MULTI-ROBOT COVERAGE WITH DYNAMIC COVERAGE

INFORMATION COMPRESSION

Zachary Wilson, Taylor Whipple and Prithviraj Dasgupta

Computer Science Department, University of Nebraska, NE 68182, Omaha, U.S.A.

Keywords:

Multi-robot coverage, Exploration, Information compression.

Abstract:

We consider the problem of distributed terrain or area coverage of an initially unknown environment using a

set of mobile robots. We describe a distributed algorithm that is able to solve the distributed coverage problem

without having each robot exchange its complete coverage map with other robots. The central part of our

technique is a compression algorithm used by a robot to approximate the regions that have been previously

covered and a ﬁtness function that calculates the degree of accuracy of the approximated coverage infor-

mation. The operation of our coverage algorithm is evaluated through experiments on simulated as well as

physical Corobot robots. We have quantiﬁed the extent of overhead introduced by our coverage algorithm to

prevent robots from performing repeated coverage. Overall, our results show that the robots are able to cover

the environment within different environment settings while signiﬁcantly reducing the amount of coverage

information communicated between different robots.

1 INTRODUCTION

Over the past few years, multi-robot area or terrain

coverage has emerged as an important research direc-

tion in multi-robot systems (Stachniss et al., 2008).

Using multiple, autonomous robots to perform the

coverage task in a distributed manner offers several

advantages that improve the system’s performance -

the system can scale efﬁciently with an increase in the

number of robots which in turn improves the speedup

of the coverage task, the communication overhead in

the system can be reduced as compared to a central-

ized system, and the system is robust against fail-

ures of individual robots. However, a major chal-

lenge in implementing a multi-robot system is to de-

sign efﬁcient coordination behaviors among the dif-

ferent robots. Two such challenges in the context of

multi-robot coverage are: the recording and integrat-

ing the coverage histories of all robots and making au-

tonomous decisions about future coverage regions for

each robot based on these histories, and reducing the

energy and time expended in the coverage process by

avoiding re-covering regions that have already been

covered. Several researchers have developed multi-

robot systems that describe different techniques to

perform area coverage while addressing these issues.

These techniques range from dispersion-based mech-

anisms where robots do not record or exchange indi-

vidual coverage information with each other (Batalin

and Sukhatme, 2002; Howard et al., 2002), to ap-

proaches in which the environment is modeled as a

graph and the coverage problem is treated as con-

structing the least-cost spanning tree (Hazon and

Kaminka, 2008; Rutishauser et al., 2009). In con-

trast to these approaches, our paper targets the mid-

dle ground lying between pure dispersion-based ap-

proaches, and, approaches that build a complete map

or representation of the environment on each robot.

In this paper, we investigate a complementary yet im-

portant issue in multi-robot coverage - reducing the

amount of coverage information exchanged between

robots in the system while ensuring that coverage per-

formance is not adversely affected. We describe a

coverage algorithm that interleaves coverage informa-

tion exchange between robots with dynamic compres-

sion of the coverage information to cover the environ-

ment with limited communication between the robots.

We have veriﬁed our coverage algorithm via experi-

ments on both simulated and physical Corobot robots

while showing that a system of multiple robots using

our coverage algorithm is capable of covering differ-

ent types of environments with very limited commu-

nication overhead.

236

Wilson Z., Whipple T. and Dasgupta P..

MULTI-ROBOT COVERAGE WITH DYNAMIC COVERAGE INFORMATION COMPRESSION.

DOI: 10.5220/0003538202360241

In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 236-241

ISBN: 978-989-8425-75-1

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

2 MULTI-ROBOT COVERAGE

WITH COMPRESSED

COVERAGE MAPS

We consider a scenario where R mobile robots are de-

ployed into an initially unknown two-dimensional en-

vironment. Each robot is localized with respect to the

environment using an on-board localization device.

The objective of the multi-robot distributed coverage

problem is to explore the environment while ensur-

ing that the area collectively covered by the robots is

maximized and the overlap between the regions cov-

ered by different robots is minimized. The basic idea

in our approach is to enable each robot to repeatedly

select a portion of the environment to cover by deﬁn-

ing a bounded polygon. The robot then records the

boundary coordinates of this polygon and uses a de-

terministic coverage pattern to cover the inside of the

polygon. Before proceeding to deﬁne another polyg-

onal block the robot has to inform other robots about

the region within the block that it has just covered,

so that other robots do not repeat coverage of this re-

gion. Communicating this information as is could in-

cur signiﬁcant communication overhead of communi-

cating many coordinate points, as well as signiﬁcant

computational overhead of merging overlapping poly-

gons. To address this problem, we describe a cover-

age algorithm where each robot compresses its cover-

age information using a polygonal approximation al-

gorithm prior to communication. This results in each

robot getting an approximate, yet fairly accurate map

of the regions that are known to be covered, so that

it can avoid repeated coverage of previously explored

regions and navigate towards previously unexplored

regions.

The state transition diagram for a robot in our sys-

tem is shown in Figure 1. Each robot has four states

of operation - block clearing, block deﬁne, dispers-

ing and history-compressing. To begin coverage, each

robot selects an unexplored location - a location that,

according to the robot’s current coverage information

in its coverage history, has not yet been covered by

itself or by another robot. After selecting an unex-

plored location, the robot starts deﬁning the boundary

of the block it plans to cover.

Deﬁning and Covering Blocks. The ﬁrst step for a

robot r performing coverage is to select a block or

sub-region to cover. To achieve this, a robot ﬁrst de-

ﬁnes the block virtually as a regular polygon with n

vertices and each edge of length d, with the start and

end vertices of the polygon rooted at the robot’s cur-

rent location. The robot then uses the block deﬁning

behavior to trace the edges of this virtual polygon and

Figure 1: State transition diagram for a robot’s behaviors.

determines if any edges or vertices of the block are

occupied by obstacles or if any portion of the block

is unreachable. On reaching each vertex of the block

the robot is deﬁning, a robot checks to see if any other

robot within its communication range has reported in-

formation that its current location has already been

explored. In this case, the robot aborts block-deﬁning,

discards the set of recorded vertices, and disperses to

an unexplored location to start deﬁning another block.

On the other hand, if the robot completes deﬁning the

bounded polygon block without encountering a pre-

viously explored location, it changes its state to block

covering and starts covering the inside of the block

whose boundary it just deﬁned; a robot uses the on-

line, single-robot spanning tree coverage (STC) algo-

rithm (Gabriely and Rimon, 2001) to cover a block

whose boundary it has deﬁned.

After a robot has ﬁnished covering a single block,

it selects the next block to cover. At the block se-

lection level, a robot prefers to cover regions that are

adjacent to its most recently covered block, if such a

region is available for coverage. Such a local block

selection rule ensures that the coverage performed by

a single robot in a navigable, previously uncovered

region remains contiguous and ’holes’ of uncovered

regions that need to be covered later are not left in be-

tween covered blocks. Contiguous block selection is

realized by a robot by selecting the start point for the

next block as the vertex along the edge of the recently

covered block, that is farthest from the start point of

the covered block, as illustrated in the bottom part of

Figure 3. The vertices of contiguous blocks covered

by a robot are appended to its short term coverage his-

tory.

Map Compression and Map Merging. As robots

cover multiple polygonal blocks, the size of the short

term coverage history grows linearly for each robot.

However, communicating the short term history be-

MULTI-ROBOT COVERAGE WITH DYNAMIC COVERAGE INFORMATION COMPRESSION

237

Figure 2: Effect of vertex compression of two overlapping

rectangles with a combined polygon with m = 4. The gray

area (light and dark) is the desiredArea, the stroked area is

the gainedArea and the dark gray area is the lostArea.

tween all pairs of robots in the system is expensive

if boundary vertices are uncompressed. Additionally,

making calculations for determining covered regions

with a large number of vertices on every robot in-

volves considerable overhead. To prevent the rapid

growth of the coverage information, a robot com-

presses its covered boundary vertices using a polygo-

nal approximation algorithm called compressPolygon

for a line curve called the min − ε algorithm (Perez

and Vidal, 1994), and combines the compression with

the coverage information it has received from other

robots. It then recompresses the combined region.

This algorithm ensures that, after compression, the re-

gion is bounded by only a ﬁxed number of vertices de-

noted by m. However, using an approximation algo-

rithm for compressing a set of polygons introduces an

error in the compressed region, as illustrated in Figure

2. To mitigate the effect of the erroneous region intro-

duced by the compression algorithm, we have used a

ﬁtness function that tries to balance the loss in de-

sirable region (denoted by lostArea) and the gain in

undesirable region (denoted by gainedArea) as com-

pared to the actual area of the combined, but uncom-

pressed polygons (denoted by desiredArea), as given

below:

f itness = w ×

desiredArea − gainedArea

desiredArea + gainedArea

+(1 − w) ×

desiredArea − lostArea

desiredArea

. (1)

The ﬁrst fraction in Equation 1 denotes the error intro-

duced by the amount of unnecessary area included in

the approximated polygon while the second fraction

denotes the error introduced by the loss in actual area

of the uncompressed, combined polygons due to the

approximation. The weight w determines the prefer-

ence between these two errors, and, depending on the

Figure 3: Path of a robot showing the deﬁnition and cov-

erage of contiguous blocks. When contiguous block deﬁ-

nition fails due to the obstacle on the right-end of the di-

agram, the robot iteratively selects a new virtual polygon

whose percentage overlap with previously covered regions

falls below a certain threshold.

application domain, can be used to tolerate or reject

repeated coverage. The value of the ﬁtness function

is used to determine whether the approximated poly-

gon will be accepted for storage in the robot’s long

term history. If the ﬁtness function value lies above

a threshold of f

T hr

, the approximated polygon is ac-

cepted. On the other hand, if this value lies below the

threshold, the approximated polygon is rejected and

the original polygons are stored in the long term his-

tory as disjoint polygons without combining or com-

pressing them.

To combine the polygonal covered regions re-

ceived from other robots’ long term history, a robot

ﬁrst determines if the polygon representing its short

term history overlaps with the polygons in the long

term history. If there is no overlap, the robot stores

these two polygons as disjoint polygons in its long

term history; otherwise, it calculates the convex hull

of the combined polygons, uses the polygon vertex-

compression algorithm and ﬁtness function value de-

scribed above to store the the polygon with a ﬁxed

number of vertices within its long term history. Im-

mediately after updating the long term history, a robot

communicates its long term history to other robots

within its communication range.

Dispersing and Selecting Unexplored Locations. A

robot needs to select a new location to start coverage

from when it is initially placed in the environment and

after it has completed covering a series of contiguous

blocks. The new start location must not overlap with

any of the regions previously covered by the robot it-

self or by other robots. Also, the contiguous block

selection by a robot fails when the edge of the next

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

238

block it is planning to select is occluded by an obsta-

cle or a wall, as shown in Figure 3. In this scenario

too, the robot has to select a previously unexplored lo-

cation to start deﬁning a new block. Selecting a new

location requires the robot to check its own short term

coverage history, as well as its fused long term cov-

erage history. The scenario in which a robot selects

an unexplored location is shown in Figure 3. The

robot ﬁrst selects a virtual polygonal area p at random

within the environment. It then calculates the overlap

between this region p and the region it is aware of as

being covered from its coverage history. If the per-

centage overlap is below a threshold that is initialized

to O

T hr,init

, the virtual polygon p is accepted as the

polygon to start coverage from next and the robot se-

lects one vertex of p to as the start vertex for using sin-

gleBlockDeﬁne with this polygon. If the percentage

overlap crosses the threshold for n

T RIES

successive at-

tempts, the robot reattempts to select another virtual

polygon at a different location while increasing the

threshold by a factor δ

T hr

. If a polygon with over-

lap below O

T hr,max

cannot be found, the robot aborts

trying to select an unexplored location and stops. If

the selectUnexploredLocation algorithm successfully

returns a valid location, the robot uses an A* search

algorithm to plan its path to reach the location.

3 EXPERIMENTAL RESULTS

For verifying our coverage algorithm we have run sev-

eral experiments using Corobot robots within a robot

simulator called Webots. The Corobot robot is a four-

wheeled platform. Two cross-beam IR sensors with

a maximum range of 80 cm were placed on the front

of the robot for obstacle avoidance while one IR sen-

sor with a maximum range of 80 cm was placed on

each side of the robot to enable wall-following. Each

robot has wireless communications capabilities, and

a localization module (Hagisonic Stargazer RS kit)

that provides 2-D coordinates of the robot’s position

within the reference frame of the environment and has

an accuracy within ±2 cm of the robot’s actual loca-

tion. A photograph of the Corobot robot is shown in

Figure 4(a). The default speed of the robot was set to

5.2 cm/sec. A robot deﬁned a single block as a square

(n = 4) with each side’s length as d = 1 m. The dis-

tance at which a robot checks if it is still inside the vir-

tual block while following a wall is set to 0.1 m (one

half the length of a side of the robot). For the map

compression algorithm, the ﬁtness threshold value for

discarding a compressed polygon is f

T Hr

= 0.0 to

achieve a fair balance between introducing undesir-

able region and discarding desirable regions. Finally,

for the selectUnexploredLocation algorithm, the ini-

tial and maximum values of the overlap threshold

for discarding a polygon are O

T hr,init

= 0.0 (start op-

timistically with a target of ﬁnding a polygon with

no overlap), and O

T hr,max

= 0.95 (stop ﬁnding new

locations for starting a block deﬁne when 95% of

two polygons overlap in successive tries) respectively.

The threshold increment, in case of successive n

T RIES

failures, is δ

T hr

= 0.05, so that the selectUnexplored-

Location algorithm does not take excessively long to

reach the termination condition when successive at-

tempts to ﬁnd a new location end in failure.

Evaluating the min-ε Compression Algorithm. In

our ﬁrst set of experiments we measure the efﬁciency

of the min- ε algorithm used for coverage informa-

tion compression in our coverage algorithm. For the

dataset used as input for this algorithm, we generated

2-D point-sets with set-sizes ranging from 4 − 200.

Each point set corresponds to a set of polygons within

a 10 × 10 m

region. Figure 4(b) shows the effect of

using the standard zip algorithm called deﬂate (Sa-

lomon, 2006) to compress different sizes of the point

sets. We observe that the zip algorithm achieves very

nominal compression, close to 2% for point set sizes

> 150. This can be attributed to the fact that the data

points in each point set are generated randomly and

there is very little, if at all any, correlation between

the points in each set. In contrast, our coverage infor-

mation algorithm ﬁrst computes a convex hull of the

points in each point set, then performs min-ε com-

pression on the hull, ensuring that the amount of data

stored is constant. However, constant data size comes

at the cost of the accuracy of the region enclosed by

the polygons in the point sets. In Figure 4(c), we

show the decrease in the ﬁdelity of the region when

we approximate the region in a convex hull using the

min-ε algorithm. We see that when the compression

ratio is higher (3 points per convex hull), the accu-

racy quickly decreases to about 65%. On the other

hand, using more points in the min-ε compression re-

sults in higher accuracy of the region. Based on these

results, for the rest of our experiments we have used

4 points (as parameter m) in the min-ε algorithm to

approximate the region enclosed by the convex hull,

which yields about 90% accuracy in the approximated

region.

Webots Experiments. For our next series of exper-

iments we veriﬁed the operation of our coverage al-

gorithm. The arena for these experiments is 20 × 20

square region. We consider four different envi-

ronments within this arena: (a) no obstacles (b) 10%

of the arena’s area occupied by obstacles, (c) 25% of

its area occupied by obstacles, and, (d) walled ofﬁce

space with two narrow regions connected by a nar-

MULTI-ROBOT COVERAGE WITH DYNAMIC COVERAGE INFORMATION COMPRESSION

239

(a) (b) (c)

Figure 4: (a) Photograph of a Corobot ﬁtted with a Stargazer localization device. (b) Compression ratio obtained using the

DEFLATE zip library. (c) Ratio of the area of the approximated polygon calculated using the min-ε algorithm and the area of

the convex hull for different sizes (m = 3, 4, 6 and 8 vertices) of the compressed set.

row channel. All experiments were run for a dura-

tion of 2 hours (real time), unless otherwise stated. In

each environment, 2, 3 and 4 robots were used and the

robots were started at random locations within each

environment. All results are averaged over 10 simu-

lation runs.

In our ﬁrst set of experiments under this cate-

gory, we observe the area covered by the robots in the

different environment conﬁgurations. The coverage

achieved by 2, 3 and 4 robots in the different environ-

ment settings after 2 hours of simulation are shown in

Figures 5(a) - (d). We observe that across the different

environments, as the number of robots increases the

coverage performance improves. Overall, we see that

within 2 hours with 4 robots we are able to get com-

plete coverage in most of the environments, except

the corridor environment; however, we also observe

that when the environment becomes more complex,

the robots have to decide on regions to cover more of-

ten and therefore end up with less coverage in the 2

hours. For the corridor environment complete cover-

age was obtained after 8 hours of simulation.

For our next set of experiments, we quantify the

overhead of our coverage algorithm in terms of the

distance traveled by the robots, as shown in Figures 6

(a) and (b). We observe that as we increase the num-

ber of robots the amount of useful region covered per

robot reduces while the amount of overhead region

increases, due to robots covering longer distances to

select previously unexplored locations. Finally, we

also observe that as the environment becomes com-

plex with more obstacles, the overhead distance of the

robots increases. This observation can be attributed

to the fact that more obstacles in the environment re-

sult in robots encountering those obstacles and abort-

ing their block deﬁnition more often, thereby leading

to more overhead distance while traversing between

covered regions. Overall, this set of experiments show

that complex environments, as well as increasing the

2 robots 3 robots 4 robots

(a)

(b)

(c)

(d)

Figure 5: The amount of coverage achieved with 2 (left col-

umn), 3 (middle column) and 4 (right column) robots in

the different environment settings after 2 real-time hours of

simulation in Webots within a 20 × 20 m

arena (a) with

no obstacles in it, (b) with 10% of its area occupied by ob-

stacles, (c) with 25% of its area occupied by obstacles, (d)

divided into corridors.

number of robots within the same environment re-

sult in more overhead distance being traveled by the

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

240

(a) (b) (c)

Figure 6: Distances traveled (m) by each robot (a) while covering the environment and (b) while not covering the environment

(overhead) under the different robot and environment conﬁgurations. (c) Frequency of communication between robots in the

different scenarios.

robots.

The ﬁnal set of experiments under this category

shows our main objective of this paper - the efﬁcacy

of the coverage information compression algorithm

on the amount of communication between the robots.

By using the min-ε algorithm that encodes any con-

vex polygon with a ﬁxed number (m = 4) of 2-D data

points, we ensure that every communication between

any pair of robots will be contain only 4 2-D data

points. If k bytes are used to encode real numbers,

each communication will be no more than m × 2 × k

bytes. The results of this experiment shown in Fig-

ure 6(c) illustrate that the frequency of coverage data

transmission varies from infrequently to moderately

frequently, depending on the environment. We per-

formed all the experiments reported here on the phys-

ical Corobot robots as well and got commensurate re-

sults (omitted for space constraints).

4 CONCLUSIONS

In this paper we have described a distributed cover-

age algorithm for a multi-robot system that dynami-

cally compresses the coverage information to reduce

the communication overhead between the robots. Our

ongoing work is focussed on dynamically adjusting

the dimension of a block depending on the coverage

performance of each robot and investigating lossless

compression techniques for the coverage data to in-

crease the accuracy of the fused covered regions.

REFERENCES

Batalin, M. and Sukhatme, G. (2002). Spreading out: A

local approach to multi-robot coverage. In in Proc.

of 6th International Symposium on Distributed Au-

tonomous Robotic Systems, pages 373–382.

Gabriely, Y. and Rimon, E. (2001). Spanning-tree based

coverage of continuous areas by a mobile robot. An-

nals of Math and Artiﬁcial Intelligence, 31:77–98.

Hazon, N. and Kaminka, G. (2008). On redundancy, efﬁ-

ciency, and robustness in coverage for multiple robots.

Robotics and Auto. Systems, 56(12):1102–1114.

Howard, A., Mataric, M., and Sukhatme, G. (2002). Mo-

bile sensor network deployment using potential ﬁelds:

A distributed, scalable solution to the area coverage

problem. In in Proc. of 6th Int’l. Symp. on Distributed

Autonomous Robotic Systems, pages 299–308.

Perez, J. and Vidal, E. (1994). Optimum polygonal approxi-

mation of digitized curves. Pattern recognition letters,

15(8):743–750.

Rutishauser, S., Correll, N., and Martinoli, A. (2009).

Collaborative coverage using a swarm of networked

miniature robots. Robotics and Auton Systems,

57(5):517–525.

Salomon, D. (2006). Data Compression: The Complete

Reference. Springer.

Stachniss, C., Mozos, O., and Burgard, W. (2008). Efﬁcient

exploration of unknown indoor environments using a

team of mobile robots. Annals of Mathematics and

Artiﬁcial Intelligence, 52(2-4):205–227.

MULTI-ROBOT COVERAGE WITH DYNAMIC COVERAGE INFORMATION COMPRESSION

241