Path Planning for Autonomous Vehicles with Dynamic Lane Mapping

and Obstacle Avoidance

Ahmed El Mahdawy and Amr El Mougy

Department of Computer Science and Engineering, German University in Cairo, Cairo, Egypt

Keywords:

Autonomous Vehicles, Path Planning, Obstacle Avoidance.

Abstract:

Path planning is at the core of autonomous driving capabilities, and obstacle avoidance is a fundamental part

of autonomous vehicles as it has a great effect on passenger safety. One of the challenges of path planning

is building an accurate map that responds to changes in the drivable area. In this paper, we present a novel

path planning model with static and moving obstacle avoidance capabilities, LiDAR-based localization, and

dynamic lane mapping according to road width. We describe our cost-based map building approach and show

the vehicle trajectory model. Then, we evaluate our model by performing a simulation test as well as a real

life demo, in which the proposed model proves to be effective at maneuvering around static road obstacles, as

well as avoiding collisions with moving obstacles such as in pedestrian crossing scenarios.

1 INTRODUCTION

Road trafﬁc injuries kill approximately 1.35 million

people each year (WHO, 2020). Among the pri-

mary risk factors for road trafﬁc deaths are speed-

ing, distracted driving and driving under the inﬂu-

ence, all preventable human errors (WHO, 2020). Au-

tonomous driving features have the power to alert the

driver of surrounding dangers and potentially fatal er-

rors. Fully autonomous driving systems have to be

aware of the vehicle’s surroundings with high accu-

racy, and need to be able to plan ahead the motion of

the vehicle in a way that does not impose any danger

on surrounding pedestrians or trafﬁc, while maintain-

ing some level of driving comfort inside the vehicle

by reducing sudden acceleration or changes of direc-

tion of the vehicle.

Path planning is the means by which autonomous

vehicles plan ahead their movements and navigate

through the environment. There are multiple chal-

lenges in planning an autonomous vehicle’s path

through a dynamic environment:

1. Building an ofﬂine coordinate-based map that will

provide a basis for the vehicle’s real-world posi-

tion and its planned trajectory.

2. Localizing the vehicle’s current position on the

map, and planning a short-term path through these

points. There can be multiple candidate points for

the vehicle’s next step. The best candidate must

be decided based on the positions of the obstacles

(e.g. trafﬁc and pedestrians) detected by the vehi-

cle’s sensing modules.

3. Finding the best heading and acceleration for the

vehicle to ensure a safe path possibly also taking

comfortability into account (favouring smoother

paths with less sudden acceleration).

Grid-based approaches are commonly used for the of-

ﬂine map, representing the drivable environment as a

set of grid cells (called waypoints) with ﬁxed posi-

tions.

Acquiring accurate information about the vehi-

cle’s position is essential for path generation. GPS-

based approaches may not provide the needed accu-

racy for autonomous navigation. Another approach

is to use a pre-generated point cloud map stored on

the vehicle. A point cloud map is a set of 3D points

mapping the environment, usually recorded from live

LiDAR data.

In the path ﬁnding step, given that a map of the

environment exists and we know the current position

of the vehicle on the map, we are interested in gener-

ating a plan of the ideal path for vehicle over the next

few seconds. This plan should be in the same domain

as the environment map (meaning that we are not con-

cerned with the vehicle’s exact trajectory yet, only its

next positions on the map).

A cost function provides a way to numerically rep-

resent the likeliness that any given selection in the ve-

El Mahdawy, A. and El Mougy, A.

Path Planning for Autonomous Vehicles with Dynamic Lane Mapping and Obstacle Avoidance.

DOI: 10.5220/0010342704310438

In Proceedings of the 13th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2021) - Volume 1, pages 431-438

ISBN: 978-989-758-484-8

431

hicle’s path is the most ideal one. In the case of grid-

based maps they can be used to assign a cost value

to each node in the grid. A shortest path algorithm

can then take into account these costs in order to ﬁnd

a path of least cumulative cost. Cost functions must

take into account the chance of collision that is intro-

duced by taking a given path. A cost function should

never favor a path that puts the vehicle into a collision

trajectory. Cost functions may also consider the com-

fortability of a given path based on factors such as the

frequency of lane switches (Boroujeni et al., 2017), or

the acceleration or jerk in the generated path (Elban-

hawi et al., 2015).

The vehicle trajectory step involves transforming

the motion plan from the environment map domain

into real-world physical coordinates, and creating a

trajectory plan that steers the vehicle along the nodes

of the generated path. In some grid-based approaches,

cubic spline interpolation is used to convert the grid

path into an continuous curve that can be traced by

the vehicle (Francis et al., 2018) (Lemos et al., 2016).

Other approaches aim to model speciﬁc maneuvers

such as lane changes using polynomial curves (Zhang

et al., 2013).

In this paper, we propose a novel path planning

system for autonomous vehicles. The proposed sys-

tem takes into consideration the position of surround-

ing static obstacles (such as road irregularities) and

the position and trajectory of moving obstacles (such

as road trafﬁc and pedestrians), and generates a path

and trajectory plan for the vehicle valid for the next

few seconds that safely maneuvers the vehicle around

the surrounding obstacles. The system should be able

to accurately localize the vehicle within a pre-mapped

environment and follow a mapped path. Waypoints

will be dynamically expanded into a set of lane way-

points by acquiring information about the road width

at each waypoint from drivable area information.

The remaining sections of the paper are organized

as follows. In Section 2 we review the most pertaining

research in literature. In Section 3, we discuss the im-

plementation details of our path planning architecture,

and in Section 4 we discuss the performance evalua-

tion. Finally, Section 5 offers concluding remarks.

2 RELATED WORK

Grid-based map building approaches have been ex-

tensively researched and applied. In grid-based ap-

proaches, the environment is approximated by a set

of 2D or 3D points. This allows each point to be as-

signed a cost based on the surrounding obstacles. A

shortest path ﬁnding algorithm can be applied to de-

termine the best route through these points. (Francis

et al., 2018) (Boroujeni et al., 2017) This allows lanes

in the road to be each represented by a grid point,

where moving from one point to another on the lat-

eral axis represents a lane change. However, in this

approach, lane positions are ﬁxed and have to be de-

termined when building the map. This is non-ideal

in environments that do not have deﬁned lanes (such

as in a university campus), since the vehicle will be

bound to ﬁxed positions regardless of the available

drivable area and the vehicle dimensions.

Non-grid based approaches for path planning have

also been investigated. One such approach is discrete

optimization, where ﬁnite set paths are generated and

the best path is selected at each planning step (Hu

et al., 2018) (Montemerlo et al., 2008). In the pa-

per by Hu et al. (Hu et al., 2018), the center line

of the road is constructed by interpolating the way-

point map, and in each planning step, a set of paths are

constructed by varying the amount of deviation from

the center position of the road. Paths which intersect

static and moving obstacles are eliminated. These ap-

proaches may be more computationally expensive as

the candidate paths have to be generated at each com-

putation step.

The use of potential ﬁelds has been researched as

a non-grid based approach for path planning in vehi-

cles and ground robots (Ahmed et al., 2015) (Daily

and Bevly, 2008). In this approach, the environment

is modeled as a vector ﬁeld where the planning goal

is modeled as an attraction force, and obstacles are

modeled as repulsion forces. The selected path for the

vehicle is the path following the gradient of the ﬁeld.

This provides a ﬂexible and dynamic model for the

environment since the vehicle is not bound to any set

of discrete paths. However, this approach may fail to

correctly determine the best path in some cases, due

to encountering local minima in the vector ﬁeld.

3 SYSTEM ARCHITECTURE

In this paper, we present our waypoint-based path

planning architecture with LiDAR-based localization,

dynamic lane mapping and static and moving obstacle

avoidance. We utilize road width information at each

waypoint from real-time drivable area data to dynami-

cally map the positions of lanes according to a deﬁned

lane width. Information about the position of static

obstacles and the position and velocity of moving ob-

stacles are integrated to provide a cost for each lane

waypoint. Finally, we use the pure pursuit algorithm

(Coulter, 1992) for trajectory planning.

The project implementation is built on ROS

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

432

(Robot Operating System), a framework designed to

assist the development of robot software. It provides

a communication protocol that the modules of a robot

platform can use to establish communication channels

between each other. These channels are based on a

publisher/subscriber model.

Ofﬂine map

Lane constructor

Waypoint cost visualizer

Perception modules

Path ﬁnder

Path visualizer

Pure pursuit

Figure 1: Overview of system architecture.

Our proposed system is made of three main compo-

nents as shown in Figure 1: the lane constructor, path

ﬁnder, and pure pursuit modules, which will be ex-

plained in this section. The ofﬂine map component

represents the list of waypoints. The perception mod-

ules use raw sensor data to sense parameters such as

drivable area and the positions and measured veloci-

ties of obstacles. These modules are outside the scope

of this paper, but we assume that we can obtain these

parameters.

3.1 Ofﬂine Map

The ofﬂine map is a directed graph of GPS coordi-

nates called waypoints. Since the waypoints are con-

nected, they imply a heading. Waypoints are used to

mark a section of the road. Since the lateral position

of the vehicle does not depend on the lateral position

of the waypoint on the road, they should not be used

to mark lanes. Each waypoint is also associated with

the maximum driving speed value for this section of

the road.

Waypoints are loaded from the ofﬂine map pro-

gressively with a set look-ahead distance starting

from the current vehicle position.

A point cloud map of the environment is saved

locally, and Normal Distributions Transform (NDT)

matching (Biber and Strasser, 2003) is used to de-

termine the vehicle’s position and velocity within the

map from live LiDAR data.

3.2 Lane Construction

Since waypoints do not carry information about the

road width or lane positions (and not all roads have

clearly deﬁned lanes), we need to be able to construct

our own lane positions for the vehicle.

From drivable area data, we can know the width

of the road at any waypoint position. Since waypoints

have a heading, we can construct a line at the way-

point position normal to the waypoint heading. This

line will intersect with the boundaries of the driv-

able area of the road. The road width is then calcu-

lated as the distance between the leftmost and right-

most points of intersection along the constructed line,

shown in Figure 2 as W

and W

respectively.

The road width is used to determine a reasonable

number of lanes at the position of each waypoint.

Given the left and right distances from the waypoint

to the road boundaries W

and W

respectively, and

the desired lane width L, we can calculate the number

of lanes N as:

N =





(1)

Lanes are centered within the drivable area of the

road, and are not separated by any distance. The new

waypoints are positioned at the center of each con-

structed lane, as shown in Figure 3. These waypoints

are passed to the next step, the path ﬁnder module.

Figure 2: Calculation of

road width W at the way-

point N2.

Figure 3: Constructed lane

waypoints.

3.3 Assigning Costs

A cost value in the interval [0, 1] is assigned to each

lane waypoint. These values are primarily assigned

according to the proximity of nearby obstacles. A

waypoint having a cost of 1 is considered to be im-

passable.

The cost of a waypoint can be interpreted as the

measured risk of driving through it. A waypoint hav-

ing a cost closer to 1 is likely to be in close vicinity

of one or more obstacles. As a safety measure, the

speed of the vehicle is linked to the waypoint cost: as

the cost approaches 1, the driving speed approaches

0. Thus, if V

is the target driving speed, V

is the

maximum speed set to the current waypoint, and C is

the waypoint cost, the target speed can be expressed

as:

Path Planning for Autonomous Vehicles with Dynamic Lane Mapping and Obstacle Avoidance

433

= V

∗ (1 − C) (2)

3.3.1 Static Obstacles

Static obstacles are modeled as circular regions hav-

ing a position and a radius. Lane waypoints are also

assigned a circular region having a diameter equal to

the lane width, as shown in Figure 4. If the obstacle

region interesects the waypoint region, the waypoint

is assigned a cost of 1.

Since the waypoint region covers the width of the

lane, and practically the distance between consecutive

waypoints will be very small, a lane that intersects an

obstacle will always be blocked.

Figure 4: A static obstacle, shown as a solid gray circle,

intersects the regions of the N2 lane waypoints.

3.3.2 Moving Obstacles

Moving obstacles are modeled as a single point in

space having a velocity vector. Obstacles are expected

to follow this vector at constant velocity. Changes in

the velocity of an obstacle can only be accounted for

at the next planning interval, after the velocity vector

is updated.

To ﬁnd the possibility of collision with a moving

obstacle at a given waypoint, a velocity vector for

each waypoint is deﬁned to be a vector pointing in

the same heading as the waypoint and having a mag-

nitude equal to the current vehicle speed.

To determine for a given waypoint whether the

chance of collision with a moving obstacle exists

within a deﬁned time frame, we obtain the paramet-

ric equations for the moving obstacle and the vehicle

driving along the waypoint velocity vector. We are in-

terested in ﬁnding two parameters t

and t

, the time

parameters for the obstacle and waypoint equations

respectively, that result in the equality of the position

vectors of the vehicle and waypoint. A solvable sys-

tem indicates that the two constructed straight lines

intersect. Furthermore, if the magnitude in difference

between the two parameters t

and t

is within a

deﬁned range, this indicates that the obstacle and the

vehicle will pass through the same point in space at

nearly the same time. This range can depend on the

physical size of the vehicle and the separation dis-

tance required.

This process is repeated for each waypoint and

moving obstacle pair. A waypoint whose check fails

with any of the detected moving obstacles (i.e. the

difference in the parameters t

and t

is too small)

is assigned a cost of 1.

3.3.3 Cost Smoothing

The techniques described so far can detect whether

a waypoint is in direct contact with an obstacle, or

in the path of a moving obstacle. In both cases, the

waypoint should be completely blocked. Thus, we

can only assign waypoints a cost of 0 or 1 depending

on whether the waypoint intersects with an obstacle.

This can result in paths that are in very close con-

tact to an obstacle when safer alternatives exist. For

example, in Figure 5, the vehicle is initially driving

in the leftmost lane, so it continues to drive in that

lane until the last waypoint that is not in contact with

the obstacle, and then makes a lane switch to the mid-

dle lane right before encountering the obstacle. All

waypoints in the path have a cost of 0, so the vehicle

moves at the maximum allowed speed. In this sce-

nario, the selected path is unfavorable as it moves the

vehicle dangerously close to an obstacle at possibly

high speeds.

We can represent the costs in the grid of waypoints

in Figure 5 by the following 2D matrix:

W =







1.0 0.0 0.0

0.0 0.0 0.0







(3)

In order to achieve a cost gradient, a discrete 2D con-

volution is used. This kernel is used in the simulation:

K =







0.1 0.5 0.1

0.2 1.0 0.2

0.2 0.5 0.2

0.1 0.3 0.1

0.0 0.2 0.0

0.0 0.1 0.0







(4)

is the center of the kernel. For edge cells, zero

padding is used. All values of the output matrix are

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

434

bound to [0, 1]. The kernel values are selected to in-

troduce a cost to the waypoints leading to the obsta-

cle, the ﬁrst waypoint ahead of the obstacle, and the

lanes adjacent to the blocked lane. Changing these

values effectively changes the obstacle avoidance pro-

ﬁle of the vehicle. For example, increasing the val-

ues will cause the vehicle to decelerate more sharply

when approaching an obstacle, favoring safety versus

comfortability. The matrix size determines the dis-

tance from the obstacle at which the vehicle starts the

avoidance maneuver.

Figure 6 shows the generated path after using the

costs from the W ∗ K matrix on the waypoint grid.

Figure 5: Generated path

in a 3-lane road with

a static obstacle, without

cost smoothing.

Figure 6: Generated path

after cost smoothing.

3.4 Path Finding

The best path in a lane waypoint grid is modeled as

a shortest path problem. As shown in Figure 3, lane

waypoints can be modeled as a directed graph where

each node connects to the next node in the same lane,

and the next nodes in the left and right lanes signify-

ing a lane change.

The D* lite algorithm (Koenig and Likhachev,

2002) is used to ﬁnd the shortest path between the

current waypoint and any of the goal waypoints. Goal

waypoints are the ﬁnal set of lane waypoints in the

loaded section of the ofﬂine map.

To decrease the number of lane changes, a con-

stant value is added to the traversal cost when making

a lane change. As a result, the planner will not make a

lane change unless the difference between the cost of

the current lane waypoint and the target lane waypoint

is greater than a certain constant value.

3.5 Vehicle Trajectory

An implementation of the pure pursuit algorithm

(Coulter, 1992) is used to steer the vehicle along the

generated path. Pure pursuit ﬁnds a curvature that

moves the vehicle from its current position to a goal

position. The goal position is calculated by construct-

ing a circle with a deﬁned search radius centered

around the vehicle position. Then, a straight line is

constructed between each two consecutive waypoints.

The intersection point between the search circle and

the ﬁrst line that intersects it is set to be the goal way-

point.

The search radius is typically a function of the cur-

rent vehicle speed. The changes in vehicle heading

become steeper as the search radius decreases. For

purposes of the simulation, it is set to the vehicle

speed multiplied by 2.5, as this value was found in

testing to result in smooth steering curves while not

deviating too far away from the waypoint plan during

turns.

Figure 7: Pure pursuit target construction.

The goal is to ﬁnd the radius of the circle that joins the

vehicle position V with the target point T , such that

the chord length from V to T is equal to the search

radius l. The radius can be expressed as: (Coulter,

1992)

r =

(5)

The arc joining V and T with radius r is the ﬁnal in-

tended trajectory of the vehicle.

4 PERFORMANCE EVALUATION

4.1 Simulation Experiments

The LGSVL Simulator provides an environment for

testing autonomous driving functionalities in a 3D en-

vironment. The simulator integrates with the ROS

platform, providing a vehicle model which can be

controlled using ROS commands, and simulates sen-

sors typically used in autonomous driving such as

camera, LiDAR and GPS.

Path Planning for Autonomous Vehicles with Dynamic Lane Mapping and Obstacle Avoidance

435

The simulator was used to test the static and mov-

ing obstacle avoidance capabilities of the proposed

system by two means: Simulating a static obstacle

ahead of the vehicle position in the same driving lane,

and simulating a moving obstacle moving laterally in

front of the vehicle (i.e. a person crossing the road).

The distance from the obstacle to the vehicle and the

deceleration of the vehicle are evaluated.

The test route is a straight 4-lane road section 556

meters long, with a single turn. The target speed for

the test was set to 25 km/h. Higher speeds were not

tested due to technical constraints of the simulation

environment.

4.1.1 Results of the Simulation Test

During the test, the vehicle managed to stay within a

safe distance from all introduced obstacles.

Figure 8: Vehicle path within a point cloud map of the en-

vironment.

In the static obstacle tests, the vehicle initiated a lane

change approximately 14 meters away from the obsta-

cle. Figure 9 shows the maneuver made by the vehi-

cle as the obstacle comes into the look-ahead distance

of the planner. The vehicle changes to the ﬁrst lane

from the third lane, and continues driving in the third

lane until encountering the next obstacle. The reason

for the double lane change is due to the conﬁgura-

tion of the convolution matrix described in Section

3.3.3, which assigns a cost to the lanes adjacent to

the obstacle. Since the vehicle does not drive into the

higher cost region (shown as the yellow and orange

waypoints in Figure 9), the vehicle’s driving speed

stays constant at 25 km/h for the duration of the lane

change.

Figure 9: Vehicle trajectory at different frames during static

obstacle avoidance, showing the waypoint plan (blue line)

and the pure pursuit trajectory (white arc).

The forward and lateral acceleration (shown in

Figure 10) of the vehicle was recorded during the

maneuver. The lateral acceleration reaches a peak

value of 2.88 m/s

(0.29g) when initiating the lane

change, and then reaches 1.84 m/s

(0.19g) in the op-

posite direction as the vehicle returns to its forward

position. To ensure the lateral stability of the vehi-

cle in lane changes the lateral acceleration should not

be above 0.4g (Sun and Wang, 2020), which the pro-

posed model does not exceed.

Figure 10: Graph of the forward (blue) and lateral (orange)

acceleration of the vehicle during static obstacle avoidance.

In the moving obstacle tests, a moving obstacle mod-

els a pedestrian crossing the road. Since the direction

of movement of the obstacle is lateral to the road, all

lines are blocked (shown in Figure 11), and the vehi-

cle needs to stop completely. The vehicle reaches a

full stop 10 meters away from the obstacle’s line of

motion, and then begins to accelerate after the obsta-

cle passes the vehicle’s lane.

Figure 11: Waypoint map during a moving obstacle test.

Figure 12 shows the acceleration of the vehicle as it

encounters the moving obstacle, while the vehicle is

stopped, and as it continues its route.

Figure 12: Graph of the forward acceleration of the vehicle

during moving obstacle avoidance.

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

436

4.2 Field Test

A live demo of the path planning modules was per-

formed using a modiﬁed electric golf cart. Data pro-

cessing and vehicle control is done locally on a com-

puter running the ROS platform. The steering column

and throttle actuators of the vehicle are electrically

connected to an Arduino controller, which receives

commands from a ROS node running on the vehicle

computer through a serial connection.

The steering angle is set to the curvature of the

pure pursuit arc described in Section 3.5. The throttle

value is initially set to 0, and a change to the throt-

tle value is calculated every interval which is propor-

tional to the difference between the target and current

velocities. A full stop of the vehicle is performed by

setting the throttle value to 0. Engine braking assists

in stopping the vehicle in a distance that is sufﬁciently

short for purposes of the demo.

4.2.1 Mapping

A point cloud map of the testing area was created

using LiDAR mapping, and waypoints were mapped

tracing the testing route. The waypoints were placed

1 meter apart. The route is approximately 175 meters

in length. The route includes a straight section, then

a short slightly uphill climb, followed by a series of

sharp turns. The target speed for the route was set

to 7 km/h as a safety precaution, due to the multiple

turns in the path and to minimize the risk of collision.

The route has a single lane due to space constraints of

the testing area.

4.2.2 Results of the Field Test

Two trials were performed: A ﬁrst trial where the ve-

hicle makes a full route with no obstacles, and a sec-

ond trial with a simulated pedestrian crossing event

once the vehicle reaches the target speed. The vehi-

cle’s position, heading and velocity data was recorded

for the duration of the two runs.

In the ﬁrst run, the vehicle managed to maneu-

ver around the sharp corners, however it had prob-

lems maintaining its heading in the straight sections,

as shown in Figure 13. This was found to be due to

inaccuracies related to the steering controller of the

vehicle for small steering angles (up to 10 degrees).

Figure 14 shows the vehicle speed for the dura-

tion of the ﬁrst trial. The vehicle takes 10 seconds to

accelerate to the target speed of 7 km/h. The speed

slightly ﬂuctuates between 6 and 8 km/h (1 km/h de-

viation) for several seconds following accelerating.

This can be resolved by further tuning of the throttle

Figure 13: Actual vehicle path of the test route (red line)

versus the waypoint map (blue line) within a point cloud

map of the ﬁrst trial.

(a) Vehicle speed

(b) Vehicle acceleration

Figure 14: Vehicle speed and acceleration graphs for the

ﬁrst trial (no obstacles).

controller of the vehicle. The speed drops at approx-

imately t = 58 s when the vehicle reaches the uphill

part of the route, then the vehicle slowly accelerates

back to its target speed.

The acceleration of the vehicle reaches a maxi-

mum of 0.25 m/s

when accelerating from a stopping

position to the target speed, and a minimum of -0.5

m/s

when stopping at the end of the route.

For the second trial, three pedestrian crossing

events were initiated at t = 11 s, 41 s, and 59 s dur-

ing the test. The speed and acceleration of the vehi-

cle (shown in Figure 15) were recorded for the dura-

tion of the trial. In each event, a simulated obstacle

was placed 7 meters ahead of the current position in

the path of the vehicle and removed several seconds

later. The distance between the vehicle and the ob-

stacle position was recorded, shown in Figure 15 (b).

The vehicle starts to decelerate as soon as the obstacle

is detected and manages to stop an average of about 3

meters away of the obstacle in the three events.

Path Planning for Autonomous Vehicles with Dynamic Lane Mapping and Obstacle Avoidance

437

(a) Distance between vehicle and obstacle in meters

plotted against the current vehicle speed in km/h

(b) Vehicle acceleration

Figure 15: Vehicle speed and acceleration graphs for the

second trial (obstacle testing).

5 CONCLUSIONS

In this paper, we present a novel path planning ap-

proach with static and moving obstacle avoidance,

and dynamic lane mapping from road width calcu-

lated from real-time drivable area data. We evaluate

our approach by means of a simulation test, as well

as a real world demo by implementing and running

the model on a vehicle modiﬁed to allow autonomous

driving functionalities.

The proposed model was tested on speeds of up to

25 km/h. Thus, further testing needs to be performed

in order to verify the validity of the model with higher

speeds. A limitation in the approach is that the con-

volution matrix described in Section 3.3.3 is static, so

the separation distance between the vehicle and sur-

rounding obstacles does not change depending on the

driving speed. Such limitation would pose safety risks

when driving at high speeds. Therefore, the convolu-

tion approach needs to be adjusted with high speed

driving taken into consideration. Moreover, the pro-

posed approach needs to be improved to ﬁnd the in-

tersection between obstacles and waypoints, as it may

not cover cases where an obstacle is positioned in cer-

tain positions of the road outside the waypoint region

but still posing a risk to the vehicle. Finally, a conﬁr-

mation window for the drivable area needs to be im-

plemented in order to account for short variations in

drivable area width and the number of lane waypoints.

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