complex number

and determined if the eigenvalues are real

Approximate clothoid-based local path generator determined by the minimum value of . A method for generating an approximate clothoid-based local path in a device comprising a processor and a memory, the method comprising:
setting a stability parameter of the automatic parking system;
setting a parking completion point on a parking space coordinate system using a parking space image captured through a camera;
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; and
and controlling the vehicle in longitudinal and lateral directions according to the generated local path. A computer readable program for performing the method according to claim 9 .

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