Robot Boats as a Mobile Aquatic Sensor Network
Kian Hsiang Low† , Gregg Podnar‡ , Stephen Stancliff‡ ,
John M. Dolan‡ , and Alberto Elfes§
Dept. Electrical and Computer Engineering† , Robotics Institute‡ , Carnegie Mellon University
5000 Forbes Avenue Pittsburgh PA 15213
NASA Jet Propulsion Lab§
MS:198-235 4800 Oak Grove Drive Pasadena CA 91109
{bryanlow, gwp, stancliff, jmd}@cs.cmu.edu, [email protected]
ABSTRACT
This paper describes the Multilevel Autonomy Robot
Telesupervision Architecture (MARTA), an architecture
for supervisory control of a heterogeneous fleet of networked unmanned autonomous aquatic surface vessels
carrying a payload of environmental science sensors.
This architecture allows a land-based human scientist to
effectively supervise data gathering by multiple robotic
assets that implement a web of widely dispersed mobile
sensors for in situ study of physical, chemical or biological processes in water or in the water/atmosphere
interface.
Categories and Subject Descriptors
I.2.9 [Robotics]: autonomous vehicles, sensors; I.2.11
[Distributed Artificial Intelligence]: intelligent
agents, multiagent systems
General Terms
Algorithms, Design, Experimentation, Human Factors
Keywords
telesupervision; autonomous surface vessels (ASV); sensor web; inference grids; log-Gaussian process.
1.
INTRODUCTION
Earth and ocean science research use data obtained
from space, the atmosphere, the land, surface water,
and the ocean to improve understanding of the Earth
and its natural processes. Developing better models of
ocean processes is crucial for assessing global warming
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ESSA Workshop ’09, April 16, 2009, San Francisco, California, USA
Copyright 2009 ACM 978-1-60558-533-8/09/04 ...$5.00.
and for meteorological and ecological studies, while surface water quality data give us insight into the suitability of the water for human use. Both are necessary
for assessing water’s ability to support aquatic life. At
least three in every four humans depend on “surface water as their primary source of drinking water”1 . Water
resources in a region are critical to economic growth as
well as to quality of life.
Freshwater sensing is typically done with fixed sensors
near tributaries and using periodic sampling. Ocean
sensing is typically done with satellites, buoys, and
crewed research vessels. Satellites are limited by cloud
cover, temporal and geographical coverage, and resolution. Manned research vessels are expensive to deploy,
and fixed sensors and anchored buoys cannot be easily moved to cover larger areas or to monitor regions of
increased interest.
Deploying mobile sensor platforms to augment fixed
sensors and sensor buoys will help us better understand
and model how contaminants/pollutants move and affect our environment, from industrial chemical and oil
spills, to Harmful Algal Blooms (HABs). These platforms will also enable in situ meteorological studies of
the atmosphere/ocean interface for hurricane prediction.
This paper describes a multi-robot science exploration
software architecture and system called Multilevel Autonomy Robot Telesupervision Architecture (MARTA)
[11]. MARTA was initially developed for supervisory
control of multiple robot assets exploring the lunar surface [4, 8, 12]. It has subsequently been expanded and
instantiated in a system called TAOSF (Telesupervised
Adaptive Ocean Sensor Fleet) for coordination and control of multiple robot boat exploration vehicles for oceanic
[5, 6, 13] and freshwater research [10]. For the ocean
boats, we have selected as an application the characterization of HABs [1], while for the freshwater vehicles, we
are concentrating on their use in water quality studies.
1
National Research Council. Earth Science and Applications
from Space: National Imperatives for the Next Decade and
Beyond, 2007.
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terprises,
and Emergent Space Technologies, provides
vehicle development, payload integration and testing,
operations, and maintenance of the OASIS fleet and
ground systems.
The OASIS platform is approximately 18 feet long and
weighs just over 3000 lbs. The vehicle has a payload
capacity of 500 lbs, and is designed to be self-righting
to ensure survivability in heavy seas. It supports a wide
range of communication links including spread spectrum
radio, a cellular phone link, and an Iridium satellite link.
Three platforms (named OASIS-1, OASIS-2, and
OASIS-3) are operated by NASA WFF and support operations for the TAOSF project. OASIS shakedown operations have been performed since early 2005 in the
waters of the DELMARVA region, including the Chincoteague Bay and Pocomoke Sound. The first open-
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L)2'-#"'+)C$&"'("*&)0+",-')4'42"3#?/-"2'X9/&$-0'3",3)23.'
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dard Space Flight Center via the Internet. It is from
this distribution point that NOAA weather researchers
will receive ocean and ocean/atmosphere interface sensor data.
2.2
The Robotic Sensor Boats (RSBs)
For the mobile deployment of freshwater quality sensors, a fleet of small and relatively inexpensive Robotic
Sensor Boats (RSBs) is being developed at CMU (Figure 2). The design is based on commercially available
components such as the hull, drive system, and communications system. Customization is kept to a minimum
with the primary focus being kept on the sensing and
navigation requirements.
The hull is a relatively inexpensive roto-molded recreational kayak that is fitted with a ducted thruster on
and
science data,
data, and
and well
well as
as control
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are all
all
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To develop
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handled over
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(Fig.
3).
Figure
2. Robot
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Boat (RSB)
under development.
being
built,
a smaller
platform
was adapted
(Fig. 3).
Figure 3. Initial testing of the telemetry and communications
package on a small (1m length) platform.
3. THE MARTA ARCHITECTURE
The MARTA system architecture (Fig. 4) provides an
integrated approach to multi-robot coordination and
multi-level robot-human autonomy. It allows multiple
robotic sensing assets (both mobile and fixed) to function
in a cooperative fashion, and the operating mode of
different robot platforms to vary from full autonomy to
teleoperated control.
Figure2:
2.
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development.
Figure
Robot
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2. Robot
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Figure 3. Initial testing of the telemetry and communications
Figure 3. 3:
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Figure
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3. THE
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handled over a cellular modem. To develop and test the
control and communication packages while the RSB is
being built, a smaller platform was adapted (Figure 3).
3.
THE MARTA ARCHITECTURE
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both onboard each robot and at the telesupervisor’s
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both by the Fleet Planning and Navigation Monitoring module and by the human telesupervisor. Adaptive
replanning of the robot assignments is based on sensor inputs (dynamic sensing) and coordination between
multiple assets, thereby increasing data-gathering effectiveness while reducing the human effort required for
tasking, control, and monitoring of the vehicles. The assets depicted in Figure 4 include two OASIS platforms,
a drift buoy that reports its position as it moves with
the current, and a Robot Sensor Boat for surface water
operations.
Figure 4. MARTA Telesupervision Architecture
Figure 4. MARTA Telesupervision Architecture
Multi-level autonomy includes low-level autonomy on
each independently operating robot; autonomous mon4. MAPPING
ALGALand when necitoring
of the fleet;HARMFUL
adaptive replanning;
4. MAPPING
HARMFUL
ALGAL
essary,
intervention
by
the
human
telesupervisor either
BLOOMS (HABS)
BLOOMS
(HABS)
with
manual
replanning,
or
by
taking
control
Interest in Harmful Algal Bloom (HAB)direct
detection
has of
Interest
in teleoperation.
Harmful Algal Bloom (HAB) detection has
agrown
robot in
via
recent years for scientific, commercial and
grown
in recent
years for
scientific,
and
Algorithms
for science
analysis
of thecommercial
acquired data
can perform an initial assessment of the presence of specific science signatures of immediate interest. This can
be done both onboard each robot and at the telesupervisor’s workstation. Web-based communications support
both control and communications of the robotic fleet
over long distances, and the sharing of newly sensed
and historical data with remote experts.
rhodamine WT (water-tracing) dye as a HAB surrogate
for initial experiments and tests.
For investigating an algal bloom, researchers at CarnegieMellon University take control of the OASIS platforms
and provide the high-level planning and monitoring. The
OASIS collection of weather-related data mentioned
4.
MAPPING
HARMFUL
ALGALsensing
BLOOMS
earlier
is not interrupted,
but the additional
for
investigating
(HABS)the algal bloom is brought online to map the
extent of a bloom, chlorophyll concentrations, and with
Interest in Harmful Algal Bloom (HAB) detection has
additional sensors, eventually allow a shore-based
grown
in the
recent
years
for scientific,
commercial
public
biologist
ability
to determine
the species
of the algae
health
reasons.
Depending
on
the
type
of
algae
present,
to assess whether it is harmful. If it is, local authorities
HABs
beenat shown
to be businesses,
dangerous fisheries,
to sea lifeand
and
can behave
notified
aquaculture
to
human
health.
beaches.
There is a significant interest in identifying environmental factors that contribute to the occurrence of HABs,
so
these may be
incorporated in bloom predic5. that
INFERENCE
GRIDS
tionObservation
algorithms.of natural
These processes
factors may
include
time of
is limited
by spatial
year,
salinity,
and
sea-surface
temperature
to
predict
the
and temporal sensor footprint, coverage, resolution,
abundance
(low,
medium,
or
high)
and
type
of
HABs.
sampling rate, and measurement uncertainty. Markov
MARTA
will (MRFs)
provideprovide
the following
Random
Fields
a naturaladvantages
formulation over
to
existing
for observing
analyzing distributed
HABs:
representsystems
spatially
and and
temporally
We use
discretized version of MRFs,
•observations.
Dynamic tasking
anda adaptation;
called a spatio-temporal Markov Random Lattice (ST• Higher in situ resolution and greater insensitivity to
MRL), to encode the data obtained by the different
cloud cover in comparison to current satellite systems;
sensors and agents. Each cell in the lattice corresponds to
•a Access
to and and
greater
than
spatial volume
a timeagility
slice, in
andcoastal
stores awaters
stochastic
what is
available
through buoys;
vector
with
the probabilistic
state description of the
processes
that have
been measured
at the given
•various
Real-time
multipoint
science
data observations
and
location
and
time
interval.
Efficient
updating
are
generation of associated interpretations methods
by remotely
used
to improve
the probabilistic descrption encoded in
located
oceanographers.
Since HABs are sporadic ocean phenomena, we are using rhodamine WT (water-tracing) dye as a HAB surrogate for initial experiments and tests.
For investigating an algal bloom, researchers at Carnegie Mellon University take control of the OASIS platforms and provide high-level planning and monitoring.
The OASIS collection of weather-related data mentioned
earlier is not interrupted, but the additional sensing for
investigating the algal bloom is brought online to map
the extent of a bloom, chlorophyll concentrations, and
with additional sensors, eventually allow a shore-based
biologist the ability to assess whether the algal species
are harmful. If they are, local authorities can be notified
at aquaculture businesses, fisheries, and beaches.
5.
5.1
FIELD TESTS
Field Test 1 - Aug. 2007
For controlled experiments such as mapping while compensating for drift currents, geometric patches of rhodamine water-tracing dye are laid (Figures 5 and 6).
An aerostat, tethered to a manned tender boat, carries
an instrument package aloft including GPS, altimeter,
compass, and video camera to provide validation images
of data gathered by OASIS platforms that are mapping
with fluorometers.
Methodology: Inference Grids. Observation of natural processes is limited by spatial and temporal sensor
footprint, coverage, resolution, sampling rate, and mea-
sensor model was derived from information on the
sensitivity and performance of the sensors. The Inference
Grid map of rhodamine dye for one of our mapping
experiments (Fig. 5) is shown in Fig. 6.
platform is in the lower part of the image, close to the
rhodamine dye tracks that serve as a surrogate for algal
blooms during field testing. Fig. 7 shows the search
pattern executed by the OASIS boat to find the surrogate
algal bloom, and Fig. 8 displays an Inference Grid
showing the areas with high probability of dye presence
(in red), high probability of dye absence (in green), and
high entropy or lack of information (in grey). Finally, in
Fig. 9 an Inference Grid with inferred hypotheses of algal
blooms (dye tracks) is presented. The areas of high
entropy can be used to replan the search pattern of the
boat. Figure
Figure
5: OASIS-2
andOASIS-3
OASIS-3
mapping
a
5. OASIS-2 and
mapping
a
of rhodamine
water
tracing dye.
dye.
patch of patch
rhodamine
water
tracing
1
27
20
10
1
6. FIELD TESTS
For controlled experiments such as mapping while
compensating for drift currents, geometric patches of
rhodamine water-tracing dye are laid (Figs. 5 and 6). An
aerostat, tethered to a manned tender boat, carries an
instrument package aloft including GPS, altimeter,
compass, and video camera to provide validation images
of data gathered by OASIS platforms that are mapping
with fluorometers.
1
F
prob
abse
Fig. 6 shows an aerial view from the aerostat of the test
area in the Chesapeake Bay; the OASIS robot boat
Figure
Aerial view
from
the aerostat
observation
Figure
6: 6.Aerial
view
from
the aerostat
obserplatform.
The chaseThe
boat chase
(with aerostat
tether) is
in the
vation
platform.
boat (with
aerostat
upper part
of the
the image,
OASIS
boatimage,
in the lower
tether)
is in
upperthe
part
of the
thepart,
OAand
the
rhodamine
dye
tracks
laid
by
the
chase
boat
which
SIS boat in the lower part, and the rhodamine
serve as surrogate HABs are visible towards the right part of
dye tracks laid by the chase boat to serve as surthe image.
rogate HABs are towards the right part of the
image.
surement uncertainty. Markov Random Fields (MRFs)
provide a natural formulation to represent spatially and
temporally distributed observations. We use a discretized version of MRFs, called a spatio-temporal Markov
Random Lattice (ST-MRL), to encode the data obtained
by the different sensors and agents. Each cell in the
lattice corresponds to a spatial volume and a time slice,
and stores a stochastic vector with the probabilistic state
description of the various processes that have been measured at the given location and time interval. Efficient
updating methods are used to improve the probabilistic
description encoded in the lattice as new observations
flow in from the various sensors and platforms being
Figure
7. A slanted view of the ocean area where the test was
used
[2].
conducted.
A spiral
pattern was
executed
by theaddiboat.
Associated
with search
the ST-MRL
we also
maintain
The measured
rhodamine
concentrations
shown as
tional
stochastic
lattice-based
layers forare
inference
anda
vertical “ribbon”
along
the to
route
taken
the OASIS
decision,
which are
used
plan
andbycontrol
the boat.
activities of the robot platforms [3]. These layers include
Fig
7. R
[1] A
Berg
Expl
Proc
Stan
[2] E
Mau
J. M
Arch
Oper
Inter
and
TX,
Figure 6. Aerial view from the aerostat observation
platform. The chase boat (with aerostat tether) is in the
upper part of the image, the OASIS boat in the lower part,
and the rhodamine dye tracks laid by the chase boat which
serve as surrogate HABs are visible towards the right part of
platform is in the lower part
of the image, close to the
the image.
platform is dye
in the
lower
of as
theaimage,
close
the
rhodamine
tracks
thatpart
serve
surrogate
fortoalgal
rhodamine
dye tracks
that serve
as 7a surrogate
algal
blooms
during
field testing.
Fig.
shows theforsearch
blooms
during field
search
pattern executed
by thetesting.
OASISFig.
boat 7to shows
find thethe
surrogate
pattern
executed
by
the
OASIS
boat
to
find
the
surrogate
algal bloom, and Fig. 8 displays an Inference Grid
algal
bloom,
and with
Fig. high
8 displays
an of
Inference
Grid
showing
the areas
probability
dye presence
showing
the
areas
with
high
probability
of
dye
presence
(in red), high probability of dye absence (in green), and
(in
highorprobability
of dye absence
(in green),
highred),
entropy
lack of information
(in grey).
Finally,and
in
high
entropy
or
lack
of
information
(in
grey).
Finally,
in
Fig. 9 an Inference Grid with inferred hypotheses
of algal
Fig.
9
an
Inference
Grid
with
inferred
hypotheses
of
algal
blooms (dye tracks) is presented. The areas of high
blooms
(dyebetracks)
presented.
The areas
entropy can
used tois replan
the search
patternofofhigh
the
entropy
can
be
used
to
replan
the
search
pattern of the
boat.
boat.
1
27
1
27
10
20
30
39
10
20
30
39
Figure 9. Inference Grid with inferred hypotheses of algal
blooms (dye tracks).
27
20
20
10
10
20
20
7. REFERENCES
[1] A. Elfes, J. M. Dolan, G. Podnar, S. Mau, and M.
Bergerman. "Safe and Efficient Robotic Space
Exploration with Tele-Supervised Autonomous Robots."
Proceedings of the AAAI Spring Symposium 2006,
Stanford, CA, USA, March 27-29, 2006.
10
10
1
Results and Analysis. Figure 6 shows an aerial view
from the aerostat of the test area in the Chesapeake
Bay; the OASIS robot boat platform is in the lower
part of the image, close to the rhodamine dye tracks
that 7.serve
as a view
surrogate
for algal
during
field
Figure
A slanted
of the ocean
area blooms
where the
test was
Figure
7. A A
slanted
of pattern
the ocean
area
where
thethe
test
was
conducted.
spiral view
search
executed
by
boat.
testing.
Figure
7 shows
thewas
search
pattern
executed
conducted.
A spiral
search
wassurrogate
executed
by
the boat.
The
rhodamine
concentrations
are shown
as
a
bymeasured
the OASIS
boat
topattern
find the
algal
bloom,
The
measured
rhodamine
concentrations
are
shown
as athe
vertical
“ribbon”8 along
the route
taken by the
OASIS
boat.
and Figure
displays
an Inference
Grid
showing
vertical “ribbon” along the route taken by the OASIS boat.
areas with high probability of dye presence (in red), high
probability of dye absence (in green), and high entropy
or lack of information (in grey). Finally, in Figure 9, an
1
[2] E. Halberstam, L. Navarro-Serment, R. Conescu, S.
Mau, G. Podnar, A. D. Guisewite, H. B. Brown, A. Elfes,
Figure 8. Inference Grid showing the areas with high
J.Figure
M. 8:
Dolan,
M.
Bergerman.
Robot
Supervision
8.of
Inference
Grid
showing
the"A
areas
with
high
Figure
Inference
Grid
showing
the
areas
probability
dyeand
presence
(in
red),
high
probability
ofwith
dye
Architecture
for
Safe
and
Efficient
Space
Exploration
probability
dye presence
(in
red), high
probability
dye and
high
probability
ofhigh
dye
presence
(in
red),of high
absence
(in of
green),
and
entropy
or lack
of information
Operation."
Proceedings
of
the
10th
Biennial
absence
(in
green),
and
high
entropy
or
lack
of
information
(in grey). (in green), and high
probability of dye absence
(in grey).
International
Conference
on Engineering,
Construction,
entropy
or lack
of information
(in grey).
and Operations in Challenging Environments, Houston,
TX, USA, March 5-8, 2006.
1
Figure 7.7:A A
slanted
view view
of the ocean
where
the test
was
Figure
slanted
of thearea
ocean
area
where
conducted.
A spiral
search pattern
was executed
bypattern
the boat.
the
test was
conducted.
A spiral
search
The measured
concentrations
are shown rhoas a
was
executedrhodamine
by the boat.
The measured
vertical “ribbon”
along the route
by the
boat.
damine
concentrations
aretaken
shown
asOASIS
a vertical
“ribbon” along the route taken by the OASIS
boat.
vehicle navigation cost and risk to reach an area of interest; hypotheses of scientific events to be explored
further; information metrics such as entropy to determine how the knowledge of a natural process is evolving,
and where critical information is missing; and others.
The augmented informational structure that incorpoFigure
6. Aerial
view fromand
the aerostat
observation
rates
both
the ST-MRL
the information-theoretic
Figure 6.The
Aerial
view
from
theaerostat
aerostattether)
observation
platform.
chase
boat
(with
is in the
inference
and chase
decision
layers aerostat
is calledtether)
an Inference
platform.
The
boat
is in part,
the Grid
upper
part of
the image,
the(with
OASIS boat in
the lower
(IG)
[3,
7].
upper
of the image,
the OASIS
the lower
part,
and
thepart
rhodamine
dye tracks
laid byboat
the in
chase
boat which
MARTA/TAOSF
system,
useright
the which
Inference
andIn
the
rhodamine
dye tracks
laid
by
thewe
chase
boat
serve
asthe
surrogate
HABs
are visible
towards
the
part of
Grid
(IG) model
tothe
represent
multiple
serve
as surrogate
HABs
are
visible towards
the spatiallyright part ofand
image.
the image. concerning both ocean
temporally-varying properties,
processes and HABs. The rhodamine dye concentration measurements taken by the OASIS platforms during field tests are used as input to the Inference Grid
mapping process. The fluorometer measurements are
used to compute the presence or absence of dye for each
cell in the area traversed by each OASIS boat. The
probabilistic sensor model was derived from information on the sensitivity and performance of the sensors.
The Inference Grid map of rhodamine dye for one of our
mapping experiments (Figure 5) is shown in Figure 8.
27
1
10
20
30
39
1
10
20
30
39
1
Figure 9.
GridGrid
with inferred
hypotheseshypotheof algal
Figure
9:Inference
Inference
with inferred
Figure
9. Inference
Grid(dye
with
inferred
blooms
(dyetracks).
tracks).hypotheses of algal
ses
of algal
blooms
blooms (dye tracks).
Inference Grid with inferred hypotheses of algal blooms
(dye tracks) is presented. The areas of high entropy can
7. used
REFERENCES
be
to replan the search pattern of the boat.
7. REFERENCES
5.2
Field Test 2 - Jul. 2008
[1] A. Elfes, J. M. Dolan, G. Podnar, S. Mau, and M.
[1]
Elfes,
M. the
Dolan,
G.
Podnar,
and
M.
InA.
this
fieldJ.
test,
rhodamine
WT S.
dyeMau,
is laid
down
Bergerman.
"Safe
and
Efficient
Robotic
Space
Bergerman.
"Safe
and
Efficient
Robotic
Space
in
two
stripes.
The
OASIS-2
boat
follows
a
raster
scan,
Exploration with Tele-Supervised Autonomous Robots."
Exploration
with
Tele-Supervised
Autonomous
which
progresses
along
the dye
stripes.
The Robots."
OASIS-2
Proceedings
of the
AAAI
Spring
Symposium
2006,
Proceedings
of
the
AAAI
Spring
Symposium
2006,
boat’s
trajectory
in
global
(GPS)
coordinates
(i.e.,
with
Stanford, CA, USA, March 27-29, 2006.
Stanford,
CA,isUSA,
March 27-29,
added
drift)
drift-corrected
to 2006.
produce a correspond[2] E. Halberstam, L. Navarro-Serment, R. Conescu, S.
ing
trajectory in (water)
surface coordinates
(i.e., with[2]
R. Conescu,
S.
Mau,E.G.Halberstam,
Podnar, A. L.
D. Navarro-Serment,
Guisewite, H. B. Brown,
A. Elfes,
out
drift).
From
Figure
10,
we
can
observe
that
the
Mau,
G.
Podnar,
A.
D.
Guisewite,
H.
B.
Brown,
A.
Elfes,
J. M. Dolan, and M. Bergerman. "A Robot Supervision
latter
drift-corrected
trajectory stretches
over
a shorter
J.
M. Dolan,
andSafe
M. and
Bergerman.
Robot
Supervision
Architecture
for
Efficient "A
Space
Exploration
and
distance
(i.e.,
233m)
as
compared
to
that
of
the
former
Architecture forProceedings
Safe and Efficient
Exploration
and
Operation."
of Space
the 10th
Biennial
trajectory
380.9m). on
With
drift
the dye
Operation."(i.e.,
Proceedings
of
the correction,
10th
Biennial
International
Conference
Engineering,
Construction,
stripes
do notConference
“run
away”on
from
the boat. Construction,
International
Engineering,
and
Operations
in Challenging
Environments,
Houston,
Our
aim
is
to
reconstruct
the
(drift-corrected)
rhoand USA,
Operations
Challenging
Environments,
Houston,
TX,
Marchin5-8,
2006.
damine
WT
dye
map
(i.e.,
in
surface
coordinates)
using
TX, USA, March 5-8, 2006.
the sparse dye data collected along OASIS-2 boat’s tra-
140
t=780s
120
Global coordinates
Surface coordinates
100
START
t=1s
t=780s
8.5
120
8
t=1
t=780
100
80
60
7.5
80
7
60
6.5
40
20
0
0
50
100
150
200
250
300
350
400
Figure 10: Comparison of OASIS-2 boat’s trajectories with and without added drift (respectively, green and black paths). The units for the
axes are in meters.
jectory over a 380.9m×87.5m sampling region (i.e., 780
fluorometer readings over a period of 13 minutes). In
particular, we want to investigate if the dye-stripe phenomenon can be inferred from the reconstructed map.
Methodology: Log-Gaussian Process. The dye
data (see Figure 11) collected by OASIS-2 boat is characterized by continuous, spatially correlated, positively
skewed (Figure 12) fluorometer measurements. Using
this sparse dye data, we will reconstruct the dye map
in surface coordinates, which spans 233m by 102.4m.
The properties of the fluorometer measurements suggest the use of the non-parametric probabilistic inference model called the log-Gaussian process (`GP). The
advantage of this modeling technique is that it does not
require any assumptions on the distribution underlying
the sampling data. Furthermore, the prediction of fluorometer measurements at unobserved locations can be
performed at any desired map resolution. We will now
describe the log-Gaussian process briefly and refer the
interested reader to [9] for more details.
Let X be the domain of the dye map corresponding to
a finite, discretized set of locations. Each location x ∈ X
is associated with an observed fluorometer measurement
yx and its corresponding random counterpart Yx . Let
{Yx }x∈X denote a `GP defined on the domain X . That
is, if we let Zx = log Yx (i.e., Yx = exp{Zx }), then
{Zx }x∈X is a Gaussian process (GP). This means the
joint distribution over any finite subset of {Zx }x∈X is
Gaussian. The GP can be completely specified by its
(prior) mean and covariance functions
4
µZx = E[Zx ] ,
4
σZx Zu = cov[Zx , Zu ]
for x, u ∈ X . Let the data d denote n pairs of sampled locations and their corresponding observed measurements. Let x and zx denote vectors comprising the
location and measurement components of the data d. If
the data d are available, the distribution of Zx remains
a Gaussian with the posterior mean and variance
4
µZx |d = E[Zx | d] = µZx +
>
Σxx Σ−1
xx {zx
− µZx }
(1)
6
40
5.5
20
5
0
0
50
100
150
200
250
4.5
8.5
9
8
8
7.5
7
7
6.5
6
6
5
5.5
4
0
5
50
150
100
100
150
4.5
50
200
250
0
Figure 11: Continuous, spatially correlated fluorometer readings (measured in mg/m3 ) of the
drift-corrected trajectory (measured in meters).
4
2
σZ
= var[Zx | d] = σZx Zx − Σxx Σ−1
xx Σxx
x |d
(2)
where, for the location components v, w in x, µZx is
a column vector with mean components µzv , Σxx is a
covariance vector with components σzx zv , Σxx is the
transpose of Σxx , and Σxx is a covariance matrix with
components σzv zw . Note that the posterior mean µZx |d
(1) is the best unbiased predictor for predicting the
log-measurement zx at the unobserved location x. An
important property of the Gaussian posterior variance
2
σZ
(2) is its independence of zx .
x |d
The `GP has the (prior) mean and covariance function
4
µYx = E[Yx ] = exp{µZx + σZx Zx /2} ,
4
σYx Yu = cov[Yx , Yu ] = µYx µYu (exp{σZx Zu } − 1)
for x, u ∈ X . We know that the distribution of Zx
given the data d is Gaussian. Since the transformation
from zx to yx is invertible, the distribution of Yx given
the data d is log-Gaussian with the posterior mean and
variance
4
2
µYx |d = E[Yx | d] = E[exp{Zx } | d] = exp{µZx |d +σZ
/2}
x |d
(3)
4
2
σY2 x |d = var[Yx | d] = µ2Yx |d (exp{σZ
} − 1)
x |d
(4)
2
where µZx |d and σZ
are the Gaussian posterior mean
x |d
(1) and variance (2) respectively. Note that the log-
300
250
8.5
20
8
30
7.5
40
200
Sample frequency
10
7
50
6.5
60
150
6
70
100
80
50
100
0
5.5
5
90
0
4
4.5
50
100
150
200
(a)
4.5
5
5.5
6
6.5
Measurement
7
7.5
8
8.5
9
Figure 12: Positively-skewed fluorometer readings (mg/m3 ): The positive skew results from a
small number of high measurements and a huge
pool of low measurements.
2.5
10
20
2
30
40
1.5
50
60
Gaussian posterior mean µYx |d (3) is the best unbiased predictor for predicting the actual measurement
yx = exp{zx } at the unobserved location x. On the
other hand, exp{µZx |d } is a biased predictor of the actual measurement yx = exp{zx }. This can be observed
from (3) that µYx |d ≥ exp{µZx |d }.
Results and Analysis. The log-Gaussian process is
used to predict the fluorometer measurements at 233 ×
103 = 23999 unobserved locations that are evenly spaced
throughout the sampling region in surface coordinates
(Figure 13). Figure 13a shows the predicted map (3)
while Figure 13b shows the variance (4) associated with
the predicted locations. From Figure 13a, we can observe two roughly parallel dye stripes running from the
right with higher concentration to the left with lower
concentration. The left part of the dye stripes appears
to be more diffused, thus resulting in a smaller interstripe gap. From the lengthscale hyperparameters of
the log-Gaussian process (obtained using maximum likelihood estimation), we also learn that there is a much
higher degree of spatial correlation between fluorometer measurements along the horizontal axis than along
the vertical axis. This allows the two dye stripes to be
inferred relatively well.
Using the predicted dye map (Figure 13a), we further
perform binary classification (Figure 13c) via columnwise thresholding to determine if each map location is
in a dye stripe or not. From Figure 13, we can see that
the top dye stripe is better identified than the bottom
one. Figure 14 shows the row-wise profile of the predicted dye map (Figure 13a); each circle denotes the
mean predicted fluorometer measurement for a particular row (≈ 0.9945m wide). If we set the threshold to
the mean fluorometer measurement of the predicted dye
map (i.e., ≈ 5.3188mg/m3 ), Figure 14 then shows that
the top and bottom dye stripes in Figure 13 are approximately 15.9m and 22.9m wide, respectively, with
an inter-stripe gap of roughly 9.9m.
1
70
80
0.5
90
100
0
50
100
150
200
(b)
10
20
30
40
50
60
70
80
90
100
20
40
60
80
100
120
140
160
180
200
220
(c)
Figure 13: Map inference of rhodamine dye concentration: (a) Prediction, (b) variance, and (c)
binary classification via thresholding. The units
for the axes are in meters.
6.4
6.2
6
5.8
5.6
5.4
5.2
5
0
10
20
30
40
50
60
70
80
90
100
Figure 14: Row-wise profile showing the plot
of mean predicted fluorometer measurement
(mg/m3 ) vs. row number. The red circles are
above the threshold, which is set to the mean
fluorometer measurement of the predicted dye
map. The blue circles are below the threshold.
6.
CONCLUSIONS
The MARTA-based TAOSF multi-level autonomy control architecture provides many advantages over existing systems for observing and analyzing HABs including: dynamic tasking and adaptation; higher in situ
resolution and greater insensitivity to cloud cover (as
compared with satellite systems); access to and greater
agility in coastal waters than that available through
buoys; real-time multipoint science data observations
and generation of associated interpretations by remotely
located oceanographers.
By using the TAOSF architecture, it increases datagathering effectiveness and science return while reducing
demands on scientists for robotic asset tasking, control,
and monitoring. The data are also made available to
other scientists via the world-wide-web both as they are
collected, and from an historical data archive server.
[5]
[6]
[7]
Acknowledgements
This work was supported by NASA award NNX06AF27G,
“Telesupervised Adaptive Ocean Sensor Fleet”, granted
under the Advanced Information Systems Technology
program of NASA’s Earth Systems Technology Office
(ESTO). The TAOSF project is a collaboration among
Carnegie Mellon University (CMU), NASA Goddard
Space Flight Center (GSFC), NASA Goddard’s Wallops Flight Facility (WFF), Emergent Space Technologies, Inc. (EST), and the Jet Propulsion Laboratory
(JPL). Work on the OASIS platforms is conducted by
Emergent Space Technologies, Inc., EG&G, and Zinger
Enterprises under award NA03NOS4730220 from the
National Oceanic and Atmospheric Administration
(NOAA), U.S. Department of Commerce.
[8]
[9]
[10]
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