USC Computer Science Technical Reports, no. 683 (1998)

PDF

Download

Open document

Flip pages

Download a page range

Maite Lpez-Snchez, Gaurav Sukhatme and George A. Bekey. "Mapping an outdoor environmnent for path planning." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 683 (1998).

Transcript (if available)

Content 1
Mapping an outdoor environmnent for path planning.
Maite López-Sánchez*, Gaurav Sukhatme and George A. Bekey.
Robotics Research Laboratory
University of Southern California (USC), USA.
(*) Visitor scholar from the Institut d’Investigació en Intel.ligència Artificial (IIIA-CSIC), Spain.
Abstract
We present an incremental map building approach that is applied by a group of cooperating
heterogeneous robots. Robots cooperate by sharing information in order to build their own maps.
Environment information comes into the mapping process from two different sources: aerial
images from a helicopter and sonar readings from several ground robots. Ground robots use the
resulting map to plan paths towards goal positions. These paths avoid detected obstacles and are
updated when there is new information about an obstacle obstructing them. Finally, we consider
environment uncertainty depending on the reliability of the information. We use uncertainty as
an estimation of the real existence of detected obstacles and we apply it in order to plan paths
that may need to go trough non-real obstacles.
1. Introduction
This research report is the result of working on a specific problem within a larger project. The
problem is one of representing and managing information about an outdoor environment in a way
that it is useful for path planning purposes. The generic goal of the longer project is to achieve
cooperative tasks with a group of heterogeneous ground based and airborne vehicles. In the work
presented herein, the different classes of vehicles accomplish cooperation by sharing information
about the environment. We consider an outdoor environment which is unknown a priori.
The global scenario of this project is a group of autonomous vehicles that consist of a helicopter
and five ground robots that cover a certain area of an arena or reach a specific position specified
as a command from a human. Our work has been focused in the representation of the
environment as well as in the generation of paths that can be useful for the ground robots to
avoid obstacles while reaching the goal position. Considering all the obstacle information that is
available at each time, we obtain the shortest paths. However, we do not always use all the
information details, therefore we can not guarantee optimality (in terms of distance) although we
obtain optimal paths for each level of detail. Nevertheless the utility of a path strongly depends
on the reliability of the information. In our approach we have two different sources of
information: first, the helicopter has a camera facing the ground that provides a birds-eye view of
the arena, and second, each ground robot has seven sonar sensors that detect ground obstacles.
Robots communicate the obstacle information they gather in order to complete the map of the
environment. Since every robot receives information about the obstacles detected by the rest of
the robots, all of them have the same individual maps (or similar, in case of transmission
problems). The distribution of information among the robots allows other robots to use
information gathered by a robot that reached a specific region before them. Nevertheless, this
does not prevent any robot to plan its own path under bad communication circumstances: since a
robot keeps its own version of the map it can still plan a path albeit with less information.
In the following section we describe how information from the different sources is preprocessed
and used as input data for mapping. The third section gives the details of how our incremental
2
mapping approach is based on the grouping of environment obstacles. The resulting map is used
to generate paths, and the fourth section illustrates this planning process. Finally, section number
five explains the way in which we include uncertainty into the mapping process.
2. Obstacle information extraction
As we have already said, two different kinds of robots gather and share information from the
environment. On the one hand the helicopter captures aerial images and, on the other hand,
ground robots detect obstacles by means of their sonar readings.
During the helicopter’s flight, image processing will be performed by its exclusively dedicated
image system. Figure 1 shows an image of a typical outdoor environment, a parking lot. This
image is of the same kind of the ones captured by the helicopter camera. Since the helicopter
chassis development is still in progress, this image was taken from a building (the perspective is
the main difference between the neighboring images that the helicopter will obtain and this
image) and processed on a sun station. Image processing has been done using Matlab 5.2 and
gives as output a set of polygons that contain some of the obstacles in the real world. The reason
for using polygons as descriptions of environmental features is that they constitute a simple and
compact way of representing information, so that their communication still allows the robots to
perform other tasks simultaneously. The following steps describe how to extract polygons from a
gray-scale image (Figure 2 shows the results of applying these steps to the image in Figure 1):
1. Obtain the most common gray that appears in the image and consider it as background
color.
2. Define lower and upper thresholds so that they specify the range of grays around the
background color that are still considered as background.
Figure 1: Outdoors environment image
3. Transform the gray image into a binary bitmap setting the background pixels to 0 and the
remaining ones to 1.
4. Apply several image processing Matlab functions (erode, dilate, clean and majority) to
increase the quality of the image by removing spurious pixels.
5. Identify the areas that result from the grouping of neighbor white pixels.
6. For each of the resulting areas, compute its Convex Hull, which is the smallest convex
polygon that includes an area.
3
7. Compute the area of each polygon and eliminate those having an area smaller than a
certain threshold.
8. Polygons are specified as a list of vertices. Some of these vertices can be discarded
without causing a significant change in the area of the polygon. (Figure 1 had 60 vertices
per polygon on average and was reduced to an average of 20 vertices per polygon).
Figure 2: Image processing resulting in polygons
Essentially, this sequence of preprocessing steps separates the foreground from the background
and attempts to represent all foreground entities as polygons. Since the helicopter has no stereo
vision, the image processing system cannot distinguish real obstacles (in the sense of ground
protuberances) from shadows or paintings, therefore there is no guarantee that a polygon will
indeed define an obstacle in the environment. See, for example, the painted vertical parking lines
which are considered to belong to the horizontal white obstacles in Figure 1. Although, obtained
polygons do not thus necessarily correspond to real obstacles, they may represent part or groups
of obstacles, they can still be considered as being helpful in identifying areas of potential danger
for the ground robots.
The information obtained from the image processing system is incomplete, so the ground robots
will need to apply reactive techniques to deal with those obstacles that where not identified in
the image but are detected by sonar. This obstacle information is also added to the environment
representation and shared among robots. In order to keep a homogeneous representation of the
obstacle information that comes from different sources, a robot that is avoiding an obstacle can
consider consecutive sonar readings to generate a polygon that approximates the edge of the
obstacle. Figure 3 illustrates an example of how a robot follows part of the edge of wall and the
resulting polygonal approximation. Basically the polygon comes from the grouping of
consecutive readings that are approximated by a line, so resulting polygons are in fact rectangles
containing those lines, with different length and orientation, but with a fixed width that has been
defined by default. In fact sonar readings are filtered in such a way that distant readings and
groupings that yield segment lines shorter than a threshold are not considered.
Wall Polygon
Sonar

Robot
. . . . . . .
Figure 3: Ground robot obstacle detection
4
Although this is beyond the scope of this work, linear grouping of sonar readings is used when
the same wall or obstacle edge is detected more than once. Two thresholds (angle and distance)
define when two linear groups of readings are considered to come from the same obstacle. When
this is the case, comparing the orientation of the first detection with the most recent one shows
how the orientation error has increased through time. Therefore, the latest segment detection can
be rotated to match the same orientation as the first detected segment, and this can be applied to
subsequent detections. Once two segments are parallel, the distance between them is used to
correct the position of the robot (it is translated in the perpendicular direction of the reading).
3. Mapping
The previous section defined how obstacle information has been retrieved and specified by
polygons, which constitute the input data of the mapping task. This section describes how these
polygons are used to incrementally create a map of the environment. Since each robot has a map,
every robot updates its own map whether it receives a polygon detected by another robot or it
detects the obstacle by itself (and then broadcasts it as well). Thus, all robots apply the method
described here simultaneously.
3.1 Related work: Map representations
When choosing a representation of outdoor environmental features, there are several
characteristics we must take into account. On the one hand, outdoor environments are especially
difficult to map because the shape and distribution of obstacles are less predictable than human-
made obstacles in indoor environments. This makes it difficult to identify and describe obstacles,
particularly, when the information comes from a single camera and local sensors embedded in
robots with dead-reckoning errors. On the other hand, it is important to deal with the uncertainty
associated with each map element when choosing the right map representation. In indoor
environments, a grid representation is the most commonly used [3,4,5,6]. Nevertheless, it is not
flexible enough in terms of obstacle positions or contradictory sensor information when used for
outdoors environments. The reason is that, for example, if an obstacle that corresponds to more
than one cell is represented in the grid and afterwards new information suggests that the obstacle
representation should be associated to other cells in the neighborhood, there is no a direct way of
moving it. Furthermore, if we want to maintain resolution, then the representation size increases
with the size of the environment. This is not the case for a symbolic representation of the
environment such as a graph with obstacle areas as nodes and their relations as edges [2,8,10]. In
such a graph representation, location is just a characteristic -that in some cases can even be
reduced to be implicit in node relations- and size depends on the number of obstacle areas, which
keep the problem tractable when outdoors.
It is also crucial to have a task oriented representation, that is, to represent information in such a
way that it is easy for the robot to use it for performing its task. In our case, the ground robots
will use the map for planning paths that go from their initial positions to the goal. Graph
representations have well known optimal path planning algorithms in the literature. This reason,
in addition to the previous ones listed above, makes us choose a graph representation for
outdoors mapping. In particular, our map consists of a Visibility graph [9]. This kind of graph
representation assumes that obstacles in the environment can be approximated by polygons so
that every vertex of each polygon is used to define a node in the graph. Edges are then defined
between ‘visible’ nodes, that is, those node pairs without any obstacle in between. The edges are
labeled with the distance between the nodes. An edge means that it is possible for a robot to go
from one node –or obstacle vertex- to the other covering the distance in a straight line without
finding any obstacle in its way.
5
3.2 Our approach: grouping obstacle information into the map representation.
Considering the polygonal information that the robots gather from the environment, the process
of building a Visibility graph is direct although the visibility check for all node pairs –i.e.
polygon vertex pairs- may be unnecessarily expensive in terms of computational time. The
purpose of our mapping task is not to give a detailed description of an environment, but a rough
approximation of those environmental features that can be a potential danger for the ground
robots when approaching a target position. What we propose is to build an efficient higher level
abstraction on top of the polygons such that a robot is able to plan its path towards a goal
position at this level. Nevertheless we keep the relation between both levels of representation so
that if occasionally the robot needs a more accurate path, it can go down into the polygon level
and still use the abstract level to simplify the amount of treated data. In general this should not
be the case because outdoors environments usually have a relatively low obstacle density. This
makes unnecessary for the robots to know the exact shape of an obstacle in order to avoid it.
Figure 4: Outdoors environment image
We characterize the higher level of abstraction as a set of Obstacle Areas. An obstacle area being
a rectangle that includes a group of overlapping polygons. Polygons can intersect due to different
reasons: on the one hand the vision system can provide polygons that overlap, and on the other
hand, an obstacle –or part of it- can be detected several times, by different means or from distinct
perspectives. Thus, map information is distributed over two levels: the first one defines how the
obstacles in the environment are distributed in different areas, and the second level goes into
more detail and specifies the polygons that belong to each area. Figure 4 presents another
example of an outdoors image and Figure 5 shows how their corresponding image processing
polygons have been grouped into rectangular obstacle areas.
Figure 5 gives a good description of the kind of obstacle areas that we can find. Isolated
obstacles in the environment yield obstacle areas with a single polygon, in these cases the gain
comes from the fact that we reduce an average number of twenty vertices per polygon to a
constant number of four. This might not seem a big improvement in the performance, but it has
the advantage that it does not dismiss important information. Since it is an isolated obstacle the
robot will still have room to surround the obstacle area rectangle. Bigger obstacle areas are
6
usually composed by several overlapping obstacles. In these cases they tend to cover bigger free
space areas -which increase the risk of covering useful areas for path planning. However the
reduction of the number of vertices grows in proportion to the number of included polygons.
Nevertheless, the vertices of those polygons that are completely contained by others are
discarded without taking any additional risk.
Figure 5: Grouping obstacles: obstacle areas are defined as rectangles containing intersecting polygons
Finally, there is a special kind of obstacle areas that are produced when polygons do not intersect
but the rectangles of their corresponding obstacle areas intersect. We call them intersecting
obstacle areas. Usually they require the system to go down to the polygon level to treat the
relations among them. Intersecting obstacle areas are the ones that provide less efficiency gain
because going to the polygon level means getting closer to the original computational costs, but
in the following sections we will show that we still have some gain in such cases.
3.3 Map structure
Our map representation consists of a set of obstacle areas and a visibility graph:
• Obstacle areas present two levels of information: the highest level specifies a rectangle that
contains a set of intersecting polygons, and the lowest level includes the list of these
intersecting polygons. In case an obstacle area is intersecting with others, the list of
references to these areas is also stored in the high level. For the low level, it can also
compute an additional polygon representing the union of the polygons in the obstacle area.
Union polygons are computed under request when refining the path that has been obtained in
the high level representation; we will see how they are useful for visibility computations.
• We create the visibility graph by considering as nodes the vertices of the obstacle area
rectangles and by establishing edges between ‘visible’ nodes: those node pairs without any
obstacle in between. Edges are labeled with the Euclidean distance among the nodes they
relate. In our approach, visibility is computed considering the obstacle area rectangles in
stead of the polygons.
7
Figure 6 illustrates how we represent the map information. Figure 6 a) shows a subset of three
obstacle areas from the nineteen obstacle areas in Figure 5. Each area has been drawn as its
rectangle and the polygons it groups, (for example, obstacle area number 1 groups six obstacles).
a).
b)
Figure 6: a) Subset of obstacle areas from Figure 5, b) its corresponding visibility graph.
Although it has not been shown in the figure, obstacle areas number 1 and 2 have a cross-
reference between them that states their intersection. Figure 6 b) is the corresponding visibility
graph. Small circles represent nodes in the graph and come from the vertices of the obstacle area
rectangles. However, not all the vertices are included because there are vertices in the
intersecting areas that may lie inside an obstacle of one of the areas it intersects with. This is the
case of the lower-right vertex of the rectangle in area 1, which is located inside the polygon of
the second area.
Keeping the level of abstraction at the obstacle-area-rectangle level speeds up the computation of
the visibility. The gain depends on the number of polygons that each obstacle area is grouping
and the number of vertices of each polygon. But the gain can be significant if we take into
account the fact that all node pairs check for every obstacle area if the area obstructs their
visibility.
Figure 7: a) intersecting obstacle areas, b) checking visibility between nodes considering obstacle area
rectangles, c) visibility considering polygons.
Unfortunately, the high level of abstraction may yield a low connection between nodes that
belong to intersecting areas. This is not the case of the intersecting areas in Figure 6 but for a
8
case like the one shown in Figure 7, it is necessary to check visibility at the polygon level
because the higher level does not connect nodes between the two parallel obstacles.
3.4 Map updating
After determining how data is represented, we describe how robots share information and how
they include new information into the current map. The idea is that each time a robot defines a
new polygon it broadcasts it to the rest of the team. Thus, all robots are able to update their
maps. To add a new polygon into the map means that it must be included into one of the obstacle
areas and that the visibility graph must be updated. Graph update is computationally expensive,
because it implies including new nodes to the graph and checking if the new polygon obstructs
the visibility of those pairs of nodes that were visible before the polygon arrival. However, this
process should be kept as cheap as possible because there might be some information that would
turn out to be useless for some robots –that is, information about obstacles that are located far
away from one specific robot trajectory. We accomplish that by considering again the high level
of information. The following pseudocode depicts the updating algorithm and in the rest of this
subsection we will see how Update uses the high level of information (i.e., obstacle area
rectangles) to restrict the computation.
Let Map be a list of obstacle areas OA
i (i=0..n)
, where each obstacle area contains a list of polygons
LP
i
={P
1
,..P
k
} and let G be the visibility graph associated to Map. Then we apply the Update
function to include a new polygon P’ into Map.
Update (Map, P’)
{ list_of_intersecting_areas = ∅
last_area_with_polygon = ∅
polygon_added = no
Repeat for all OA
i
obstacle areas ∈ Map
{ intersection = Check_Intersection(P’, OA
i
)
If (intersection = intersects_a_polygon_of_LP)
{ If (last_area_with_polygon = ∅)
Include_polygon_in_area (P’, OA
i
)
Else
Fuse_areas (last_area_with_polygon, OA
i
)
last_area_with_polygon = OA
i
polygon_added = yes
}
Else
If (intersection = only_intersects_the_rectangle)
list_of_intersecting_areas = OA
i
}
If (polygon_added = no)
{ OA’ = Create_new_Obstacle_Area (P’, list_of_intersecting_areas)
Add_Obstacle_Area (Map, OA’)
}
}
Initially, the Update function checks if the new polygon P’ intersects with any of the obstacle
areas OA
i
. An increase in efficiency comes from the fact that when P’ does not intersect with the
rectangle that is defined for an area OA
i
, there is no need of checking the intersection for the
9
polygons inside (LP
i
∈ OA
i
). When P’ intersects the rectangle and it overlaps polygons of LP
i
,
then LP
i
must contain P’: if OA
i
is the first area that intersects P’ then P’ is added to LP
i
,
otherwise it means that P’ has already been included into another OA
j, j≠i
and both areas must be
fused in order to have all overlapping polygons grouped under the same area OA
j
’ = OA
j
∪ OA
i
(with

LP
j
’ = LP
j
∪ LP
i
). Another advantage of the high level information comes when a polygon
is included into an area OA
i
in such a way that its rectangle does not grow. In this case, the
associated graph G that corresponds to the previous Map is still valid and does not need a review
of its visibility (although G may need it when OA
i
is an intersecting area).
Information about P’ intersecting the rectangle of OA
i
without overlapping polygons of LP
i
,
causes the reference of OA
i
to be stored in the variable list_of_intersecting_areas. In that way,
when P’ will be added to another area OA
k, k≠i
all areas (i.e., OA
k
together with the ones in
list_of_intersecting_areas) will become intersecting areas. Finally, if after checking the
intersection of P’ with all obstacle areas OA
i
, P’ has not yet being included, a new obstacle area
will be created and included into the Map. Notice that, in fact, this algorithm can be used to
update empty maps because it simply creates a new obstacle area for the first polygon (and
updates G correspondingly). Hence, this is the function that we use to incrementally create our
map.
4. Path planning
When using a graph, the shortest path between two positions is given as a list of connected nodes
in the graph so that it is possible for the robot to go from the initial point to the goal following
the links between the positions that the path nodes represent. In general, the initial position of a
robot and its goal do not coincide with the nodes in the graph. Therefore, to compute the path
between two positions, it is necessary to first include them as nodes into the visibility graph (and,
of course, establish their connections by computing their visibility). Then, the A* algorithm [7]
is applied to obtain the path. A* is optimal for this problem because we can use the Euclidean
distance as a heuristic and its triangular inequality property makes it conservative.
Visibility graphs give shorter paths than those methods (such as Voronnoi Diagrams) that try to
keep the robot as far away from all obstacles as possible. In fact, when the shape of obstacles is
well known and can be approximated by polygons, the method yields optimal paths.
Unfortunately, we can not guarantee optimality because of the robots' limited obstacle sensing,
but we can come as close as the information allows us to be. If paths that are close to obstacles
present a danger, then it is always possible to grow the obstacles by half the width of the robot,
to provide some margin.
Obstacle expansion is also useful to guarantee paths that can be actually traversed by the robot.
This step can be done in the data acquisition stage, however, we have not done it because we
deal with polygons that do not correspond to real obstacles and growing them can only yield to
poorer paths. Our underlying idea is therefore to have robots that are able to compute an
approximated path towards a goal position, and then a robot can roughly follow the path,
applying reactive techniques when its internal map does not correspond to the environment that
it is actually sensing.
Figure 8 shows an example of the kind of paths that result when applying the planning algorithm
to the visibility graph G. Since G has been created considering the higher level of information,
the resulting paths go trough the vertices of the obstacle area rectangles.
10
Figure 8: Path that considers high level information in the map from image in Figure 1.
4.1 Path update
Adding information into the map does not necessarily mean changing the current path. In fact, a
robot can be following its own path and receiving simultaneously information about other
locations in the environment without changing its trajectory. Only information about obstacles
that are obstructing the current path triggers the path planning algorithm. Figure 9 illustrates how
the path is updated when the information in Figure 2 was not received at once. The left part of
Figure 9 shows the path generated by a ground robot that is located at the initial position and has
only received twenty polygons from the helicopter image processing system. The path in the
right side of Figure 9 has been generated after receiving ten more polygons from the image. The
final path that considers all forty-two obstacles extracted from the image in Figure 1 was already
shown in Figure 8.
Figure 9: Left: path planning considering twenty obstacles; Right: path after adding ten new polygons
11
Figure 10: image that might need a path refinement
4.2 Refining the path
In the previous sections we have seen how we can consider the higher level of information and
still obtain useful paths. Nevertheless, when the image processing provides obstacle polygons
that are a rough approximation of the real obstacles and the resulting obstacle areas cover most
of the space in the environment, it may be worth to work at the lower level of information
without losing more accuracy. Figure 10 is an example of such situation; the extracted obstacles
and the resulting obstacle area rectangles are shown in Figure 11. In this figure the path obtained
considering the high level of information has been displayed together with the path that uses the
lower level of detail. They have been labeled path and repath respectively. As expected, the use
of more accurate information results in a refined path that is shorter than the higher level path. In
fact, this is always the case and the gain depends on how accurate the rectangle areas
approximate the obstacles they contain (notice that he gain is 0 for those paths that avoid
obstacles going trough vertices that coincide with the rectangle vertices).
Figure 11: planning at two different levels: path considers obstacle areas and repath avoids obstacles.
12
When going from the high level of information down to the lower level, what we are doing is to
generate a new visibility graph that has as nodes the vertices of the obstacles instead of using the
vertices of the obstacle area rectangles. Figure 12 shows an extreme case that illustrates the
difference. In Figure 12 a) two obstacles are included into their respective obstacle area
rectangles. The problem is that some of the rectangle vertices lay inside the obstacles, and
therefore, they are not included as nodes into the visibility graph. Therefore, the visibility graph
that results from considering the high level (see Figure 12 b)) can not generate any path going
between the two obstacles. On the contrary, Figure 12 c) shows how this is possible when the
obstacle vertices are used.
Figure 12: a) two obstacles and their corresponding obstacle area rectangles, b) the resulting high-level
visibility graph, c) visibility graph at the low level.
Planning at the polygon level of detail is a computationally expensive process that means to
create a new graph including all polygon vertices as nodes and computing all the visibility
between them. Fortunately, we can still use the path obtained from the high level planning to
choose the obstacles on which planning should be focused.
Figure 13: planned path in the map from Figure 5
The basic idea is that information from a less accurate path can help the planning process to
discard polygons that are far away from the path. Therefore our approach is to always compute
the plan at the higher level, and if required, use it to create a local map in which to apply
planning. This local map is built using the obstacle areas that contain the nodes in the path. The
difference now is that instead of including as nodes the vertices from the obstacle area
rectangles, we include the vertices of the union polygon. The union polygon is an optional part
of the obstacle area that is now computed by combining all the polygons inside the area. For
13
those areas having more than one polygon, this can reduce the number of vertices to include into
the graph, especially for polygons contained in others.
As another example, we can use the map from Figure 5 to plan a path between an initial and a
goal position. Figure 13 shows the first path that has been computed considering the higher level
of information. In that manner, we use this path to choose the four obstacle areas that are used to
build the local map that appears in Figure 14. In this case, the refined path is very similar to the
high level path due to the accuracy of the rectangles in approximating the obstacles of the
involved obstacle areas. We have chosen this example to illustrate the amount of obstacle areas
that can be discarded when building the low-level visibility graph (which appears on the right
side of Figure 14). On the left side of Figure 14 we can see the union of the polygons of the
involved areas and how the refined path goes closer to the obstacles than the one in Figure 13.
Figure 14: Local map: refined path from the path in Figure 13 (on left) and its visibility graph (on right)
It is not always the case that the refined path that results from the planing on the local map
avoids all the obstacles in the global map. In order to guarantee that, it is necessary to go up to
the obstacle area level and verify that there are no obstructing global map areas. If there is any
obstructing area, it is included in the local map and the local planning process is repeated.
In addition to the refinement of paths, both Figure 11 and Figure 13 illustrate another especial
situation of the path planning. In cases where the rectangles of the obstacle areas cover bigger
areas than the obstacles they contain, it is possible that the initial or final points of the path lay
inside an obstacle-area rectangle without being located inside any obstacle of this area. As we
have already said, the corresponding point must be included into the visibility graph establishing
the relations with the rest of the nodes in the graph. The difference now is that we compute the
visibility by using a combination of both levels of information. On the one side, we consider the
obstacles inside the obstacle area that contains the point and, on the other side, we still use the
high level of information –i.e., the rectangles- for the rest of the obstacle areas.
5. Considering Uncertainty
When building the map of an environment, there can be different sources of uncertainty, for
example, odometry and sensor errors are the main cause of uncertainty in obstacle positioning.
However, if we consider that in our approach obstacle information is mainly extracted from an
aerial camera, uncertainty about what is and what is not an obstacle becomes the main concern.
14
Shadows, different materials or color changes are just some of the environment features that can
lead the vision system to the identification of wrong objects. One way of facing this uncertainty
is to associate with each polygon a certainty degree of its correspondence to real obstacles in the
environment. We obtain the certainty degree by taking the product of the area of the polygon and
the reliability of the sensor that detected the polygon. In our case we have two kinds of sensors –
a camera and sonar sensors- and we assume reliability as being less than 1 for both sensors. In
the same manner, we compute the certainty degree of an obstacle area by adding certainty
degrees of all polygons inside this area.
The addition of uncertainty about the existence of an obstacle changes the concept of the
visibility graph. Considering that a polygon might not be a real obstacle, those node pairs that
were not connected because of this polygon visibility obstruction, should now have an edge
connecting them.
When planing over a regular visibility graph, the cost of an edge is usually considered to be the
Euclidean distance between the two nodes. Considering node uncertainty, more edges must be
added in order to represent relations between nodes whose connections might not be obstructed
even if the map has some polygons obstructing them. Nevertheless, the cost for these edges must
be now weighted distances, with the weights depending on the certainty of the obstacles they go
through. The value that we use as an edge cost is the Euclidean distance plus the addition of all
the certainty degree of those obstacle areas obstructing the visibility of the edge. Thus, visibility
is now checked for the complete graph and edge costs are updated by adding or subtracting
certainty degrees.
This new approach generates paths that can go through low certainty areas when there is not a
better path to follow. Unfortunately, when the path assumes that an obstacle can be passed
through and it turns out not to be the case, the robot that is following the path will need to apply
reactivity and will probably end up with a longer trajectory.
Figure 15: Parking image that is partially occluded by a tree.
Figure 15 shows an example of an image that can generate a map with a high density of non-
existing obstacles. In this case the image processing system produced eighty obstacles, and most
of them do not correspond to real obstacles but to shadows, trees, street lights or painted lines.
Although this kind of images may seem useless for the ground robots, we can use uncertainty to
15
plan paths going through these non-real obstacles. Since we have no means of distinguishing real
from non-real obstacles, path planning is done over a graph where all non-obstructed edges have
a much lower cost than those going through obstacles. In that manner, resulting paths avoid all
obstacles that are in fact possible to avoid. The path in Figure 16 illustrates this idea: it goes to
the left side of the Figure 15 parking area. This path ends in a position that is free, although a
tree makes it to appear occupied. Notice that going through this obstacle is the only way the path
can reach its goal. The rest of the obstacles are avoided so that even if some of them do not
correspond to real obstacles, those that do correspond are safely avoided.
Figure 16: Planning with uncertainty: the path goes trough an obstacle in the map that does not correspond
to a real obstacle.
6. Future work
For future work we are mainly interested in developing more refined techniques for uncertainty
treatment. For example, certainty degree values can be combined on the basis
Necessity/Possibility Theory [1] which provides a way of reinforcing certainty values in polygon
intersections. In case we need more accurate maps because polygons cover bigger areas than the
real occupied ones, it is also possible to add information about free space. If a ground robot
sensed an obstacle it is because it could be placed somewhere nearby. This information might be
useful to determine a path avoiding that obstacle by including a description of the area where the
robot was placed into the corresponding obstacle area –which must have sonar polygons. In this
way, free space areas bound sonar-detected obstacles. In addition to that, free space areas can
also be added to those obstacle areas with low certainty value polygons that were actually
crossed by ground robots, so that they force certainty values to be decreased and thus the map to
be corrected.
16
Acknowledgments
We thank Enric Celaya from the Industrial Robotics Institute (IRI-CSIC at Barcelona, Spain) to
allow Maite López-Sánchez to apply to this work what she learnt about outdoor research from
her current work in the NEMO Project. We also thank Damian Hesse for working on the image
processing and Gogksel Dedeoglu for grouping sonar readings in the ground robots.
This work is supported in part by DARPA under contract F04701-97-C-0021.
Maite López-Sánchez is a visitor supported by the Spanish Research Council (CSIC) and by the
Catalan Research Council (CUR).
References
[1] Dubois and Prade, “Possibility Theory”, Plenum Press, New York, 1988.
[2] Kortenkamp D.M., “Cognitive maps for mobile robots: a representation for mapping and
navigation”, PhD dissertation, CS dept. University of Michigan, 1993.
[3] Lim and Cho, “Physically based sensor modeling for sonar map in specular environment” in
Proceedings of IEEE International Conference on Robotics and Automation, pp. 1714-1719,
1992.
[4] Lopez-Sanchez, Lopez de Mantaras and Sierra “Incremental map generation by low cost
robots based on Possibility/Necessity grids” in Proceedings of Uncertainty in Artificial
Intelligence, pp. 351-357, 1997.
[5] Movarec and Elfes, “High resolution maps from wide angle sonar” in Proceedings of IEEE
International Conference on Robotics and Automation, pp. 116-121, 1985.
[6] Pagac, Nebot and Durrant-White, “An evidential approach to probabilistic map building” in
Proceedings of IEEE International Conference on Robotics and Automation, pp. 745-750, 1996.
[7] Pearl, “Heuristics: Intelligent search strategies for computer problem solving ” Addison-
Wesley Publishing Company, 1984.
[8]Tony J. Prescott, “Spatial representation for navigation in animats” in Adaptive Behaviour
4(2), 1996.
[9] Russel and Norving “Artificial Intelligence, a modern approach” Prentice Hall Editors.
Chapter 25: Robotics. 1995.
[10] Tod S. Levitt and Daryl T. Lawton, “Qualitative navigation for mobile robots” in Artificial
Intelligence 44, pp. 305-360, 1990
[11] Werger and Mataric “Robotic Food Chains: externalization of State and program for
minimal agent foraging” in Proceedings of the 4
th
international Conference on Simulation of
Adaptive Behavior, 1996.

Asset Metadata

Creator Bekey, George A. (author), López-Sánchez, Maite (author), Sukhatme, Gaurav Suhas (author)

Core Title USC Computer Science Technical Reports, no. 683 (1998)

Alternative Title Mapping an outdoor environmnent for path planning (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

Tag OAI-PMH Harvest

Format 16 pages (extent), technical reports (aat)

Language English

Unique identifier UC16270544

Identifier 98-683 Mapping an outdoor environmnent for path planning (filename)

Legacy Identifier usc-cstr-98-683

Format 16 pages (extent),technical reports (aat)

Rights Department of Computer Science (University of Southern California) and the author(s).

Internet Media Type application/pdf

Source 20180426-rozan-cstechreports-shoaf (batch), Computer Science Technical Report Archive (collection), University of Southern California. Department of Computer Science. Technical Reports (series)

Access Conditions The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Repository Email csdept@usc.edu

Inherited Values

Title Computer Science Technical Report Archive

Description Archive of computer science technical reports published by the USC Department of Computer Science from 1991 - 2017.

Coverage Temporal 1991/2017

Repository Email csdept@usc.edu

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

Linked assets

Computer Science Technical Report Archive