2º SIMPÓSIO BRASILEIRO DE AUTOMAÇÃO INTELIGENTE

2º SIMPÓSIO BRASILEIRO DE
AUTOMAÇÃO INTELIGENTE
CEFET-PR, 13 a 15 de Setembro de 1995
Curitiba
Paraná
Maximal Clearance Path Planning for
Autonomous Guided Robots*
\\T. L. R.oquet 1. \Vickert,
S. Botelho t and T. Telecken
CPG!vIApjInstituto de :Matemática
Universidade Federal do Rio Grande do Sul
91501-970 Porto Alegre, RS - Brazil
Abstract
Collision-free path planning is one of the main problems for autonomous mobile robots. The
Voronoi diagram is a technique that provides a roadmap with the maximal clearance with respect
to a set of obstacles. In this paper we apply this technique to make a mini ature robot navigate
from an initial configuration Qi to a goal configuratioll Q.rn simulating a static scenario in a plane
terrain.
1
Introduction
The possibility of having autonomous mobile robots is quite fa..c;cinating. In its full strength the
realization is not yet possible, but a great deal of development ha..c; been done 50 far. There are many
problems that must be well understood and solved prior one can profit from the existence of a fully
autonomous mobile robot.
In a broader view, amongst those problem5 two are of crucial importance to he solved, namely:
sensing and reasoning [4]. The first one would provide the robot with . the capability of sensory
detection and interpretation to determine its relationship with the surrounding environment. The
second, the reasoning capability, wOllld allow the robot to create its own solutions to take decisions
and perform actions according to the demands of the environment that it is emhedded in and of the
task to be accomplished.
In their own, each of these requested capabilities comprises a field of study in itself. They have
received much attention in the last couple of years and exhibited a great deal of development. From
the robotics community, many different approachs and techniques have been explored to cope with
them, either a..c; an isolated sllbject or in a more recent hybride way [1, 6].
One of the main requirements to an autonomous mobile robot is to detect the presence of obstacles
in the environment, and according to that, reason about the best path it has to take to accomplish a
task safely avoiding collisions with the obstacles. Therefore, it is highly important the development
of techniques that couples sensing and reasoning features, as for establishing collision-free pathfor
alltonomous mobile robots.
A simple instance of the path planning problem [3] can be stated as follows: Given the initial Qi
and the goal Q 9 configurations (position and orientation) of a robot and the obstacles configuration
space, determine a path connecting Qi to Qg in the configllf(ition-free space of the roboL This path
corresponds to a collision-free route. Of course, sometimes additional constraints mllst be taken into
account, such as the shortest and feasible path.
Ir
*This work has been partially supported by CNPq - Brazil.
troqueOmat.ufrgs.br
:'With the Instituto de Informática~ UFRGS.
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Several techniques have been developed to collision-free path planning [3]. 1vIost of them departures
from the assumption of a .t;tatic .t;cenario. That means the robot knows a priori its own location and
orientation as well as those of the obstacles~ and the only moving object is the robot. In a static
scenario the whole geometrical configuration is already set up. Under these considerations, the task
\vould be to determine a possible path that would conform the requirements or report failure otherwise.
Though its sim pIe scenario, this kind of situation may have practical applications for alltonomOllS
guided vehicles (AGV). For instance, an AGV may navigate in a shoptloor with obstacles.
A more complex situation would occur when the obstades are allowed to rotate with respect to
one of the workspace axis direction. This situation corresponds to a 8tationa.ry 8CenaT'to. A rather
com pIe x scenario would be the one ,vhere the obstades are allowed to move freely, generating a
dynamical .9cenario [7].
In this papel' we discuss the planar Voronoi diagram a.;; a technique to collision-free path planning
for mobile robots in a static scenario. In section 2 the Voronoi roadmap techniqne will be discussed
and a system for generating it will be presented. In section 3 we report the coupling of this system
with a mobile robot ba.;;ed on an experimental resulto Section 4 is devoted to some comments and
conclusions.
2
Roadmap technique
The Voronoi diagram retraction approach hac;; been of much interest to robot path planning problem
[10] a.;; it ha.;; the nice property of generating roadmaps with maximal dearance for environments filled
,vith obstades~ where the mobile robot shall navigate.
2.1
Planar Voronoi diagram
A planar Voronoi diagram [5] is defined a.;; a partition of the plane into regions according to the principIe
of the neare.9t neighbor. l\,·l ore precisely, let us consider the Eucledian distance d(p, Pi) from a point P to
a set of non-colinear points Pi in the plane. The Voronoi diagram for a set of point P
{PI ,P2, .. . ,pn},
is defined as the union of all regions Ri, i = 1, ... ,n, such that Ri = {p; d(p,pd ~ d(p,pj), T/Pi # pj}.
The points Pi are ca11ed Voronoi generators~ the edges between two Voronoi regions are called
Voronoi edges and the vertices where 3 or more Voronoi edges meet are called Voronoi vertices.
According to its definition, the Voronoi diagram is such that any point on the edge of two neighboring
regions is equidistant of the corresponding Voronoi generators. Therefore, points on the edges of two
common Voronoi regions are a.;; {ar way from one of the generator as to the other. In other words, if
one think of the Voronoi generators a.;; obstades, the edges are the maximal dearance paths (1vICP)
among the obstacles.
=
2.2
Roadmap generation with
VDVIEW
VDVIEW is a front-end system that is in development to allow the useI' interactiveness to spedfy the
geometry of the terrain of a static scenario, where a robot sha11 navigate. The workspace is given
by a pre-defined frame, which can map pixels values to coordinates within the workspace by dicking
the mouse at the desired position. Currently the user can interactively choose the point-like obstades
position and both, the initial Qi and goal Qg configurations of a point-like robot.
Once the useI' has spedfied those, the maximal dearance roadmap for the environment is automatically computed and displayed with the menu-function VORN [9]. In figure 1 we show the front-end
screen of VDVIEW. The obstacles are inserted by dicking the left-most mouse button at any position
within the workspace and deletion can be performed with the right-most button of the mouse. The
function CLEAR allows clearing everything within the workspace. \Vith the menu-function TARG the
use r inserts the initial and goal position of the robot; the function PATH presently passes the robot's Qi
and Qg positions to the list of generators to compute their Voronoi regions within the current environment. The Voronoi regions for Qi and Qg represent the maximal dearance regions for the robot. The
21 SIMPÓSIO BRASILEIRO DE
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function WGHT when activated let the useI' to specify a weight (radius) for a chosen poin t hy clicking
the mouse on the top of it. This last function is important to simulate an extensive obstacle, which
can he used for tolerance checking of paths.
)(: 432
v:
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2
3
4
5
369
36.1
671
2.16
469
596
303
495
5B7
652
BBB
QI:384
Qg:490
393
B79
-------
Figure 1: Voronoi-based roadmap for 5 point-like obstacles. Qi and Qg are initial and goal positions
of a robot.
The menll-fllnction VERT allows the use r interactively choose a sequence of vertices defining a MCP
from Qi to Qg along the edges of the Voronoi diagram on display. This is done hy clicking the mouse
on the chosen vertices. In figure 1 they correspond to the vertices with a little square on them. J ust
to show the system powerfulness, figure 2 provides the roadmap for a set of 30 obstacles within the
workspace. A 11CP is shown connecting the robot at Qi to Qg with minimum link paths.
3
An experimental application
To verify the capability of our path planner system an experimental test was realized with the use of
a miniature mobile robot called Khepera 1 [2], which has a serialline that allows it to be connected to
a host microcomputer. Khepera has 254 Kb of RA1'I, a 68331 microcontroller, 8 infra-red sensors and
a battery. Through the serial line commands can be given to activate the motors that drives its two
wheels. Therefore, it can move as an autonomous guided robot with the control transmitted either
by the host computer or hy its own memory.
To do the experiment, a workspace was specified according to the similarity principIe with rescaling of VDVIEW 's frame. A comoving frame was set to the rohot, specifying its initial position and
orientation configuration. The orientation of the robot is given hy the direction of the axis defined by
the line that is parallel to its two wheels.
In this experiment the robot was controled by the host computer through a set of primitives and
communication interface in a low levellanguage. The mechanical movements of the robot is done by
setting the velocities for the robot's two wheels and the time duration. Thus it can move straight
when both wheels have the same velocities, and it can make tllrns by a fine tuning of each wheel's
1 Khepera
is a trademark of the K-Team, Swiss Federal Institute of Technology.
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K:
v:
J.69
72
Uoronoi DiegraM with
J.: 64
2: 93
3: 171
4:3:58
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6::596
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8::593
9:367
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J.2:101
13:321
J.4:J.97
J.:5:474
J.6:6J.:5
J.7:7"77
J.8:837
J.9:663
20:474
2J.:426
22:J.68
23:J.J.5
24 :3J.0
2:5:460
26::532
27:731
28:904
29:850
30:699
J.23
303
200
J.60
J.J.1
216
231
3:56
287
386
437
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68:5
439
:526
4J.9
:5:56 ~---.......
6J.7
:572
699
74:5
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82:5 r - - - - - I
939
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7:58
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842
902
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Qg::598
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866
Ho~G
= 30
~
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---.-.
111
111
Figure 2: Roadmap for 30 point-like obstacles and a minimum-link path from Qi and Qg.
velocity. For instance, for it to turn around itself we set the same velocity for both 'wheels but in the
opposite directions.
With the set of commands to control the mechanical movements of the robot's wheels, a function was created to automatically read as inpllt data the sequence of Voronoi vertices, generated by
VDVIEW'S function VER!, indicating the path that ha..c;· to be followed by the vehicle. The actual
navigation along the trajectory starts when the function VER! is deactivated.
The figure 2 shows a picture of the lvICP and the actual path executed by the robot. The dots
represent the obstacles as shown in figure 1. The deviation observed are due to several factors. First
of alI, there are numerical erros dlle to round-off and the mapping of pixel vallles to represent actual
coordinates of the vertices. In addition, there are a number of other problems that adds IIp to increase
the uncertainty. For instance, there is a little uncertainty caused by the delay in the response of the
robot as the time is monitored by the internal clock of the host computer; the rescaling problem from
the software to the real world and other physical and mechanical effects.
4
Comments and conclusion
We have reported the result of an experiment where the the Voronoi diagram technique wa..c; applied
to generate maximal clearance collision-free paths for a mobile robot that ha..c; to navigate among
obstacles in a static scenario.
Currently the system VDVIEW is able to compute the roadmap for a set of point-like obstacles
selected interactively. The user can, afterwards select a sequence of vertices visually on the screen by
clicking the mouse button, defining a maximal clearance path to be navigated by the robot. Clearly
the path interactively chosen may not correspond to the shortest and feasible one among the obstacles.
AIso, it is in general cheaper for a robot to navigate on a straight line than having to execute many
rotations. Thus it is important to consider those trajectories with a minimum number of turns. Work
is in progress to implement a shortest path algorithm [8] taking into account the minimum-link and
an approach to check its feasibility, according to their wheights.
21 SIMPÓSIO BRASILEIRO DE
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Figure 3: The fuH line shows the MCP and the dashed one the actual path executed by the robot
from Qi to Qg.
Though the system is able to handle only a very simplified scenario, it is still use fui for practicaI
applications if we consider a disk-like robot with diameter 1 that has to navigate among a set of
disk-like obstacles with diameters Li, representing extended object projections on the plane, with the
mean-distance L among them such that 1 < L. This scenario is simulated hy the system with the
weights associated to each ohstacle and robot.
The experiment exhibts the cOllpling of a path planner system to gllide a mobile rohot in a
predifined static scenario. However to be able to generate its own path aIong obstacles, an alltonomous
mobile robot has to be able to detect (sensing capability) the presence of the obstacles and generate
(reasoning capability) its own trajectory to reach the goal. We intend to work further to improve
our system to be able to integrate these two capabilities. The first step is to all tomaticaIly determine
the shortest minimum-link feasible MCP and later its integration with the robot sensing features.
Although that is a quite complex task, our modest results are being an enthusiasm to continue our
research in this field.
Acknowledgments
We thank Cláudio Heckler for his coHaboration. S. Botelho, 1. \Vickert and T. Telecken thank the
CNPq for financiai support.
.~
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References
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