DYNAMIC OBSTACLE AVOIDANCE FOR AN ACKERMAN

VEHICLE

A Vector Field Approach

Tommie Liddy, Tien-Fu Lu

School of Mechanical Engineering, The University of Adelaide, SA 5005, Adelaide, Australia

David Harvey

Aerospace Concepts, 17 Yallourn St, ACT 2609, Fyshwick, Australia

Keywords: Autonomous navigation, Vector field, Obstacle avoidance, Ackerman vehicle, AGV.

Abstract: A vector field navigation system was shown to avoid dynamic obstacles and reach a goal with a pre-

specified position and heading using a simulated Ackerman vehicle. The navigation system was divided

into two distinct vector fields, an environmental field which was created for goal oriented navigation and

obstacle field which was designed for obstacle avoidance. Discussed in this paper were the methods of

obstacle avoidance and combining the two fields of the navigation system. The obstacle avoidance method

created a rotational vector field centred on a single obstacle. Algorithms were created to select the obstacle

that would be the centre of the field and the direction of rotation of the field. A parameter based method

was used to combine the obstacle field and the environmental field. A simulation workspace was created to

show the navigation behaviours created by combining these methods and a sample of these results were

presented in this paper.

1 INTRODUCTION

The use of vector fields can be a simple and

mathematically low cost method of both navigation

and obstacle avoidance for an autonomous vehicle

(Borenstein, 1989). Many methods use multiple

vector fields to produce a navigation strategy. The

typical form of this approach is to have one vector

field represent the desired motion of an unobstructed

vehicle and another represent the motion required

for obstacle avoidance (Xiao 1998; Ge, 2002; Lui,

2006). These vectors are than added together to

achieve all navigation goals. This method can

produce a local minimum which will effectively stop

a vehicle from reaching its goal and the unstable

movement of a vehicle (Koren 1991; Lui 2006).

There are methods that produce a single field

acting to avoid obstacles and reach a desired goal

(Kim, 1999; Loizou 2003; Lindermann 2006).

These approaches offer benefits such as smother

travel but rely on prior knowledge to create the field.

If no prior knowledge of obstacles and navigational

boundaries are available these methods cannot be

applied to a real time dynamic environment.

Through this paper a navigation system will be

introduced that allows an autonomous vehicle to

avoid dynamic obstacles in real time. A multiple

vector field approach was taken to create this

navigation system. An Environmental vector was

created using a method outlined in Liddy 2007. An

obsrtacle vector was created using the configuration

of the obstacles the mobile platform had detected as

well as the relative vehicle and waypoint positions.

A method described for combining these two vector

fields will also be shown, building apon the

algorithms presented in Liddy 2008.

The results presented in this paper will show that

this method was able to produce a navigation

strategy allowing an Ackermann vehicle to

successfully navigate a dynamic scenario. The

inherant limitations of the system will also be

examined. Primarily the ability of the navigation

method to cope with obstacles moving at roughly the

same speed as the vehicle.

Liddy T., Lu T. and Harvey D..

DYNAMIC OBSTACLE AVOIDANCE FOR AN ACKERMAN VEHICLE - A Vector Field Approach.

DOI: 10.5220/0003383100930098

In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 93-98

ISBN: 978-989-8425-75-1

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

2 SIMULATION ENVIRONMENT

Experiments were conducted in a simulated

environment. A mathematical model (Liddy, 2007,

Hashim, 2009) was used to represent the mobile

platform with dimensions shown in Table 1 and

Figure 1. The environment in which the simulated

vehicle travelled was considered flat in the X-Y

plane. Waypoints were used as navigational

markers and consisted of a position in the X-Y plane

and a heading

()

WPWPWP

,, . Each obstacle

consisting of a array of positions in the X-Y plane, a

length and width along the x and y axis and a

velocity

()

OBOBOBOBOB

vwlyx ,,,

. An obstacle

would move from one point in the position array to

the next at v

. For simplicity the obstacles were all

made to have the same dimensions for all tests

=310mm w

=400mm) and the velocity of all

obstacles was set to the same value for each

individual test.

Table 1: Vehicle dimensions and properties.

Property Symbol Value

Vehicle length L 300mm

Vehicle width W 300mm

Maximum steering angle δ 25˚

Maximum steering rate



30˚/sec

Vehicle velocity V 1000mm/sec

Figure 1: Dimensions of the simulated vehicle.

A sensor model was also employed to simulate

the ability of the mobile platform to detect obstacles.

The model was designed to sort the obstacles present

in the navigation environment as either visible or not

visible. An ideal model of a planar laser scanner

was used to achieve this. The model was given a

sensor range of 3000mm (D

SEN

=3000mm) and a

sensor angle of ±90˚ from the vehicle’s X-axis

(θ

SEN

=90˚). These characteristics (D

SEN

and θ

SEN

)

were used to form a visible region in front of the

vehicle. All obstacles in that region were considered

to be detectable and were made visible to the mobile

platform. This included any dynamic obstacle,

however information regarding their trajectory was

not made known the mobile platform. The mobile

platform stored the last known position of obstacles

when they were no longer in the visible region. The

obstacles were assumed to remain in that position

unless that space was shown to be clear.

The simulation tests were run as real time

navigational scenarios. The position of the vehicle

and dynamic obstacles were updated at 250ms

intervals. The mobile platform was given no prior

knowledge of the obstacles in the environment only

a starting position and waypoint. Each test was

initialised with the vehicle at a position of (0mm,

0mm) with a heading of 0˚. The criteria for

completing a test were that the vehicle must be

within 1000mm of the goal and be moving away

from said goal.

3 OBSTACLE VECTOR FIELD

The objective of the obstacle vector field was to

produce a force which acted on the mobile platform

in such a way that caused it to avoid an obstacle.

The blend function, the obstacle field rotational

direction and the pivot block determine the

characteristics of the navigation system (Liddy et al.,

2008).

3.1 Blend Function

The blend function producd a weighting value which

acted to combine the environmental vector field

) and the obstacle vector field (O

) into the

navigational vector field (N

) as shown in

Equations (1), (2) and (3).

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

+= 1,0,maxmin

iii

OFFSBf

(1)

()

∏

⇒

−−=

BfBf

(2)

(

)

VFmVFmVF

OBfEBfN *1*

11 ⇒⇒

−

(3)

Each blend function used a single parameter

from the navigation system (x

) with three constants

selected to shape the function (N

, OFF

and S

The constant N

was used to normalise the

navigation variable. The OFF

constant was used to

offset the function, specifically to select the point

where Bf

becomes greater than zero. S

was used to

control the slope of Bf

which, with the use of OFF

was used to select the point where Bf

became equal

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

to one. Each blend function was created to address

scenarios in which obstacle avoidance would be

desired

For a real time navigation system it was seen that

obstacle avoidance behaviours would be required

when an obstacle was in front of a vehicle or close to

a vehicle. To address this two blend functions were

created as shown in Table 2.

Table 2: Blend function parameters.

OFF

The minimum distance

between any obstacle and

the mobile platform.

3000mm -0.25 2

The minimum absolute

angle created between any

obstacle, the mobile

platform and the waypoint

-0.25 2

3.2 Pivot Block

The pivot block was the obstacle selected as the

centre of the obstacle vector field. This obstacle was

selected based the obstacle position relative to the

vehicle. The pivot block was classified as the

nearest known obstacle located in front of the

vehicle. The example shown in Figure 2 would have

as the pivot block even if D

because OB

would be considered to be behind the vehicle

(θ

>90˚).

Figure 2: Selection of the pivot blot, example.

3.3 Obstacle Vector Field Rotational

Direction

A vector was produced at an obstacle as a rotational

field. Navigation behaviours were developed by

basing the direction of rotation of that field on

various parameters. These behaviours could be

summarised as follows, if the vehicle was

confronted by an obstacle it was required to move

around it on what was considered the clearer side.

This was done by selecting the rotational direction

that required the vehicle turn as little as possible.

To implement this behaviour a angled histogram

was used to determine where free space was and

where obstacles blocked the immediate path. An

angle bin of 20˚ was selected and the histogram was

created over 180˚ (±90˚ from the vehicle X-axis). If

any known obstacle occupied a particular bin that

bin was set to one, otherwise it was set to zero.

Figure 3: The angled histogram with 9 bins of 20˚;

Example 1 shows the histogram when there are obstacles

clustered to the right and directly in front of the vehicle;

Example 2 shows the histogram when there are obstacle to

either side of the vehicle.

A graphical representation of the histogram is

shown in Figure 3 with two examples representing

states which could occur during run time. In the

examples shown in this figure a grey box

represented a bin was set to one and the dotted

outlined indicated the bin that contained the pivot

block. The rotational direction was selected based

on two parameters. The closest unoccupied bin to

the central bin in the histogram, and the bin

containing the pivot block. If the bin containing the

pivot block was higher than the closest unoccupied

bin to the centre the rotation direction was clockwise

(Example 1) and if the opposite was true it was anti-

clockwise (Example 2).

DYNAMIC OBSTACLE AVOIDANCE FOR AN ACKERMAN VEHICLE - A Vector Field Approach

Figure 4: Vehicle avoiding a side on collision with an elongated obstacle with a waypoint at (6000,0,0); V = 1000mm/s;

= 700mm/s: (a) time = 2.5 sec (b) time = 4.25 sec (c) time = 5.75 sec (d) time = 10.25 sec.

4 RESULTS

A series of experiments were run to show the

capabilities of the combined navigation and obstacle

avoidance methods discussed in Liddy et al. 2007;

2008 when applied to a dynamic environment.

Experiments were run on a simulation platform

under real time conditions. Initial tests focused on

the possible limitations of dynamic obstacle

avoidance with regards to vehicle and obstacle

relative speeds (Section 4.1). Further results show

the navigation traits when acting within those

limitations (Section 4.2). All results show the

vehicle and obstacle paths up to a specified time.

The desired navigation vector was attached to the

vehicle’s path at regular intervals. A blue vector

represents a blend factor of one, whereas a red

vector represents a blend factor between one and

zero.

4.1 Navigation Limitations

The tests shown in Figure 4 and 5 illustrate scenarios

where comparative speed between vehicle and

obstacle were an issue. The possibility of a side on

collision and a head on collision were examined in

these scenarios.

Under a specific condition a side on collision was

found to be unavoidable. For this collision to occur

the vehicle must initially encounter the obstacle

when a large portion of the obstacle was on the side

of the vehicle the obstacle was coming from. This

configuration was met when the vehicle encountered

the obstacle as shown in Figure 4 (a). At this point it

can be seen that the navigation algorithm steered the

vehicle around the obstacle in the direction the

obstacle was moving. Figure 4 (b) and (c) show that

the vehicle moved parallel to the obstacle and then

attempted to pass in front of the obstacle’s path.

This motion allowed the obstacle to close the

distance to the vehicle. It was found that an obstacle

speed approximately 70% of that of the vehicle was

the maximum allowable without a collision

Figure 5: Vehicle avoiding a head on collision with a

single obstacle, waypoint at (6000,0,0); V = 1000 mm/s;

= 900 mm/s: (a) time = 2.5 sec (b) time = 6.5 sec.

ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

Figure 6: Vehicle avoiding multiple obstacles in a sparsely cluttered environment with a waypoint at (20000,0,0);

V = 1000mm/s; V

= 350mm/s: (a) time = 6.25 sec (b) time = 8.75 sec (c) time = 12.5 sec (d) time = 16.75 sec.

The scenario presented in Figure 5 shows

another situation where a collision was likely to

occur. The limiting factors for this scenario were the

speeds of both the vehicle and the obstacle and the

visible distance the sensor model allowed for

obstacle detection. Essentially, the mobile platform

was required to move out of the way of the obstacle

in the time between when it identified the obstacle

and when the obstacle would close the distance to

the vehicle. Results shown indicate the maximum

speed of a single obstacle where collision did not

occur was 900mm/s as shown in Figure 5. For

larger obstacles this value would be diminished.

4.2 Dynamic Obstacle Avoidance

To examine the behaviour of the navigation

algorithm the mobile platform was placed in several

scenarios which involved multiple static and

dynamic obstacles. All dynamic obstacles were set

to move at the same speed (350 mm/s). This speed

was within the maximums obtained while analysing

the obstacle avoidance limitations (Section 4.1).

The results obtained in doing so showed the traits

inherent in the navigation method.

A scenario was run showing the mobile platform

passing through an area populated with

independently moving obstacles, shown in Figure 6.

In this scenario the vehicle initially moved directly

towards the waypoint until it encountered a set of

obstacles at 6.25 seconds, shown in Figure 6 (a). At

this instance it can be seen from the red vectors

present that the obstacle avoidance algorithm began

to influence navigation. The algorithm steered the

mobile platform to the clearer side of the area the

sensor system could see. This behaviour was

repeated a second time at 12.5 seconds, shown in

Figure 6 (c). Although in one instance the vehicle

moved in front of the obstacle and in the other it

moved behind this behaviour was still consistent

when viewed through the navigation algorithm.

While avoiding one set of obstacles the mobile

platform encountered a second set, this can be seen

in Figure 6 (b). This second encounter elongated the

duration the obstacle vector field had control of the

vehicle. During that period the pivot block was

required to switch between the four obstacles

present. The obstacle vector field and blend factor

were altered with each switch ensuring the mobile

platform avoided all obstacles.

The example presented in Figure 7 shows the ability

of the navigation system to identify gaps and steer

the vehicle through them. In Figure 7 (a) it can be

seen that the vehicle encountered a dynamic obstacle

while avoiding a set of static obstacles. The vehicle

was forced towards the dynamic obstacle due to the

structure of the static obstacles. At this point the

vehicle was able to identify a gap between the

obstacles and steer the vehicle towards it. This

behaviour indicated that when there was sufficient

space available the vehicle would pass through a gap

if it were the best option available. This behaviour

can be seen again between the 6 and 8.25 second

mark, Figure 7 (b) and (c), as the vehicle passed

between a static wall of obstacles and a dynamic

obstacle. In both instances the gap was selected

because it would lead the vehicle into clear space

and away from the obstacles directly in front of it.

DYNAMIC OBSTACLE AVOIDANCE FOR AN ACKERMAN VEHICLE - A Vector Field Approach

Figure 7: Vehicle static and dynamic obstacles in a structured environment with a waypoint at (10000,0,0);

V = 1000mm/s; V

= 350mm/s: (a) time = 4.5 sec (b) time = 6.0 sec (c) time = 8.25 sec (d) time = 12.5 sec.

5 CONCLUSIONS

Presented in this paper was a navigation algorithm

developed to operate in a dynamic environment. A

method was outlined showing the use of a blend

function and pivot block (defined in Sections 3.1 and

3.2) with an existing method of vector creation to

produce a navigation algorithm. Results gathered

using this method were shown to have measurable

limitations under specific circumstances. When

operated within these limitations the navigation

algorithm was shown to be able to safely control a

mobile platform in a dynamic environment.

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ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics