Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
10.1109/ACCESS.2017.DOI

This research was conducted by the DGIST institution-specific project
supported by the Ministry of Science and ICT (21-BRP-09 & 21-BRP-08).

Corresponding authors: Yongseob Lim<EMAIL_ADDRESS>and Gyeungho Choi
<EMAIL_ADDRESS>
# Hybrid tracker based optimal path tracking system for complex road
environments for autonomous driving

EUNBIN SEO1, SEUNGGI LEE1, GWANJUN SHIN1, HOYEONG YEO1  YONGSEOB LIM2, AND
GYEUNGHO CHOI3  Daegu Gyeongbuk Institute of Science and Technology, Daegu
42988, South Korea (e-mail: {seb5428, seunggi_lee, shinkansan,
<EMAIL_ADDRESS> Department of Robotics Engineering, Daegu Gyeongbuk
Institute of Science and Technology, Daegu 42988, South Korea  Department of
Interdisciplinary Engineering, Daegu Gyeognbuk Institute of Science and
Technology, Daegu 42988, South Korea

###### Abstract

Path tracking system plays a key technology in autonomous driving. The system
should be driven accurately along the lane and be careful not to cause any
inconvenience to passengers. To address such tasks, this paper proposes hybrid
tracker based optimal path tracking system. By applying a deep learning based
lane detection algorithm and a designated fast lane fitting algorithm, this
paper developed a lane processing algorithm that shows a match rate with
actual lanes with minimal computational cost. In addition, three modified path
tracking algorithms were designed using the GPS based path or the vision based
path. In the driving system, a match rate for the correct ideal path does not
necessarily represent driving stability. This paper proposes hybrid tracker
based optimal path tracking system by applying the concept of an observer that
selects the optimal tracker appropriately in complex road environments. The
driving stability has been studied in complex road environments such as
straight road with multiple 3-way junctions, roundabouts, intersections, and
tunnels. Consequently, the proposed system experimentally showed the high
performance with consistent driving comfort by maintaining the vehicle within
the lanes accurately even in the presence of high complexity of road
conditions. Code will be available in https://github.com/DGIST-ARTIV.

###### Index Terms:

Intelligent vehicles, Vehicle driving, Autonomous vehicles, Path tracking,
Lane detection, Driving stability.

=-15pt

##  I Introduction

In recent years, the requirements for the driving system of the autonomous
vehicle are increasing in difficulty with respect to levels of driving
automation proposed by SAE [1]. In level 4-5 of vehicle autonomy, the vehicle
should perform the main driving and request humans to transfer control only in
special circumstances or in areas where autonomous driving is not possible.
For this reason, combining the two fields of perception and control algorithm
is emerging as a very important area in autonomous driving. Hence, end-to-end
deep learning tracking algorithms [2, 3, 4] or methods using reinforcement
learning [5] have been studied, but these methods are difficult to response
flexible changes in the surrounding environment.

The deep learning based lane detection and the GPS based driving path tracking
were also applied to deal with complex road environments. The control method
used geometric model-based path tracker, Pure pursuit and Stanley controller,
which are widely used in the control field.This research proposes a path
tracking system that is able to pass through not only highways and motorway
roads, but also urban and complex road environments. In high-speed and low-
speed, tunnel, and steep curve, the system quickly changed the appropriate
tracking method and reflected it in driving stability for different speeds. In
lane detection, the algorithm designed to process the deep learning method has
been applied the three lane fitting methods in parallel to provide the most
optimized path.

In the paper, the modified path tracking algorithm is designed to
simultaneously process vision data to GPS data, in other words, local and
global coordinates. Vision and GPS based driving guidance lines cause
uncomfortable driving textures when driving along the lines. Accurately
following the lane is also an act that does not take into account driving
stability or driver acceptance. To solve this problem, this paper suggested an
optimal path tracking algorithm to ensure high driving stability and
comfortableness in the presence of high complexity of road conditions.

This optimal path tracking algorithm appropriately selects the most stable
tracker out of modified trackers, which is called Hybrid tracker based optimal
path tracking system in this paper. This system receives sensor information at
the same time as each tracker calculation, estimates the driving environment,
and transfers the control authority to the most suitable tracker. With
parallel system to minimize the stability degradation. This method guarantees
consistent driving stability even in the presence of various driving
environments with different characteristics. Furthermore, it has the advantage
that additional correction of the computational speed is not required on the
hybrid system even if each tracker is modified. Consequently, this paper notes
that there are several advantages of using the Hybrid tracker based optimal
tracking system: (a) it is capable of driving in a complex road environment
with high performance of driving stability and accuracy; (b) additional
correction of the computational speed is not required even if each tracker is
modified; (c) the proposed algorithm enhances high usage of vision based lane
following which can be widely used in real-world environments; (d) Finally,
our selection system induces the improvements of driving stability and
tracking performance despite of its simple implementation. To demonstrate the
generality of proposed system, we installed the system in an autonomous
vehicle and were confirmed its performance at the DGIST campus and high-speed
driving proving ground. Consequently, the experimental results represents that
our proposed system significantly improves accuracy and stability on all seven
cases at a low computational cost.

This paper is structured as follows: Section II describes related works.
Section III-B shows lane processing algorithm using result from deep learning.
Section III-C introduces the modified path trackers and respective features.
Section III-D describes the coordinate system transformation and interpolation
for the path from the perception part. Section III-E demonstrates path tracker
selection. Section IV shows experimental results and discussions of path
trackers and proposed system. Finally, Section V provides the conclusion.

##  II Related Works

###  II-A Path Tracking Algorithm

Generating a path that the vehicle should take to its destination and
following the generated path are the most essential parts of an autonomous
vehicle. There are three types of path tracking algorithms, which are divided
into geometric model-based, kinematic model-based, and dynamic model-based
algorithm [6]. Among these three path tracking algorithms, the simplest
algorithm type is the geometric model-based path tracking algorithm such as
Pure pursuit, Stanley controller, and Vector pursuit.

The algorithms used in this paper are Pure pursuit and Stanley controller.
Pure pursuit and Stanley controller use the same 2-dimension bicycle model
regardless of vehicle type, so that the calculation is simple and easy to
apply compared to other path tracking algorithms [7]. Unfortunately, it was
reported that these two algorithms work well only on low-speed and general
roads [8]. Conversely, when the curvature of the road turns to large or the
speed of the vehicle becomes high, it is unable to follow the generated path.
Therefore if both kinematic model and dynamic model are used, tracking
performance can be improved in more diverse environments. However, the above
simple algorithms (i.e., Pure pursuit and Stanley controller) were
appropriately modified in order to achieve maximum efficiency with limited
computer performance.

Pure pursuit’s tracking performance depends on the look-ahead distance, which
leads importantly to set an appropriate look-ahead distance. Otherwise, unlike
other path tracking algorithms, Stanley controller does not use a look-ahead
distance, so parameters have not to be tuned [9]. Comparing multiple path
tracking algorithms [6], Pure pursuit shows robustness to low-speeds and large
errors, but it does not work well at high-speeds [10, 11]. However, Stanley
controller has a faster rate of convergence to the ideal path than the Pure
pursuit, but there are cases where the steering angle sometimes diverges on a
road with a large curvature. Thus, this study focuses on modifying the
existing algorithms to minimize the disadvantages mentioned above and to
validate the modified tracking algorithm in various situations.

###  II-B Lane Detection Networks

Studies about end-to-end network performance for lane detection are as
follows. PointLaneNet [12] redefined the lane structure and lane distance to
facilitate the training of the network. PINet [13] combined point estimation
and point instance segmentation, but there were limitations in the presence of
the local occlusions or unclear lanes. The lightweight model ENet-SAD[14] has
been proposed by applying self attention distillation (SAD) methods to the
existing ENet[15]. SCNN [16] and ENet-SAD obtain diverse and rich contextual
information to solve these limitations. In the autonomous driving system,
various methods are attempted to reduce the delay from sensor recognition to
vehicle maneuvering as much as possible. Recently, deep learning is
essentially considered in the perception field, but it has also disadvantages
that it is not able to secure both processing speed (i.e., inference time) and
performance (i.e., accuracy) due to the limitation of GPU hardware. However,
processing performance varies depending on the size of the network parameter
or the computational complexity of the layer. The recent deep learning
methodologies have proposed various methods to solve these obstacles. ENet-SAD
improved the processing speed by applying self-attention approach. Its
processing speed secured 10 times faster comparing with SCNN. In addition, a
method of actively using conventional computer graphics technology has been
proposed to improve the performance of deep learning algorithms. Thus, this
paper proposed fast and accurate lane processing algorithm using the results
of ENet-SAD. As a result, low-latency and highly reliable lane detection
system has been designed and validated in the presence of diverse road
conditions.

###  II-C Ensemble method

Recognizing lanes in raw images and extracting information about lanes in
segmentation images are necessary processes. In machine learning, ensemble
method combines predictions from multiple models rather than a single model,
so that the final result achieves better performance. There are various
methods such as voting and bootstrap aggregating (Bagging) in the ensemble
method. The voting method compares the results predicted by various algorithms
for the same dataset and chooses the final result. There are also two types of
voting: hard and soft voting. Hard voting simply chooses the results that
received the most votes among the predictions from different models. Soft
voting selects the highest result by summing the probability of the predicted
results from different models. Moreover, Bagging is a method of voting to
determine the final results predicted by one algorithm on various datasets
sampled differently by allowing overlap. In Teow’s handwriting recognition
research, the best results came out by adopting soft voting [17]. Soft voting
increased the accuracy and stability of aggregation as a result of prediction
in signal segments [18]. Thus, this paper adopted soft voting that can be
parallel processing guaranteed fast computational speed in lane fitting
algorithm.

##  III Approach

###  III-A Sensor layout

The locations of each sensor are shown in Fig.1. Three sensors were used:
camera, GPS, and IMU. Logitech’s Brio 4K Pro Webcam for camera, Synerex’s RTK
GNSS MRP-2000 for GPS, and WitMotion’s HWT901B for the IMU were utilized. The
camera, GPS and IMU were installed at a distance of 155cm, 93cm, 80cm from the
ground and 213cm, 82.5cm, 378cm from the front part, respectively shown in
Fig. 1. The entire autonomous driving system of the test vehicle is equipped
with one main computing unit and one discrete deep learning inference unit.
Vehicle control and decision were operated by the embedded computer of
Nuvo-8108GC, and a computer based on Titan Xp GPU for deep learning based lane
detection algorithm was used. Detailed specifications for each sensor are
listed in TABLE I.

Figure 1: Sensor installation on the test vehicle. TABLE I: Specifications of sensors. Sensor | Specification
---|---
| Camera
---
(Logitech Brio 4K Pro Webcam)
FoV 90 degree, up to 60 frame
| Real Time Kinematic GPS
---
(Synerex MRP-2000)
| RTK Accuracy : 0.010m +1ppm CEP
---
Fix time: 10 $\sim$ 60 sec
| IMU
---
(WitMotion HWT901B)
| Angle Accuracy (after calibrated):
---
X, Y-axis: 0.05°(Static),
X, Y-axis: 0.1°(Dynamic)
| Computer
---
(Nuvo-8108GC)
| CPU: Intel Xeon E 2176G,
---
GPU: NVIDIA RTX 2080 Ti,
32GB RAM
| Computer
---
(Deep learning Inference)
| CPU: Intel I7-9700F,
---
GPU: NVIDIA TitanXp,
32GB RAM
|

###  III-B Fast Optimal Lane Processing Algorithm

####  III-B1 Data Preparation

A numerous and high-quality dataset is required for deep learning network to
avoid overfitting. First of all, ENet-SAD with the published lane dataset
CULane [16] and TuSimple [19] have been trained in this research. ENet-SAD
inferred the better results when trained on CULane containing urban, rural and
highway road types. CULane contains a total of 133,235 images, including
training set of 88,880, validation set of 9,675 and test set of 2,782. This
study developed an annotation tool that had the same file structure as CULane,
and gathered approximately 45,000 images for road types in Korea.

The lane has linearity and the constant width of the lane. Since ENet-SAD
learned the characteristics of the lane, the lane can be recognized even if
there are objects or shadow covering the lane. The augmented data are also
able to be obtained in a range that keeps the properties of lane. A total of
11 types of augmentation were applied without spatial information damage,
including weather changes, brightness changes, shadow occlusion and resolution
changes. As a result, total dataset consisted of 600,000 images with CULane
and the Korean urban dataset. More dataset was obtained through augmentation,
leading to the improved lane detection performance.

####  III-B2 Post-process for Segmentation Image

The post-processing for lane segmentation images inferred from the ENet-SAD.
The post-processing consists of inverse perspective mapping(IPM) and erosion
filter. Due to the characteristic of camera, parallel lanes meet at the
vanishing point and straight lines with the same thickness tend to become
thinner as approaching the vanishing point. Images taken by camera have the
distortion from the real circumstances described above and this distortion
narrows the range of steering, which is able to impair steering sensitivity.
To solve this phenomenon, IPM was used and it was possible to preserve the
thickness and parallelism of straight lanes by converting to top view images.
During converting the curve lanes, there is an area with thicker lanes which
adversely affects the computational speed of the lane fitting process. The
segmentation image with thin lanes could be obtained using the erosion filter.
Therefore, this process leads to faster computational speed in lane fitting
because it reduces the number of pixels that need to be processed. Lane
fitting will be detailed in section III-B3. The Fig. 2 shows enlarged images
of raw output from the ENet-SAD multiplied by a constant. The lanes are
separated by different colors. Comparing the leftmost lane of Fig. 2(a) and
Fig. 2(b), the thickest part is 66 pixels and 49 pixels, respectively. By
simplifying data, the computational cost could be reduced.

(a)

(b)

Figure 2: Before and after using erosion filter (a) segmentation image without
erosion filter, (b) segmentation image with erosion filter.

####  III-B3 Lane Fitting

The lane fitting finds the regression function that best represents the pixel
coordinates detected as lane in the segmentation image. Specifically, the
methods used in lane fitting are linear, quadratic and cubic least squares
fitting. Equation (1) expresses a least squares polynomial fitting function.
The coefficient values (i.e., $c_{i},i=1,2,$ …, $m$) for minimizing the
squared error was derived from (1).

$\displaystyle\begin{pmatrix}p_{0}(x_{1})&p_{1}(x_{1})&p_{2}(x_{1})&\dotso&p_{m}(x_{1})\\\
p_{0}(x_{2})&p_{1}(x_{2})&p_{2}(x_{2})&\dotso&p_{m}(x_{2})\\\
\vdots&\vdots&\vdots&\ddots&\vdots\\\
p_{0}(x_{n})&p_{1}(x_{n})&p_{2}(x_{n})&\dotso&p_{m}(x_{n})\end{pmatrix}\begin{pmatrix}c_{1}\\\
c_{2}\\\ \vdots\\\ c_{m}\end{pmatrix}=\begin{pmatrix}y_{1}\\\ y_{2}\\\
\vdots\\\ y_{n}\end{pmatrix}$ (1)

where $m$ means degree, $c_{i}(i=1,2,$ …, $m)$ is coefficients,
$p_{i}(x)(i=1,2,$ …, $m)$ is $x$ to the $i$ power respectively.

The analyzed lanes consist of four lanes, which are defined as left-left lane,
left lane, right lane, and right-right lane. Coefficient values were found by
using linear, quadratic, and cubic least squares fitting of all four lanes.
Some pixel coordinates were sampled by applying the coefficients obtained from
the three fitting functions. Using the obtained variance as metric, the
mentioned four lanes were expressed by selecting the fitting function with the
smallest variance. Based on the fitting function that best represents lanes,
31 points are obtained for each lane, and the driving guidance line is
provided in the form of a point group using the fitting function corresponding
to the left lane and right lane. Although one of the two main lanes is not
detected, driving guidance line (hereinafter referred to as a path) can be
provided by adding an offset because a lane has certain width. The procedure
for vision recognition parts configured the seamless system, allowing the
tracker to process the path directly. The process of overall lane fitting
algorithm can be seen in Fig. 3. Algorithm 1 shows a pseudo code that contains
the overall fast optimal lane processing described in the section III-B.

Figure 3: Procedures of the lane fitting algorithm. Algorithm 1 Overall fast
optimal lane processing algorithm

1:$I$: Segmentation image from deep learning network

2:$O$: Driving guidance line consisting of points

3:$I_{p}$: Top view image after post-processing for $I$

4:$w$: Width of $I$

5:$h$: Height of $I$

6:$L_{coord}$: Two-dimensional lists of coordinates for lane points

7:$L_{func}$: Two-dimensional lists of function for lane

8:$I_{p}$ $\leftarrow$ Run IPM

9:$I_{p}$ $\leftarrow$ Apply the erosion filter

10:for $iteration=1,2,\ldots,w$ do

11: for $iteration=1,2,\ldots,h$ do

12: Get the pixel coordinates segmented by lane

13: from $I_{p}$ and store them in the $L_{coord}$

14: end for

15:end for

16:for $iteration(i)=1,2,3,4$ do

17: Run lane fitting algorithm on the $L_{coord}[i]$

18: Store the best function expression in the $L_{func}[i]$

19:end for

20:if left lane and right lane are exist then

21: $O$ $\leftarrow$ Calculate the center points with

22: $L_{func}[1]$ and $L_{func}[2]$

23:else

24: if only left is exist then

25: $O$ $\leftarrow$ Calculate the left lane

26: points with $L_{func}[1]$ and add offset

27: else

28: if only right is exist then

29: $O$ $\leftarrow$ Calculate the right lane

30: points with $L_{func}[2]$ and add offset

31: else

32: $O$ $\leftarrow$ Lane does not exist

33: end if

34: end if

35:end if

###  III-C Path Tracking Algorithm

####  III-C1 Pure Pursuit

Pure pursuit has been recognized one of the path tracking algorithms that
follow the target point. In this algorithm, a vehicle is treated as a bicycle
model, and the geometric explanation of the Pure pursuit is shown in Fig. 4.
The basic calculation method of Pure pursuit is as follows.

When drawing a circle with the radius of the look-ahead distance ($ld$) based
on the rear wheel of the vehicle, the point that overlaps the given path is
taken as the target point. The steering angle ($\delta$) of the vehicle is
calculated using $\alpha$, which indicates the difference between the
direction toward the rear wheel of the vehicle and the direction toward the
look-ahead distance. At this time, the steering angle can be expressed as (2).

Figure 4: Geometric explanation of Pure pursuit.

$\displaystyle\delta=\tan^{-1}(\frac{2L\cdot sin(\alpha)}{ld})$ (2)

where, $L$ represents wheel base of the vehicle and $ld$ means the look-ahead
distance respectively.

There are static and variable look-ahead distances. With a static look-ahead
distance, the Pure pursuit achieves poor results because the target point is
always fixed in the same radius regardless of the vehicle speed. Therefore, a
variable look-ahead distance was used in order to achieve better results and
expressed as a function of velocity in this study. The variable look-ahead
distance was expressed as (3).

$\displaystyle ld=190+100\cdot[\frac{1}{exp\\{-(\frac{v-20}{15})\\}}-0.5]$ (3)

Moreover, a PID controller based filter was added to prevent sudden bouncing
or shaking of the steering angle. Anti-windup logic was added to prevent the
divergence of error due to integral calculation. The compensator generating a
smooth profile of the steering angle was also implemented as described in
Algorithm 2.

Algorithm 2 Steering angle compensation algorithm

1:$\delta$: Steering angle calculated with Pure pursuit and filter

2:$com\\_\delta$: Steering angle after compensation

3:$T$: Threshold

4:if $\delta$ \- $prev\\_steer$ ¿ $T$ then

5: $com\\_\delta$ = $prev\\_steer$ \+ $T$

6:else if $prev\\_steer$ \- $\delta$ ¿ $T$ then

7: $com\\_\delta$ = $prev\\_steer$ \- $T$

8:else

9: $com\\_\delta$ = $\delta$

10:end if

11:$prev\\_steer$ = $com\\_\delta$
return $com\\_\delta$

In this study, the modified Pure pursuit was developed to follow the vision
and GPS based path provided by the perception part. There are two types of
pure pursuit depending on sensor used. Pure pursuit using a vision based path
is indicated as Pure pursuit (vision), and Pure pursuit using a GPS based path
is indicated as Pure pursuit (GPS). Both Pure pursuit (vision) and Pure
pursuit (GPS) become unable to drive on very large curvature roads, but
stability of steering angle is highly secured on straight or slight curve.
Pure pursuit (vision) is more responsive than Pure pursuit (GPS) due to fast
computational speed of vision. However, Pure pursuit (vision) is unable to
compute further path than Pure pursuit (GPS) which can be driven in areas
without lanes.

####  III-C2 Stanley Controller

Like the Pure pursuit, the Stanley controller calculates the steering angle
based on the bicycle model. Two types of errors are used to calculate the
steering angle. The two errors consist of a cross-track error and a heading
error. The cross-track error refers to the minimum distance between a given
path and a front wheel of the vehicle. The heading error refers to the
difference between the direction vector of the path and the direction vector
of the vehicle. Using these two errors, the steering angle can be obtained and
a geometric explanation for this algorithm is shown in Fig. 5.

Figure 5: Geometric explanation of Stanley controller.

$\displaystyle\delta(t)=\theta_{e}(t)+\theta_{d}(t)=\varphi(t)+\tan^{-1}\frac{ke(t))}{k_{s}+v_{f}(t)}$
(4)

where $\varphi(t)$($\theta_{e}(t)$) is heading error, $e(t)$ is cross-track
error, $v_{f}(t)$ is the speed of the vehicle, $k$ and $k_{s}$ are gain
parameters respectively. $k$ and $k_{s}$ in parameter types are expressed in
(4). Since it is difficult to implement perfect tracking performance with only
these two parameters, $k_{1}$ and $k_{2}$ should be added before
$\theta_{e}(t)$ and $\theta_{d}(t)$, respectively. Therefore, the modified
Stanley controller expression can be written the same as (5).

$\displaystyle\delta(t)=k_{1}\theta_{e}(t)+k_{2}\theta_{d}(t)=k_{1}\varphi(t)+k_{2}\tan^{-1}\frac{ke(t))}{k_{s}+v_{f}(t)}$
(5)

This modified Stanley controller was used to follow the global path provided
by the HD map. Stanley (GPS) and Stanley (vision) represent Stanley controller
using GPS based path and vision based path respectively. Stanley (GPS)
receives the current position of the vehicle through GPS and the position of
the front wheel of the vehicle can be calculated using $L$, the wheel base of
the vehicle. In case of using the modified Stanley (GPS), the vehicle shakes a
lot. Nevertheless, Stanley (GPS) is necessary because it can be driven in very
large curvatures.

Stanley controller does not use the vision based path due to the method of
determining the steering angle. As described above, Stanley controller uses
the heading error and the cross-track error to calculate the steering angle.
Since the vision based path starts from the front wheel of the vehicle, the
cross-track error is not able to exist as zero. With Stanley (vision), the
steering angle must be calculated only from the heading error. Therefore,
Stanley (vision) was not used because of its low tracking performance.

###  III-D Path Processing Method

The cameras, GPS and HD map were used to generate paths. GPS and HD map are
essential to get the path, when lane detection was not able to properly
perform or in the case of large curvature road. It was explained in the
Section III-B that the path could be retrieved from raw image through the
camera. The process of creating a vision based path included a process in
which the tracker uses the path immediately. In order to use the GPS based
path directly in the tracker like the vision based path, coordinate
transformation is required. The process of smoothly connecting paths becomes
also necessary for more stable driving. Therefore, path processing method
includes the coordinate transformation and interpolation.

####  III-D1 Path Processing Method based on Vision (Pure Pursuit)

The processing method of path based on vision used in Pure pursuit will be
explained as follows. The points obtained in section III-B are assigned a
corresponding distance estimated from the camera extrinsic parameter. The
look-ahead distance varies with velocity of vehicle and the look-ahead point
also changes. The target point, the closest point to the look-ahead point,
affects the steering angle. Since the points are not continuous, the target
point changes from time to time, which leads to instability in steering. In
order to ensure that the target point is located as close to the look-ahead
point as possible, the number of points was increased by selecting the two
closest points to the look-ahead point and using linear interpolation between
the two points. The stability of the steering angle is compensated by tracking
the target point at the same location as the look-ahead point.

####  III-D2 Path Processing Method based on GPS (Stanley Controller)

The processing method of global path used in Stanley controller is shown in
Fig. 6. First of all, the yaw value of the vehicle is obtained using IMU. The
global path is received from the HD map and provides 30 points with an
interval of about 1 meter based on the current location of the vehicle. In
order to use this path in Stanley controller, it is necessary to connect 30
points smoothly in a curve. Therefore, cubic spline interpolation was used to
approximate these points as curves. Cubic spline interpolation represents a
method of smoothly connecting given points using a cubic polynomial. By
applying this, 30 points that come in at intervals of 1 meter are interpolated
at intervals of about 0.1 meter, and all yaw values corresponding to each
point are calculated. Using the interpolated path and vehicle’s yaw value, the
distance to the point on the path closest to the current vehicle and yaw at
which point can be calculated. Using these values, the steering angle is
finally obtained by the Stanley controller.

Figure 6: Path processing method based on GPS used in Stanley controller.

####  III-D3 Path Processing Method based on GPS (Pure Pursuit)

The processing method of the global path used in Pure pursuit provides 30
points at about 1 meter intervals based on the current location. The
coordinate system of the global path uses the UTM coordinate system and the
coordinate system used in the Pure pursuit requires local path. Therefore, the
heading of the vehicle was always set to be the same as the direction of the
y-axis, and coordinate transformation converting the global path into a local
path was used. Since 300 by 300 pixel image coordinate was used, scaling was
performed to fit the units of the coordinate system. These path coordinate
transformations are shown in Fig.7, and the coordinate transformation
equations are formulated in (6) and (7). The data-flow diagram for the path
processing method based on GPS used in Pure pursuit is shown in Fig. 8.

$\displaystyle\begin{split}new\\_path\\_x=150-10\cdot[cos\\{-(90+yaw)\\}\cdot(path\\_x-\\\
global\\_x)-sin\\{-(90+yaw)\\}\cdot(path\\_y-global\\_y)]\end{split}$ (6)

$\displaystyle\begin{split}new\\_path\\_y=300+10\cdot[cos\\{-(90+yaw)\\}\cdot(path\\_x-\\\
global\\_x)-sin\\{-(90+yaw)\\}\cdot(path\\_y-global\\_y)]\end{split}$ (7)

(a)

(b)

Figure 7: Path coordinate transformation (a) UTM coordinate system, (b) pixel
image coordinate system. Figure 8: Path processing method based on GPS used in
Pure pursuit.

###  III-E Optimal Path Tracker Selection

The most important part of hybrid tracker based optimal path tracking system
becomes optimal path tracker selection. Optimal path tracker selection chooses
an appropriate path tracking algorithm among Pure pursuit (GPS), Pure pursuit
(vision), and Stanley (GPS) considering instability of steering angle, GPS
reliability, vision reliability, and road information. The selected trackers
can be changed in short intervals alternately because this algorithm ensures
real-time and selects the optimized tracker. The instability of steering angle
is predetermined based on the driving tendency of the Stanley controller and
Pure pursuit. GPS determines the reliability of the sensor using horizontal
dilution of precision (HDOP) and RTK precision information. Vision checks the
information of the path received from section III-B and determines the
detection reliability of the lane itself inside the system. It also determines
road information such as curvature, roundabout, and intersection of the path
to be driven based on HD map. The key role in the optimal path tracker
selection is to observe the information provided by the sensors and to switch
securely the path tracker.

The instability of the steering angle is determined according to the following
results shown in Fig. 9. Comparing the steering values, the vibration of the
steering angle using Pure pursuit becomes smaller than using the Stanley
controller. When Pure pursuit was used, it converged to 0 degrees in 4
seconds, whereas when Stanley was used, it oscillated within 10 degrees and
-10 degrees even after 4 seconds. It can be deduced that the driving stability
would be better if the Pure pursuit with higher stability of steering angle
was used in the range of driving with in-track maintained.

(a)

(b)

Figure 9: Steering at straight road (a) steering angle using Pure pursuit, (b)
steering angle using Stanley controller.

In this paper, GPS state information is named as GPS reliability, HD map based
road information is named as HD map data and vision based lane detection state
information is named as lane reliability. Each evaluating method is explained
as follows.

First, HDOP refers to the degree of interfering with the positional precision
of the horizontal coordinate by parsing from the information of NMEA 0183 of
GPS. Therefore, HDOP and RTK precision information was obtained from GPS, and
GPS reliability was evaluated by combining them. The normal operating standard
of HDOP was set to 3 or less experimentally. The information of RTK precision
is divided into 3 levels, which the highest level (Fixed) was treated as 2,
the lower levels in turn were treated as 1 (Float) and 0 (No Fixed). The Fixed
option was chosen in this research as the highest level because GPS only works
well with Fixed, which compensates for signals using LTE. If HDOP is less than
3 and the RTK precision information satisfies Fixed option, the GPS determines
only that it is operating normally as shown in TABLE II.

TABLE II: Criteria on determination of the GPS availability. RTK precision information | HDOP | GPS reliability
---|---|---
No Fixed(0) | $HDOP<3$ | ✕(0)
$HDOP\geq 3$ | ✕(0)
Float(1) | $HDOP<3$ | ✕(0)
$HDOP\geq 3$ | ✕(0)
Fixed(2) | $HDOP<3$ |  $\bigcirc$(1)
$HDOP\geq 3$ | ✕(0)
|  |

The method of evaluating the lane reliability is explained as follows. In the
300 by 300 window, the location of the current vehicle was set to (150,0) and
the vision based path in the direction of heading was provided as point group
information. By expressing the location and point group information as an
image, it was possible to determine the pixel distance as metrics for the
relationship between the path and the current vehicle location.

The pixel coordinates of the x-axis were scaled at 0.03 meter per pixel. The
width of a road equals 100 pixels. Considering width of the vehicle, if the
vehicle is off one-fifth the width of the road from its current location, it
could be deduced that the test vehicle invaded the center line. Therefore, if
the Equation (8) is satisfied, the vision based path is determined to be
stable and 1 is provided as lane reliability.

$\displaystyle|150-lpts|<W_{r}/5$ (8)

where $lpts$ is x coordinates of lane points and $W_{r}$ is width of a road in
the pixel coordinates respectively.

When lanes are unclear in the intersection and the roundabout, it is difficult
for vision to recognize them. In tunnel or a road on a hillside, GPS status is
not good, which leads GPS based path to a low reliability. Therefore, the
driving stability should be improved by receiving information of road terrain
in advance and selecting the optimal path tracking algorithm.

By using the optimal path tracker selection with these information, each of
the disadvantages was compensated and solved simply by switching the tracking
algorithm following each path of vision and GPS.

The criteria of this system for selecting the tracking algorithm using the
data described above is summarized in TABLE III.

TABLE III: Criteria of optimal path tracker selection.

GPS reliability | HD map data | Lane reliability | Selected path tracker
---|---|---|---
0 | * | * |  | Pure pursuit
---
(vision)
1 | 1 | 1 |  | Stanley controller
---
(GPS)
1 | 1 | 0 |  | Stanley controller
---
(GPS)
1 | 0 | 1 |  | Pure pursuit
---
(vision, GPS)
1 | 0 | 0 |  | Pure pursuit
---
(vision, GPS)
|  |  |

  * •

’*’ means that it doesn’t matter if there is any value (0 or 1).

Figure 10: General overview of the Hybrid tracker based optimal path tracking
system.

Each part from perception to control was described in detail above. In order
to reduce the computational cost, the perception and control sections were
closely connected, and the trackers were configured as parallel systems. An
overview of the architecture of Hybrid tracker based optimal path tracking
system used in this paper is shown in Fig. 10.

##  IV Experimental results

This section includes the performance analysis about the proposed Hybrid
tracker based optimal path tracking system (hereinafter referred to as
Hybrid). All of the tested algorithms were mounted on Hyundai Ioniq Electric
2020 and were tested on a shuttle route of DGIST and on high-speed circuit
proving ground. Tested roads comprise a variety of roads, including two-lane
or four-lane roads, intersection, as well as steep curve, tunnels, roundabout
and so on. In addition, the shuttle route includes both uphill, flat and
downhill, enabling acceleration testing. The high-speed circuit consists of
three-lane one-way and banked curve whose radius is 100 meters. The roads in
DGIST can be assumed as Korean urban road and the high-speed circuit might be
assumed highways. Therefore, tested paths were considered good road conditions
for verifying the system at low and high speeds (i.e., 0 km/h to 100 km/h).

The DGIST shuttle route was analyzed into normal road environments and complex
road environments. Roadways relatively easy to follow among the DGIST shuttle
route are called the normal road environment. The three types of normal road
environment were selected as straight, slight curve of radius 157.5 meters and
steep curve of radius 53 meters because tracker is able to drive properly on
these roadways using only one of the vision and GPS based path.

Sections of the road relatively difficult to follow among the DGIST shuttle
route are called the complex road environment, and the four sections were
designated as straight road with multiple 3-way junctions, roundabout of
radius 14 meters, tunnel, and intersection. The reasons why the sections were
selected as the complex road environment will be explained as follows.

Unlike roads belonging to the normal road environment, the intersection and
roundabout have very large curvature and the cameras cannot recognize the
lanes in the road of large curvature. In addition, since lanes occasionally
disappears for straight roads with multiple 3-way junctions, GPS based path is
required. Due to the low reliability of GPS in the tunnel, the vision based
path is only available.

###  IV-A Performance of Fast Optimal Lane Processing Algorithm

The performance of fast optimal lane processing algorithm will be explained in
this section. The Fig. 11 shows the image overlapping the raw image with the
lane of top view image processed by the fast optimal lane processing
algorithm. In the Fig. 11, (a), (b), (c) and (d) show the results of lane
processing algorithm at straight road, roads with lane covered by vehicles,
curve road, tunnel respectively. The results of straight roads consist of
uphill, flat and downhill roads. The results of the tunnel show that the
vehicle passes through the tunnel. The algorithm recognizes lanes despite of
structures or vehicles on the road, such as speed bump, eye-inducing rods,
vehicles. It can be deduced that this algorithm robustly recognizes lanes in
various road environments and find the best fitting regression function.

The time-averaged to infer lanes from ENet-SAD is taken 23.53ms. The time-
averaged to fit the pixel coordinates is measured 4.42ms. The sum of several
delays is approximately found 5ms. Therefore, the final runtime is 32.95ms.

(a)

(b)

(c)

(d)

Figure 11: Estimation results after applying the fast optimal lane processing
algorithm with diverse road conditions (a) straight roads, (b) roads with lane
covered, (c) curve roads, (d) tunnel.

###  IV-B Evaluation on Real-world

The modified Pure pursuit, Stanley controller and Hybrid system have been
tested and analyzed in complex road conditions. Two types of driving guidance
line, the vision based path and the GPS based path can be used by each path
tracking algorithm. There are four possible cases; Pure pursuit (vision), Pure
pursuit (GPS), Stanley (vision), and Stanley (GPS). As for these four cases,
the other three cases excluding Stanley (vision) which had poor performance
have been studied in this paper. The detailed reason for excluding the Stanley
(vision) was explained in section III-C2.

Therefore, the three modified trackers were optimized for coordinate
transformation and post-processing algorithms of various sensor parts.
Tracking performance and driving stability have been evaluated by comparing
the Hybrid and three modified trackers with ideal path based on HD map.
$Success$ represents that the tracking algorithms drove in the designated area
without hitting the curb or moving into the opposite lane

To determine the tracking performance of each tracker, RMSE ($lateral$), RMSE
($longitudinal$) and $distance$ were used in metric unit. These values
represent the difference between the ideal path and the real driving path.
RMSE ($lateral$) and RMSE ($longitudinal$) stand for the root mean square
error of latitude and longitude, respectively. The ”$distance$” signifies the
difference between the ideal path and the real driving path.

Driving stability has been determined using the RMSE ($yaw$) and RMSE
($steer$) in degree unit. RMSE ($yaw$) expresses the difference between the
yaw of the vehicle and the yaw of HD map. RMSE ($steer$) means the difference
between the steering angle directly driven by a human in an ideal path and the
steering angle calculated by each path tracking algorithm. The $yaw$ indicates
vehicle’s heading, and the $steer$ means a value that determines the direction
of the vehicle. The small RMSE ($yaw$) value represents that the planned
driving direction becomes similar to the ideal driving direction. The small
RMSE ($steer$) value also implies that the steering value calculated by the
tracking algorithm becomes similar to steer of the human, since it is compared
to the driving smoothly of human. Therefore, if both values show small, it
implies driving stability is high because the algorithm follows the path
smoothly without fluctuation. Thus, the driving stability can be evaluated
with values of RMSE ($yaw$) and RMSE ($steer$).

These six experimental results were summarized in TABLE IV and V to find
easily out the differences, and the Top-2 results for each column was
emphasized in these tables.

####  IV-B1 Test Results Under Normal Road Environment

(a)

(b)

(c)

(d)

(e)

Figure 12: Test result at normal road environments (a) straight road, (b)
slight curve, (c) enlarged graph of (b), (d) steep curve, (e) enlarged graph
of (d). TABLE IV: Quantitative results by different path tracking algorithms
under normal road environments (i.e., straight, slight curve, steep curve).

Scenes | Methods | $Success$ | Tracking Performance | Driving Stability
---|---|---|---|---
RMSE ($lateral$) $\downarrow$ | RMSE ($longitudinal$) $\downarrow$ |  $Distance$ $\downarrow$ | RMSE ($yaw$) $\downarrow$ | RMSE ($steer$) $\downarrow$
Straight | Pure pursuit (vision) | $\bigcirc$ | 0.091 | 0.019 | 0.068 | 0.079 | 1.314
Pure pursuit (GPS) | $\bigcirc$ | 0.223 | 0.007 | 0.155 | 0.174 | 1.755
Stanley (GPS) | $\bigcirc$ | 0.196 | 0.065 | 0.146 | 0.158 | 2.406
Hybrid | $\bigcirc$ | 0.377 | 0.049 | 0.285 | 0.025 | 1.300
Slight curve | Pure pursuit (vision) | $\bigcirc$ | 0.027 | 0.283 | 0.207 | 17.742 | 2.270
Pure pursuit (GPS) | $\bigcirc$ | 0.239 | 0.577 | 0.598 | 16.685 | 2.894
Stanley (GPS) | $\bigcirc$ | 0.131 | 0.553 | 0.463 | 16.247 | 3.430
Hybrid | $\bigcirc$ | 0.027 | 0.169 | 0.144 | 16.933 | 1.929
Steep curve | Pure pursuit (vision) | $\bigcirc$ | 0.450 | 0.397 | 0.522 | 57.994 | 2.865
Pure pursuit (GPS) | $\bigcirc$ | 0.129 | 0.492 | 0.384 | 62.959 | 3.199
Stanley (GPS) | $\bigcirc$ | 0.145 | 0.174 | 0.166 | 63.501 | 5.406
Hybrid | $\bigcirc$ | 0.321 | 0.370 | 0.414 | 52.047 | 3.485

  * •

The unit of RMSE ($lateral$), RMSE ($longitudinal$) and $Distance$ is meter.
The unit of RMSE ($yaw$) and RMSE ($steer$) is degree.

Fig. 12 shows graphically the tracking results of Pure pursuit (vision), Pure
pursuit (GPS), Stanley (GPS) and Hybrid in three different scenes. In Fig.
12(a), (b) and (d) shows the results; a straight road, a slight curve road,
and a steep curve road. Graph (c) and (e) are enlarged views of the yellow
boxes in graphs (b) and (d) in Fig. 12, respectively. It can be seen in the
figure that Pure pursuit (vision), Pure pursuit (GPS), Stanley (GPS), and
Hybrid are all almost identical to the ideal path in the normal road
environment. Numerical interpretation of the graph is demonstrated in TABLE
IV.

Thus, it can be concluded that all of modified trackers successfully drove the
suggested section without infringement on the lane from the $Success$ column
in TABLE IV). As mentioned in section III-C in this paper, each tracker
clearly shows high performance in the certain section of the road due to the
characteristics of each tracker. Therefore, this implies that the result of
modified each tracker produces optimal performance for each situation. Hybrid
system shows intermediate or higher results in the overall result. Since the
Hybrid system operates by selecting several optimal trackers at a fast
computational speed, it is possible to secure at least the average performance
of each tracker.

In the case of straight road, the overall tracking performance (i.e., RMSE) of
Hybrid system is lower than the peak performance of other base trackers. It is
because Hybrid is the system composed of the above three trackers. The Hybrid
system also guarantees of both stability and tracking performance, whereas
these slight losses may occur. As shown in TABLE IV and V, in terms of
stability, the Hybrid achieves the highest performance. RMSE ($yaw$) and RMSE
($steer$) values were lower than the second best performances of Pure pursuit
(vision) by 0.054 and 0.014 in degree unit respectively. Thus, it convinces
that Hybrid is superior in terms of driving stability. It is also found that
Hybrid has a tendency to lack the ability to compensate for residual errors in
a straight road situation as it is changed to multiple trackers due to the
fast selection speed. However, due to these characteristics, robustness of the
stability for the Hybrid system improved the overall driving performance.

The driving performances show the most effective in the slight curve due to
the characteristics of Hybrid. It is also able to be found that other roads
have a clear difference in performance between vision and GPS, but slight
curve shows relatively similar performance. In other words, the Hybrid has the
best overall performance in slight curve because the tracking performance of
multiple trackers is properly used. Conversely, RMSE ($yaw$) leads to 16.933
degrees out of ideal path, which is the third best among the four algorithms.
However, the difference between the value of the best algorithm and Hybrid was
only 0.686 degrees which equals to only 0.04% differences with the results of
the other algorithms. Since the value of RMSE ($steer$) was the smallest one,
it can be explained that the driving stability of Hybrid system provides the
best comfortableness.

Moreover, in the steep curve, due to the limitations of vision, trackers using
GPS are mainly used. In this case, Stanley (GPS) shows high precision for this
road environment. However, due to bad stability, Hybrid uses only Pure pursuit
(vision) and Pure pursuit (GPS) to secure overall driving performance. As an
experimental result, the tendency of error becomes similar that of Pure
pursuit (vision). The tracking performance of Hybrid gets worse than the
performance of Stanley (GPS) since Hybrid uses Pure pursuit trackers. Thus, it
can be deduced that relatively low tracking performance of Hybrid system is a
result of the algorithm operation to ensure stability. When human drives on
the steep curve, they usually do offset driving for driving stability. Since
the proposed system does not have environment recognition, it is important to
precisely follow the provided path. Hence, when the importance of the in-track
is high, such as the steep curve, the Hybrid drives by focusing on the in-
track rather than the stability. In the steep curve, the results show Stanley
(GPS) has the best tracking performance, but show Stanley (GPS) has poor
driving stability. Therefore, it can be concluded that Hybrid secured driving
stability by properly switching two trackers, Pure pursuit (vision) and Pure
pursuit (GPS), which have good stability performance in the secured tracking
performance situation. Considering the value of RMSE ($steer$) compared to
humans with offset driving, the smaller value of RMSE ($yaw$) than 5 degrees
compared to other trackers imply that the overall driving performance of
Hybrid in steep curve represents superior.

(a)

(b)

(c)

(d)

Figure 13: DGIST shuttle route and experimental results at complex road
environments (a) DGIST shuttle route, (b) straight road with multiple 3-way
junctions, (c) roundabout, (d) intersection. TABLE V: Quantitative results by
different path tracking algorithms under complex road environments (i.e.,
straight road with multiple 3-way junctions, roundabout, tunnel,
intersection).

Scenes | Methods | $Success$ | Tracking Performance | Driving Stability
---|---|---|---|---
RMSE ($lateral$) $\downarrow$ | RMSE ($longitudinal$) $\downarrow$ |  $Distance$ $\downarrow$ | RMSE ($yaw$) $\downarrow$ | RMSE ($steer$) $\downarrow$
Straight road with multiple 3-way junctions | Pure pursuit (vision) | $\bigcirc$ | 0.152 | 1.063 | 0.862 | 0.461 | 1.671
Pure pursuit (GPS) | $\bigcirc$ | 0.029 | 0.290 | 0.219 | 2.871 | 2.434
Stanley (GPS) | $\bigcirc$ | 0.081 | 0.183 | 0.142 | 0.125 | 2.734
Hybrid | $\bigcirc$ | 0.056 | 0.214 | 0.157 | 0.018 | 1.660
Roundabout | Pure pursuit (vision) | ✕ | - | - | - | - | 8.252
Pure pursuit (GPS) | ✕ | - | - | - | - | 6.431
Stanley (GPS) | $\bigcirc$ | 0.415 | 0.403 | 0.471 | 187.166 | 5.912
Hybrid | $\bigcirc$ | 0.232 | 0.486 | 0.377 | 172.815 | 5.708
Intersection | Pure pursuit (vision) | ✕ | - | - | - | - | 6.664
Pure pursuit (GPS) | $\bigcirc$ | 0.130 | 0.263 | 0.227 | 75.829 | 6.046
Stanley (GPS) | $\bigcirc$ | 0.424 | 0.109 | 0.260 | 73.313 | 5.493
Hybrid | $\bigcirc$ | 0.439 | 0.181 | 0.330 | 65.093 | 5.481
Tunnel | Pure pursuit (vision) | $\bigcirc$ | - | - | - | - | 1.935
Pure pursuit (GPS) | ✕ | - | - | - | - | 7.704
Stanley (GPS) | ✕ | - | - | - | - | 8.305
Hybrid | $\bigcirc$ | - | - | - | - | 1.911

  * •

The unit of RMSE ($lateral$), RMSE ($longitudinal$) and $Distance$ is meter.
The unit of RMSE ($yaw$) and RMSE ($steer$) is degree.

####  IV-B2 Test Results Under Complex Road Environment

In the previous section, it was found that three tracking algorithms and
Hybrid system succeeded in driving the normal road environment. However, there
were some sections where three algorithms except Hybrid could not properly
control the vehicle in roundabout, intersection, and tunnel shown in the Fig.
13. The Fig. 13(a) shows that the path in which the proposed system actually
drove the entire DGIST shuttle route closely matches the ideal path. Each road
in the complex road environment is marked by a black box in Fig. 13(a).
Figures of (b), (c) and (d) comprise a combination of the roadway actual
tested, the driving graph and the graph extending the yellow box. Fig. 13(b)
shows the results of tracking straight roads with multiple 3-way junctions and
the enlarged graph demonstrates that Pure pursuit (vision) has poor tracking
performance due to the absence of lanes in the area with 3-way junctions. Fig.
13(c) displays the results of tracking the roundabout. Pure pursuit (vision)
was unable to follow because the lane of the roundabout was not clear and Pure
pursuit (GPS) was unable to follow accurately at very large curvature. Only
Stanley controller succeeded in tracking and the proposed system tracked well
by selecting Stanley controller among the three tracking algorithms. Fig.
13(d) shows the results of tracking the intersection. Pure pursuit (vision)
failed to follow the driving guidance line of the intersection. Pure pursuit
(GPS) and Stanley controller tracked the path well. Pure pursuit (GPS)
adjusted the steers quickly and Stanley controller adjusted the steers slowly,
whereas Pure pursuit (GPS) occasionally crossed the center line and tracked
the path overall.

In the complex road environment, a numerical analysis of the tracking
performance and driving stability of each algorithm are listed in TABLE V. In
straight road with multiple 3-way junctions, the algorithms using the GPS
based path have better tracking performance than the algorithm using the
vision based path since lanes are often disconnected. The $distance$ value of
Hybrid is 0.157 meter, which can be seen to have a value between the
$distance$ value of Stanley (GPS) and the $distance$ value of Pure pursuit
(GPS). It might be implied that the Hybrid selected alternately Stanley (GPS)
and Pure pursuit (GPS). In particular, the values of RMSE ($yaw$) and RMSE
($steer$) representing a driving stability showed the best among the tested
methods.

In roundabout, due to the few lanes, Pure pursuit (vision) was unable to drive
properly this road. Also, it was unable to adopt Pure pursuit (GPS) due to
very large curvature. The TABLE V also indicated that Stanley (GPS) and Hybrid
succeeded in driving the roundabout, and $distance$ value of Hybrid is about
0.094 meter closer than that of Stanley (GPS)’s $distance$ to the ideal path.
In terms of driving stability, RMSE ($yaw$) value of Hybrid showed 14.351
degrees better than that of Stanley (GPS), and RMSE ($steer$) of Hybrid is
slight difference with that of Stanley (GPS). This is the reason why there is
a big difference (i.e., 14.3 degrees) in RMSE ($yaw$) even though Hybrid
adopted Stanley (GPS) because Hybrid chose different trackers in entering the
roundabout. It can be finally induced that Hybrid becomes superior in terms of
tracking performance and driving stability.

In intersection, Pure pursuit (GPS), Stanley (GPS), Hybrid system succeeded.
The $distance$ values show all 0.330 meter or less, so the tracking
performance indicates high. Although Hybrid did not represent the highest
tracking performance among them, it guarantees the driving stability.

In Tunnel, the GPS did not work properly, so tracking performance could not be
obtained. The tracking of the tunnel area was operated well based on Pure
pursuit (vision), but the reliability of the GPS showed low and the graph
seems that the vehicle did not follow the path, as in the (e) area of Fig.
13(a). It is shown that the steer value driven by humans and the steer values
predicted by each algorithm. Fig. 14(b) shows reliability of GPS. When the
reliability of GPS becomes high, the graph background color is highlighted in
cyan, otherwise in magenta. The steer value provided by Pure pursuit (vision)
shows pretty similar to the steer value driven by humans, whereas the steer
value provided by Pure pursuit (GPS) does not. It is also shown in Fig. 14(a)
that algorithms using GPS based path are not able to pass through tunnels due
to the low reliability of GPS.

(a)

(b)

Figure 14: Experimental results in tunnel (a) comparison of steering angle
value, (b) GPS reliability.

Finally, since GPS based path was impossible to operate correctly in the
tunnel, only RMSE (steer) was obtained. RMSE ($steer$) of Pure pursuit
(vision) and RMSE ($steer$) of Hybrid are similar with 0.6 degrees
differences. Therefore, Hybrid succeeded in passing through the tunnel using
Pure pursuit (vision). In summary of experimental results, the path tracking
algorithms for the vision based path and the GPS based path were appropriately
switched through the Hybrid tracker based optimal path tracking system to
drive the shuttle route on DGIST campus.

##  V Conclusion

This paper proposes Hybrid tracker based optimal path tracking system for
autonomous vehicles. The designed system combines, evaluates and applies
several trackers to driving on complex road conditions. The proposed system
includes all of the processing algorithms of deep learning based lane
detection algorithms, coordinate system transformation, three modified
geometric trackers and optimal path selection algorithm. Based on combining
all above processes, the proposed system guarantees reasonable driving
performance for trade-off of driving stability and tracking performance in
both normal and complex road environments. This study also notes that the
quantitative comparison using ideal path and the steering value from human
shows the overall driving performance of Hybrid tracker based optimal path
tracking system. With experimental results, this study convinces to build a
seamless system from the sensor part of the autonomous vehicle to the action
part for better performance. In other words, the key to build this system was
that control and sensor recognition should be made in one process.
Consequently, as shown in experimental results, it notes that proposed system
of the optimal path selection and system architecture significantly improves
both driving stability and tracking performance in the presence of high
complexity of road conditions.

## References

  * [1] S. O.-R. A. V. S. Committee _et al._ , “Taxonomy and definitions for terms related to on-road motor vehicle automated driving systems.(2014),” 2014.
  * [2] L.-A. Tran and M.-H. Le, “Robust u-net-based road lane markings detection for autonomous driving,” in _2019 International Conference on System Science and Engineering (ICSSE)_. IEEE, 2019, pp. 62–66.
  * [3] D. Neven, B. De Brabandere, S. Georgoulis, M. Proesmans, and L. Van Gool, “Towards end-to-end lane detection: an instance segmentation approach,” in _2018 IEEE intelligent vehicles symposium (IV)_. IEEE, 2018, pp. 286–291.
  * [4] Y. Xing, C. Lv, L. Chen, H. Wang, H. Wang, D. Cao, E. Velenis, and F.-Y. Wang, “Advances in vision-based lane detection: algorithms, integration, assessment, and perspectives on acp-based parallel vision,” _IEEE/CAA Journal of Automatica Sinica_ , vol. 5, no. 3, pp. 645–661, 2018.
  * [5] Q. Khan, T. Schön, and P. Wenzel, “Latent space reinforcement learning for steering angle prediction,” _arXiv preprint arXiv:1902.03765_ , 2019.
  * [6] J. M. Snider _et al._ , “Automatic steering methods for autonomous automobile path tracking,” _Robotics Institute, Pittsburgh, PA, Tech. Rep. CMU-RITR-09-08_ , 2009.
  * [7] M. Cibooglu, U. Karapinar, and M. T. Söylemez, “Hybrid controller approach for an autonomous ground vehicle path tracking problem,” in _2017 25th Mediterranean Conference on Control and Automation (MED)_. IEEE, 2017, pp. 583–588.
  * [8] M. Kim, G. Im, and J. Park, “A comparative study of parking path following methods for autonomous parking system,” _The Journal of Korea Robotics Society_ , vol. 15, no. 2, pp. 147–159, 2020.
  * [9] N. H. Amer, K. Hudha, H. Zamzuri, V. R. Aparow, A. F. Z. Abidin, Z. Abd Kadir, and M. Murrad, “Adaptive modified stanley controller with fuzzy supervisory system for trajectory tracking of an autonomous armoured vehicle,” _Robotics and Autonomous Systems_ , vol. 105, pp. 94–111, 2018.
  * [10] M.-W. Park, S.-W. Lee, and W.-Y. Han, “Development of lateral control system for autonomous vehicle based on adaptive pure pursuit algorithm,” in _2014 14th International Conference on Control, Automation and Systems (ICCAS 2014)_. IEEE, 2014, pp. 1443–1447.
  * [11] S. Dominguez, A. Ali, G. Garcia, and P. Martinet, “Comparison of lateral controllers for autonomous vehicle: Experimental results,” in _2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC)_. IEEE, 2016, pp. 1418–1423.
  * [12] Z. Chen, Q. Liu, and C. Lian, “Pointlanenet: Efficient end-to-end cnns for accurate real-time lane detection,” in _2019 IEEE Intelligent Vehicles Symposium (IV)_. IEEE, 2019, pp. 2563–2568.
  * [13] Y. Ko, J. Jun, D. Ko, and M. Jeon, “Key points estimation and point instance segmentation approach for lane detection,” _arXiv preprint arXiv:2002.06604_ , 2020.
  * [14] Y. Hou, Z. Ma, C. Liu, and C. C. Loy, “Learning lightweight lane detection cnns by self attention distillation,” _arXiv preprint arXiv:1908.00821_ , 2019.
  * [15] A. Paszke, A. Chaurasia, S. Kim, and E. Culurciello, “Enet: A deep neural network architecture for real-time semantic segmentation,” _arXiv preprint arXiv:1606.02147_ , 2016.
  * [16] X. Pan, J. Shi, P. Luo, X. Wang, and X. Tang, “Spatial as deep: Spatial cnn for traffic scene understanding,” in _Proceedings of the AAAI Conference on Artificial Intelligence_ , vol. 32, no. 1, 2018.
  * [17] L.-N. Teow and K.-F. Loe, “Robust vision-based features and classification schemes for off-line handwritten digit recognition,” _Pattern Recognition_ , vol. 35, no. 11, pp. 2355–2364, 2002.
  * [18] C. Li, W. Zhang, G. Peng, and S. Liu, “Bearing fault diagnosis using fully-connected winner-take-all autoencoder,” _IEEE Access_ , vol. 6, pp. 6103–6115, 2017.
  * [19] kivinju. tusimple benchmark ground truth. [Online]. Available: https://github.com/TuSimple/tusimple-benchmark/issues/3#issue-372217074

|  EUNBIN SEO was born in Suwon, South Korea, in 1999. She is currently
pursuing the B.S. degree in computer science and technology with Daegu
Gyeongbuk Institute of Science and Technology (DGIST), Daegu, Korea. Her
research interests include computer vision and automatic control.
---|---
|  SEUNGGI LEE was born in Seoul, South Korea, in January 2000. He is
currently pursuing the B.S. degree in electrical engineering from Daegu
Gyeongbuk Institute of Science and Technology (DGIST), Daegu, Korea. His
research interest include communication system and wireless power transfer.
---|---
|  GWANJUN SHIN was born in Seosan, South Korea in 1999. He is currently
undergraduate students at College of Trans-disciplinary studies, Daegu
Gyeongbuk Institute of Science and Technology (DGIST). His research interests
include visual recognition and domain adaptation in machine learning. He is
also the NVIDIA Deep learning institute University Ambassadorship and
instructor.
---|---
|  HOYEONG YEO was born in Daegu, South Korea in 1999, He is currently
undergraduate students at College of Trans-disciplinary studies, Daegu
Gyeongbuk Institute of Science and Technology (DGIST). His research interests
include motion control and deep learning.
---|---
|  YONGSEOB LIM received the Ph.D. degree in mechanical engineering from the
University of Michigan, Ann Arbor, MI, USA, in 2010. He was with the Hyundai
Motor Company R&D Advanced Chassis Platform Research Group, South Korea, as a
Research Engineer. His works at Hyundai Motor Company focused on advanced
vehicle dynamics and control technologies, including active suspension,
steering and braking control systems. Moreover, He also with Samsung Techwin
Company Mechatronics System Development Group, South Korea as a Principal
Research Engineer. His works at Samsung focused on developing stabilization
control algorithm for the Remotely Controlled Robotic Arms. He is currently an
Associate Professor in the Robotics Engineering Department, Daegu Gyeongbuk
Institute of Science and Technology (DGIST), and the Co-Director of the Joint
Research Laboratory of Autonomous Systems and Control (ASC) and Vehicle in the
Loop Simulation (VILS) Laboratories. His research interests include the
modeling, control, and design of mechatronics systems with particular
interests in autonomous ground vehicles and flight robotics systems and
control.
---|---
|  GYEUNGHO CHOI received the Ph.D. degree in mechanical engineering from the
University of Alabama, AL, USA, in 1992, also Honorary PhD Degree in
Automotive & Energy Engineering conferred be Her Royal Highness Princess Maha
Chakri Sirindhorn from King Mongkut’s University of Technology North Bangkok,
Thailand in 2018. He served President in Korean Auto-vehicle Safety
Association and Editor-in-Chief in Korean Society for Engineering Education.
He has taught Thermodynamics, Heat Transfer, and Automotive Engineering in
Keimyung University and Daegu Gyeongbuk Institute of Science and Technology as
a Professor for 28 years. He is also the Co-Director of the Joint Research
Laboratory of Autonomous Systems and Control (ASC) and Vehicle-in-the-Loop
Simulation (VILS) Laboratories. His research interests include self-driving
vehicle, ADAS system, Vehicle-In-the-Loop system, and design of alternative
energy utilization.
---|---