A MONOCULAR OCCUPANCY GRID FOR LOCAL

WMR NAVIGATION

Lluís Pacheco, Xavier Cufí

Technical School, Girona University, Av. Luís Santaló s/n, Girona, Spain

Ningsu Luo, Javier Cobos

Institut de Informàtica i Aplicacions, Girona University, Av. Lluís Santaló s/n, Girona, Spain

Keywords: Autonomous mobile robots, Computer vision, Path planning, Obstacle avoidance, Reactive navigation.

Abstract: This work introduces a new methodology to infer environment structure by using monocular techniques.

The monocular field of view is constrained to the vicinity of the mobile robot. The cooperative strategy

proposed combines DFF and qualitative structure techniques to obtain environment information. The

remarkable features of the strategy presented are its simplicity and the low computational cost. In this way,

a simplified DFF method, which uses only one frame, has been implemented; hence, scenario information

can be achieved when homogeneous radiance background constraint is accomplished. Further structure

analysis is developed by computing qualitative structure through time integration series of acquired frames;

within a tessellated probabilistic representation consisting in a local occupancy grid framework.

Furthermore, the camera pose knowledge is used to correlate the different overlapping image zones.

Moreover, time integration of the monocular frames allows a larger environment description suitable for

WMR local path planning. Hence, the reported work can be used in obstacle avoidance strategies or reactive

behaviours for navigation towards the desired objective.

1 INTRODUCTION

Perception of the environment is based on the sensor

system measurements that provide distances and

structure knowledge. This essential task could be

accomplished by different range systems like

ultrasonic sensors, laser rangefinders, or vision

based systems. All these sensors have their

advantages and disadvantages. However, computer

vision based methods, are one of the most attractive.

Therefore, they have many interesting advantages

that can be summarized as follows: the falling prices

of devices and richer information compared with the

other traditional ranging devices. In this way the

increasing capabilities of the personal computers,

offer an interesting range of real time applications.

Perception systems based on camera devices have

attracted robotic research due these interesting

features. Thus, machine vision systems have used

some features of eyes, such as stereopsis, optical

flow or accommodation, as meaningful clues. SVS

(stereo vision systems), OFM (optical flow methods)

and DFF (depth from focus) are all methods that

permit 3D scene recovery. Studies comparing SVS

and DFF are reported in (Schechner and Kiryati,

1998). The results show that while SVS has greater

resolution and sensitivity, DFF has greater

robustness, requires less computational effort and

can deal properly with correspondence and

occlusion problems. The need for several images of

the same scene, acquired with different optical

setups, may be considered as a significant drawback

in using DFF methods in major robotic applications.

The scientific community has proposed the use of

special cameras, such as a multi-focus camera that

acquires three images with three different focus

positions (Hiura and Matsuyama, 1998). However,

other proposals were developed due to a lack of

multi-focus commercial cameras. The use of DFF in

WMR (wheeled mobile robots) has been reported in

(Nourbakhsh, 1997); in which Noubakhsh used three

cameras with almost the same scene to achieve

robust and efficient obstacle detection.

This work presents a new cooperative monocular

strategy; where DFF and QSM (Qualitative

425

Pacheco L., Cufí X., Luo N. and Cobos J. (2009).

A MONOCULAR OCCUPANCY GRID FOR LOCAL WMR NAVIGATION.

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 425-432

DOI: 10.5220/0002206704250432

 SciTePress

Structure Methods) are combined. Thus, one bit

depth can be obtained using the DFF methodology

as well as a set of multi-resolution focus thresholds,

when homogeneous radiance background constraint

is accomplished. However, when homogeneous

radiance constraint fails, we propose to use QSM

over discrepancy areas in order to infer environment

structure by using an occupancy grid framework.

Therefore, the main contributions of this research

are to propose the occupancy grid as a suitable

structure in order to infer qualitative obstacle

structure and obtaining larger scenario descriptions.

The results depicted are directed towards real

applications by using the WMR PRIM, which

consists of a differential driven one with a free

rotating wheel (Pacheco et al., 2008). The

experiments are orientated so as to obtain a local

map in the robot’s neighborhood that can be used to

plan navigation strategies.

This paper is organized as follows. In Section 1,

the main ideas and research objectives are presented.

Section 2 introduces the DFF methodology as well

as the algorithms and results implemented. Section 3

depicts the QSM concept and the related algorithms

used. In this way, the local occupancy grid

framework is also formulated as a way for time

integrating the acquired frames. In Section 4, the

experimental preliminary results are drawn by using

the mobile platform PRIM. In Section 5 the

conclusions and future research are presented.

2 THE CONSTRAINED DFF

SYSTEM DESCRIPTION

This section briefly introduces the DFF

methodology. The algorithms implemented as well

as their results are also depicted by using the

available WMR platform. Its significant contribution

is the use of a single image to obtain environment

information.

The DFF techniques use an image collection of the

same scene acquired at different focus positions.

Thus, the camera system PSF (point spread function)

for unfocused object points produces blurred image

points. The PSF frequency domain space transform

representations arise in a first order Bessel OTF

(optical transfer function), where its main lobe

volume can determine the FM (focus measure)

expressed as:

(

)

∫∫

= . ,

νωνω

ddIM

(1)

where I

denotes the image considered, ω and ν

represent the frequency components. Efficient

energy image measures have been proposed as FM

(Subbarao et al, 1992). Nayar has proposed a

modified Laplacian that improves the results in some

textures (Nayar and Nakagawa, 1994). The 3D scene

map and passive auto-focus consumer camera

systems are interesting applications solved by the

DFF. Recovering the 3D information from DFF

methods is known as SFF (shape from focus) (Nayar

and Nakagawa, 1994).

2.1 The DFF Monocular Algorithms

The algorithms of the machine vision system

implemented are based on important assumptions

that are generally obtained in normal indoor

scenarios, but also in many outdoor scenarios. These

constraints are flat and homogenous energy radiance

from the floor surface and experimental knowledge

of the focus measurement threshold values. Two

important aspects, image window size and camera

pose, should be considered. The size of windows

should be big enough to receive energy information.

For example, in the work of Surya, images of

150x150 pixels were used, and the focus measures

were computed in 15x15 pixel regions (Surya,

1994). The camera pose will set the scenario

perspective and consequently the floor position

coordinates that should be used in the WMR

navigation strategy. Figure 1 shows the robot and

camera configuration considered in this work,

where

and

are angles of the vertical and

horizontal field of view and the tilt camera pose

respectively. The vertical coordinate of the camera is

represented by H. The robot coordinates

corresponding to each pixel can be computed using

trigonometric relationships and the corresponding

knowledge of the camera configuration (Horn,

1998). Using trigonometric relationships, the flat

floor scene coordinates can be computed as follows:

()

≤≤=Δ

Δ+−=

Δ+−

±=

2K0

2tan

tan

2cos

ααϕ

(2)

and K

are parameters used for covering the

discrete space of the image pixels. Thus, R and C

represent the image resolution through the total

number of rows and columns. It should be noted that

for each row position corresponding to scene

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426

coordinates Y

, there are C column coordinates X

i,j

The above equations provide the available local map

coordinates when no obstacle is detected. The

algorithms used are explained in the remainder of

this subsection. The multigrid representation using

low-pass filtering processes can improve the surface

radiance homogeneity. Scale space representations

can reduce the search space, increasing the

computation performance (Gonzalez and Woods,

2002). Therefore, a Gaussian filter is applied to the

frames acquired in PAL format, at 768x576 pixels.

Three decreasing resolution levels have been used

with picture sizes of 384x288, 192x144 and 96x72.

The average image brightness is also computed. In

order to achieve greater robustness against changes

in lightness, brightness normalization is performed

(Surya, 1994). The image energy is computed, over

3x3 windows at the top level of the scale-space,

using the modified Laplacian method:

() ()

(

)( )

()( )( )

1,1,,2

1,1,2,

+−−−

++−−−=

yxiyxiyxi

xiyxiyxiyxML

(3)

where i(x,y) represents the corresponding pixel value

at spatial coordinates (x,y). The 96x72 scale-space is

decreased using a 9x7x2 array, where each cell

represents the Laplacian mean value and the

corresponding standard deviation mean computed

over 10x10 pixel patches. Another interesting

statistical parameter that has been used is the

standard deviation, which relates to the homogeneity

of the floor energy values. The 9x7x2 array is

explored, from top to bottom; floor segmentation is

carried out, using both energy and standard

deviation thresholds.

Figure 1: The robot PRIM and the monocular camera

configuration. Where α is set to 37º, β (horizontal angle)

of 48º, H set to 109cm, and a tilt angle of 32º.

2.2 One Bit DFF Experimental Results

The floor threshold has been experimentally

computed by averaging several floor images

acquired in our lab environment with different kinds

of illumination (from 200-2000 lx). Light

illumination can change from 2000 lx when light

from the sun is clearly present where there is

sunlight through the windows, to less than 200 lx in

the darker corridor zones. Figure 2 depicts high

resolution (130x130 pixel windows) corresponding

to different floor images used to compute focus

measurement thresholds where the floor texture is

clearly visible. It is in the locality of those points

where the information about radiance is obtained.

Hence, the results obtained with the available

experimental set up show the decreasing values

when the distance between the camera and the floor

is increased. A more complete description of the

energy floor radiance measures obtained for each

9x7 visual perception row is shown in (Pacheco et

al., 2007); in which the image perspective emerges

from a set of multi-resolution thresholds as a

function of the camera distances.

Figure 2: Fragments of high resolution floor images

(768x576 pixels under different light conditions

corresponding to 300, 800, 1400 and 2000 lx, respectively.

Figure 3 shows the modified Laplacian energy

and standard deviation values using 9x7 and 96x72

space-resolutions, when typical indoor obstacles are

presented. It is shown that 9x7 space resolutions can

detect radiance discontinuities but because there was

Figure 3: (a) Image with obstacles, 96x72; (b) Modified

Laplacian measures; (c) 9x7 Modified Laplacian mean

values; (d) ) 9x7 standard deviation mean.

A MONOCULAR OCCUPANCY GRID FOR LOCAL WMR NAVIGATION

427

a great lack of resolution manifested through soft

slopes. Thus, it is necessary to use a fine space-

resolution to attain the sharper edges. In this work,

9x7 resolutions are used to detect the local patches

where obstacle segmentation is computed within

96x72 space resolution.

Despite the good results achieved, some further

improvements should be considered. Hence, when

radiance floor discontinuites occur they can be

considered obstacles (false positives in some cases).

Therefore in next section OFM is introduced, within

the occupancy grid framework, to improve the one

bit DFF methodology.

3 QUALITATIVE STRUCTURE

METODS AND OCCUPACY

GRID

The camera pose and local field of view will set the

QSM algorithms reported in this section. The

different optical flow quantitative approaches are

generally based on two classical feasible

assumptions, which are BCM (brightness constancy

model), and optical flow smoothness. Thus, image

motion discontinuities are due to the depth and

motion discontinuity boundaries. Hence, there are

places where image flow changes are suddenly

useful as image segmentation clues, but can cause

problems such as optical flow estimation clusters.

Therefore, suggestions made to compute the

algorithms over small neighborhoods, or region-

based matched methods have turn on. Combining

local and global optic flow differential methods have

been proposed as a way to share benefits from the

complementary advantages and short-comings

(Bruhn, 2002).

The occupancy field can be depicted by a

probability density function that relates sensor

measures to the real cell state. The tessellated

probabilistic representation has been widely adopted

by the scientific community in navigation or

mapping issues. Indoor applications research has

been mainly concentrated on SLAM (simultaneous

localization and mapping) issues (Thrun, 2002).

Their use allows sensor fusion or multiple layer

representations to segment dynamic objects (Coue,

2006). The perception system used, in this work,

consists in monocular and odometer system data.

The use of these systems in SLAM is reported in

(Cumani et al., 2004).

The main difference of the research depicted in

this paper, as compared with Cumani research, is the

occupancy grid use that allows integration of

multiples frames without constraining their number.

Furthermore, it is obtained a local map description

suitable for navigation. Thus, the occupancy grid

developed research increase the camera narrow field

of view, which provides just the vicinity of the robot

where floor only is expected to be found. Moreover,

the floor model is also proposed as a contribution in

order to build the 2D occupancy grid; hence obstacle

binary results are time integrated within the local

occupancy grid framework by considering such

model. The obstacle structure could be inferred by

considering optical flow magnification change

discrepancies from the floor model.

3.1 The Local QSM Approach

In the present research the camera field of view

depicts only the vicinity of the WMR. Perspective

projection, as shown in Figure 4, should be assumed.

Figure 4: Camera system producing an image that is a

perspective projection of the world.

Introducing the coordinate system, where z

coordinates are aligned to the optical camera, and

the xy-plane is parallel to the image plane, the image

P’ corresponding to the point P of a scene object is

given by the following expressions:

sec'

cos

'cos''

sec

cos

rrz

==⇒=

−=−=⇒

=−==

(4)

Where z’ in the distance between image plane

and the camera lenses, and x’ and y’ are the image

coordinates. The object point coordinates, referred to

the optic center O, are given by P= (X, Y, Z), being r

de distance between P and O and

the angle. The

ratio of the distance between two points measured in

the image plane and the corresponding points

measured in the scene is called magnification m.

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()()

() ()

′

Δ+Δ

′

+Δ

′

(5)

For reduced field of views when the optical rays

are parallel to the optical axis the magnification m is

constant for all the image points. However, due to

the field of view and camera pose assumed in this

research, magnification changes are expected even

when just considering a flat floor scenario. Hence,

the perspective image formation model arises in

magnification changes. Figure 5 shows the

magnification changes of the floor model by

considering the optical axis ray as the unit of

magnification. Therefore, these changes in

magnification are made it more complicated to look

for image patches with similar motion in order to

detect obstacle depth boundaries. However, by using

the floor model and the odometer system data,

binary floor results can be predicted from frame to

frame; then predicted discontinuities arise due to the

3D non floor obstacle shapes that produce

unexpected image boundaries.

Figure 5: Magnification changes of the floor model by

considering the optical axis ray as the unit of

magnification. The bigger magnification is attained at

closer robot positions.

The machine vision system algorithms

implemented are based on binary results obtained by

the one bit DFF algorithms explained in subsection

2.2. Binary images are obtained in the 96x72 space

resolution level, and blob analysis is developed. The

blob areas and the extremes of their coordinates are

computed and small blobs are removed. Then, the

image is analyzed from top to bottom, searching for

possible non floor regions. Hence, the QSM can be

used to detect the possible obstacles, when important

floor energy radiance discrepancies are met.

Therefore, using relative robot coordinate

increments provided by the odometer system,

qualitative structure estimation could be done by

comparing predicted positions with the binary

results obtained. The time integration of the different

frames acquired is introduced in the next section.

Thus, the robot coherent interaction with the world

can be addressed by using the occupancy grid

framework that provides a robust and unified

approach to a variety of problems in spatial robot

perception and navigation (Elfes, 1989).

3.2 The Local Occupancy Grid

Framework

The occupancy grid is considered to be a discrete

stochastic process defined over a set of continuous

spatial coordinates (x, y). Hence, the space is divided

into a finite number of cells representing a 2D

position, 1

≤

R 1

≤

C. The R and C parameters

are the number of rows and columns of the grid

respectively. The cell column coordinates are

designated by X

and the rows by Y

. It is assumed

that local occupancy grid data is provided by the on-

robot perception system. The occupancy probability

is divided into two ranges only: free and occupied.

The grid can be updated by using the sensor models

and the current information. Hence, given a sensor

measurement m, the occupancy probability P(O

) for

the different cells, P(C

), can be computed by

applying Bayes rule:

()

(

)

()()

ijij

CPOCP

OCP

COP

(6)

Hence, the probability that a cell is occupied

P(O

⎜

) is given by the cell occupancy sensor

measurement statistics P(C

⎜

O) by also considering

the probability that the cell will be free P(C

⎜

/O).

Thus, free cells have binary results equal to zero;

these non-occupied cells belong to coordinates for

image pixels within floor radiance thresholds. Other

available coordinates are provided through time

integration of the acquired frames when radiance

energy is bigger than threshold values, by using the

floor model, and looking for coincidences with the

acquired frames. The unknown probability value is

set to 0.5. Therefore, by using the expression (6)

with the predicted occupied cells and acquired

frames, the grid positions belonging to the floor will

provide larger occupancy values. Obstacle positions

give intermediate occupancy probabilities due to the

discrepancies between the predicted and the

acquired image values that arise due to the 3D

obstacle shape. Next section depicts some

preliminary results experimented with the available

WMR platform.

A MONOCULAR OCCUPANCY GRID FOR LOCAL WMR NAVIGATION

429

(a) (b) (c)

(d) (e)

Figure 8.a, 8.b, 8.c, 8.d, and 8.e: It is depicted the monocular frames acquired while the WMR is avoiding the first obstacle

placed on the direction towards the objective.

4 ON-ROBOT EXPERIENCES

In this section are presented some experimental

results using the WMR PRIM. Thus, local

navigation with static obstacles is used as a

preliminary test of the research introduced in this

paper. The navigation and control strategy used,

under this reduced field of view, is introduced in

other author’s work (Pacheco and Luo, 2007).

Therefore, the maximum geometric size of the closer

obstacle is considered in order to plan safety

navigation towards the desired coordinates.

Figure 6: It is presented the real scenario that has been

drawn in Figure 7. It is shown the obstacles placed on the

floor that the WMR should avoid.

Figure 7: Simplified map scenario where the robot

trajectory toward the goal is depicted with blue dots. The

obstacles are drawn in black.

Figure 6 shows the scenario where the

experiment has been done, and Figure 7 depicts the

simplified map scenario with the WMR achieved

trajectory.

Thus, Figure 7 shows the lab environment map

and the path followed when the WMR starts at the

position (0, 0, 90º) towards the desired coordinates

(0, 460cm). The scenario contains some static

obstacles that the WMR should avoid.

Table 1 depicts the robot coordinates and acquired

frames during the WMR navigation.

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(a) (b) (c)

(d) (e)

Figure 9: Sequence of occupancy grids obtained by integrating the first 5 acquired frames.

Table 1: Coordinates from where the frames are acquired.

F.1 (0, 0, 90º) F.7 (1, 293, 76º)

F.2 (-11, 66, 110º) F.8 (4, 315, 88º)

F.3 (-21, 108, 99º) F.9 (4, 339, 96º)

F.4 (-25, 141, 97º) F.10 (6, 375, 89º)

F.5 (-26, 176, 94º) F.11 (4, 415, 100º)

F. 6 (-8, 248, 83º) F.12 (12, 456, 74º)

The first 5 frames are acquired during the

obstacle avoidance strategy of the first obstacle

placed in the middle of the corridor. Figure 8.a, 8.b,

8.c, and 8.d. show these frames.

The first obstacle avoidance strategy consists

into turn to the left in order to avoid the collision

with the obstacle that appears at the first four

frames. It is noted that fifth frame, Figure 8.e,

depicts a part of the scenario where doesn’t appear

the first obstacleThe local occupancy grid built by

integrating the first 5 frames is shown in Figure 9.a,

9.b, 9.c, 9.d, and 9.e. It is depicted that in the first

frame only the front obstacle is perceived. However,

when the other frames are integrated the left wall is

integrated. It is observed how the WMR navigation

is constrained by the different obstacles obtained on

the acquired frames and integrated within the

occupancy grid. Therefore the navigation is

constrained by both obstacles. Moreover the fifth

frame is integrated in Figure 9.e where appear as

time integrated the front obstacle and the left wall.

Hence, the monocular occupancy grid methodology

presented increases the field of view perception, and

a better navigation strategy can be planned. The

integration of multiple monocular frames also can be

used as a framework in order to infer 3D obstacle

structure.

5 CONCLUSIONS

The methodology presented in this research has

provided a local map suitable for WMR navigation.

Therefore a short-term memory has been obtained.

Navigation advantages by using short-term memory

were reported in previous research (Schäfer et al.,

07). However, experimental results conducted to

obtain the obstacle structure have some aspects that

should focus the future work. The obstacle shape is

larger than the real shape due to the magnification

changes that arise of perspective. The lack of

accuracy increases the path-width, and consequently

this can result in larger trajectories or even infeasible

path perceptions where available paths are possible.

3D obstacle structure can solve the above problem.

But, the results obtained in order to obtain 3D

information have some mismatches when

overlapping areas between predicted and obtained

blobs are analysed. The errors can be produced by

the following sources:

• Odometry errors.

• Camera calibration errors.

A MONOCULAR OCCUPANCY GRID FOR LOCAL WMR NAVIGATION

431

• Flat floor model differences.

Future work will be addressed to solve the above

problems. We believe that the occupancy grid

framework can be used to obtain 3D obstacle

structure. Therefore, there is not limitation

concerning to the number of frames that can be time-

integrated. The future goal will consist in to find a

set of parameters in order to infer 3D obstacle

structure. These set of parameters should be

independent of the source of errors pointed in this

section. The knowledge of 3D structure can afford

several benefits that can be summarised as follows:

• To reduce the trajectories.

• Visual Odometry.

• Landmark detection.

Despite the work that remains undone the

methodology presented can be used to direct the

future research. Moreover, some good features and

results are presented in this work.

ACKNOWLEDGEMENTS

This work has been partially funded by the

Commission of Science and Technology of Spain

(CICYT) through the coordinated project DPI-2007-

66796-C03-02, and by the Government of Catalonia

through the Network Xartap and the consolidated

research group’s grant SGR2005-01008.

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