LOCAL PATH PLANNING IN UNKNOWN ENVIRONMENT BY

LOCAL 3D ELEVATION MAP CONSTRUCTION

A. Usai and P. Di Giamberardino

Department of Computer and System Sciences ”Antonio Ruberti”

University of Rome ”La Sapienza”

Via Eudossiana 18, 00184 Rome, Italy

Keywords:

Mobile robot, path planning, unknown environment, stereo vision, elevation map.

Abstract:

The paper deals with the problem of computing a path for an autonomous mobile robot, provided by a stere-

ovosion camera, trough obstacles in an unknown environment with rough ground. The planner makes use of a

3D map reporting the presence and the highness of obstacles together with the shape of the ground and its dis-

continuities, under the hypothesis of stationarity. A local solution, with an expanding algorithm, is proposed.

Some experimental results are reported to validate the proposed technique.

1 INTRODUCTION

The path planning problem for autonomous robot

platforms has been a widely investigate problem char-

acterized by several possible approaches depending

on the possible hypothesis on the environment and on

the robot kinematics.

In fact, starting from the simplest problem of a ro-

bot without any kinematic constraints moving in a

perfectly known and static environment, for which a

global path plan for reaching any ﬁnal goal stating

form any initial position can be performed, for ex-

ample using the Voronoi diagrams approach or tech-

niques based on potential ﬁelds among the most fa-

mous approaches, the problem has been more and

more complicated adding one or more of the follow-

ing conditions: i. non stationary environment, i.e.

presence of moving obstacles (like other robots or

humans) or different conditions on some part (like a

door, that can be open or closed); ii. unknown or only

partially known environment, in which the presence

of obstacles (moving or not) or even the possibility

to reach the goal has to be autonomously discovered

by the robot itself; iii. the presence of some con-

straints on the robot motion, like nonholonomic ones

due to the kinematic characteristics of the platforms

(Voronets, 1901).

In the present work, the case of totally unknown en-

vironment and nonholonomic platform with unicycle-

like kinematics is considered. So the problem here

faced is the computation of a path (if any) between

an initial position and a ﬁnal one for which only the

coordinates are known, without any initial knowledge

on the presence of obstacles or discontinuities in the

ground.

The solution of the problem involves two main as-

pects. The ﬁrst is the choice of the robot sensors for

the acquisition of the necessary information on the

environment and subsequent analysis; the second is

the strategy for the construction of a feasible path for

reaching the goal.

Regarding the ﬁrst aspect, the present choice for

the sensors is to use a stereo vision system only. The

hardware used in the present application is a commer-

cial device by Videre Design, the stereo head STH-

MD1. It is composed by two ﬁxed cameras, with

parallel axes, both using CMOS sensible device with

1.3 Megapixels resolution. In the used conﬁguration,

they have two lens whose focus length f is 7.5 mm.

The main advantages of such a choice with respect to

different ones often used, like the rangeﬁnder (Iocchi

et al., 2000) for example, is the absence of physical

interaction with the environment and the similitude

with the human behavior.

As far as the second aspect is concerned, since a

visual system implies that only a part of the ﬁeld,

the visible part, at a time can be investigated, at each

step of the learning approach only a local knowledge

can be acquired; in addition, without a motion, such

knowledge cannot be increased, since a change in the

point of view is necessary to change the area in the

visible ﬁeld for investigation. Then, a local path plan-

ner for local motion, based on the construction of a

local and iteratively expanded map, is presented.

On these basis, the ﬁrst step in the proposed so-

lution is the construction of a suitable map for rep-

403

Usai A. and Di Giamberardino P. (2005).

LOCAL PATH PLANNING IN UNKNOWN ENVIRONMENT BY LOCAL 3D ELEVATION MAP CONSTRUCTION.

In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 403-406

DOI: 10.5220/0001167004030406

 SciTePress

resenting the acquired information necessary for the

computation of a feasible path. There are several kind

of maps that can be constructed starting from dis-

tance measurements, depending also from the char-

acteristics of the vision system used. Most of them

work efﬁciently under the hypothesis of indoor mo-

tion. Among them there are the occupation maps,

where only the position of obstacles are stored, as-

suming to be safe any other position on the ground

(Herbert et al., 1989). But in case of unknown en-

vironment exploration it is not possible to satisfy the

hypothesis of safety for unexplored areas: no regular-

ity assumptions can be posed.

The most suitable kind of maps for the present ap-

plication are the elevation maps, where the known

portion of the environment is represented by the

height of the ground and the objects present. On this

basis, an obstacle is represented by an area whose

height is signiﬁcantly different from its accessible

neighborhood. Such an information is enough for the

determination of a possible safe path that the mobile

robot can follow, since it can move in all that direc-

tions where the height is equal or a little bit different

(greater or lower) according to the mechanical char-

acteristics of the rover.

The path planning technique here proposed is based

on the construction of an elevation map, according

to the procedure presented in (DiGiamberardino and

Usai, 2005), generated recursively on the basis of con-

tinuous image processing during the robot motion,

which represents the acquired knowledge of the lo-

cal environment in an increasing neighborhood of the

robot.

The paper organization is then the following one.

In section 2 a short description of the technique used

for the construction of the elevation map is given.

Section 3 is devoted to the description of the proce-

dure proposed for the determination of a new connec-

tivity map and, consequently, a local path: in 3.1 the

map construction and in 3.2 the ﬁna path.

2 CONSTRUCTION OF THE

ELEVATION MAP

The basic algorithm adopted for the images analysis

is a disparity map computation starting from a cou-

ple of stereo images. In such an algorithm the cor-

respondence between the couples of conjugate points

in the two images is achieved by means of an area-

based correlation technique. It is well known that this

kind of solution is very efﬁcient for its computational

aspects, but, on the other hand, it does not produce

satisfactory results in presence of discontinuities in

the distances of the objects present in the scene: it

is sufﬁcient that one object is partially covered and

behind another one with respect to the point of view

of the cameras to produce wrong results; in fact, the

correlation of the area including parts of both the ob-

jects at different distances either associates the points

of one object to the other or produces a false object

at an intermediate distance between the two real ones.

Some pre and post elaborations are needed in order to

avoid such errors. In literature some techniques are

proposed ((Murray and Little, 2000),(Fusiello et al.,

2001)) based on a segmentation of the disparity map

in order to manipulate in a different way the sections

that potentially can produce the above described de-

formations. The result is a more clear and realistic

reconstruction with the counterpart in a slower com-

putation. In the present application we propose a dif-

ferent approach based on a standard (and pretty fast)

edge detection algorithm, making use of the addi-

tional information coming from the motion of the ro-

bot and the continuous images acquisition. The accu-

rate description of the algorithm for the construction

of the elevation map and the measures ﬁltering tech-

nic be found in (DiGiamberardino and Usai, 2005). In

ﬁgure 4, a VRML model of an outdoor environment

reconstruction is presented.

3 THE PATH PLANNING

PROCEDURE

3.1 Chessboard construction

After the construction of the elevation map, in order to

achieve the planning of a safe path in the environment,

it is necessary to derive a new topological one, gener-

ated starting from the information stored in the eleva-

tion map and combining them with the knowledge of

the mobile robot movement capabilities. Such a map

is called the chessboard. The environment is divided

into cells, storing several informations like the coef-

ﬁcients of the best ﬁt plane, the obstacles presence in

the cell and the ﬁdelity of the elevation measures in

the cell. Figure 5 shows an example of chessboard

using a color code identiﬁcation with the following

meanings: light gray (green) for free cells with good

measures, dark gray (red) when obstacle are present in

the cell and the measures are good, darkest (blue) for

cells that seems free but the measures are not enough,

lightest (yellow) for apparently occupied cell associ-

ated to poor measures.

It is interesting to see how this coding is done. First

of all, the best ﬁt plane coefﬁcients are computed by

a least square approach. Then it is possible to say if

there is an obstacle for the rover in the cell, compar-

ing the founded ﬁtting plane elevations with the ones

of the true ground trend. In particular, the cell is free

if the difference of the ground elevation and the ﬁtting

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404

plane is always smaller than h

max

, that is the height

of the taller obstacle the rover is able to pass (ﬁgure

1). Note that a free cell has to be considered occu-

pied if its slope is to high for the rover. Lastly, the

ﬁdelity of the elevation measures in the cell are com-

puted thresholding the veridicity value corresponding

to the measures of the cell.

Figure 1: The cell obstacle detection condition.

Figure 2: The cell connection condition.

Figure 3: Example of an outdoor environment.

3.2 Path planning

After the chessboard is builded, it is possible to derive

from it a connectivity graph, useful for the mobile ro-

bot path planning. In order to reduce the number of

nodes of the graph, grouping similar cells, a third data

structure is derived from the chessboard. Such a struc-

ture is a classical occupancy grid, where the ”pixels”

are marked occupied if:

Figure 4: Example of an outdoor environment reconstruc-

tion.

Figure 5: The Chessboard.

• The corresponding cell in the chessboard is occu-

pied;

• The corresponding cell in the chessboard has not

reliable measures;

• It corresponds to the frontier between two free cells

with a too high difference in height to be passed

by the robot (look at the connection condition in

ﬁgure 5).

After this (binary) occupancy map is builded, it

is necessary to augment the founded obstacles ac-

cording to the robot dimensions and ﬁlling the possi-

ble ”holes” left by the obstacle augmentation process

(think at those regions that cannot be reacted by any

other cells). In ﬁgure 6 it possible to see the planes

approximation concerning a chessboard computed by

the elevation map of an environment with two obsta-

cles. As just noticed, from the chessboard we want to

derive a simpler binary map. In ﬁgure 7, it is shown

an example of this data structure. Note how the num-

ber of cells here is less than the one in the chessboard

(ﬁgure 8). To divide the conﬁguration space in ”big”

LOCAL PATH PLANNING IN UNKNOWN ENVIRONMENT BY LOCAL 3D ELEVATION MAP CONSTRUCTION

405

Figure 6: Example of planes approximation for an environ-

ment with two obstacles.

Figure 7: The path planned by the proposed method.

convex cells, the occupancy grid is scanned line by

line and, whenever a ”change in color” is found, a new

horizontal frontier is marked. Once the new cells are

found, a connectivity graph can be used to ﬁnd which

cells are involved in a speciﬁed path from P

start

goal

. The path is then generated using splines that

connect the border points of each cell. Such points

are choose trying to minimize the distance from the

previous via-point in order to keep the path as short

as possible. In ﬁgure 7 and in ﬁgure 8, it is possi-

ble to see the planned path in the occupancy grid and

in the chessboard. Note that we are interested in the

exploration of the environment. So, in could be possi-

ble that some areas of the chessboard are unknown (or

better, the measures are not reliable). As noted before,

the not reliable cells (the ones with low veridicity rate)

in the chessboard have to be considered not feasible

for the robot motion. If a planning to a unknown area

is required, the robot will plan until an auxiliary point,

in the known area, is reached and then a new stere-

ohead acquisition is done, pointing the direction of

the desired destination point. The auxiliary point is

chosen in order to stay at the minimum sight distance

(about 50cm, in our conﬁguration) from the frontier

of the unknown area. A new path is then planned from

the actual point to the previously desired one.

Figure 8: The path imposed over the chessboard.

4 CONCLUSION

In this paper a procedure for the determination of a

local map and a feasible path for a robot moving in

an unknown environment is presented. It consists of

two main steps. Some ﬁgures show the results of each

step and then the effectiveness of the procedure. Fu-

ture work will focus on the evolution of the proposed

technique for global path planning.

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