Environmental Boundary Tracking and
Estimation Using Multiple Autonomous
Vehicles
Andrea Bertozzi
University of California, Los Angeles
Thanks to Zhipu Jin, Rick Huang, Abhijeet Joshi, Todd Wittman, Trevor
Ashley, Zhong Hu, and others
This research supported by the Army Research Office, the National
Science Foundation, and the Office of Naval Research
Outline of Talk
Prior Work
Local Boundary Tracking Algorithm
Formulation for Boundary Estimation
Formulation and Optimization
Simulation Results
Testbed Results
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Cooperative boundary tracking with unmanned
vehicles
Such general problems are of current interest
for unmanned vehicle operations with specific
applications of tracking
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coastal algae blooms
chemical plumes
adaptive ocean sampling
oil spills
Image of Exxon oil spill from http://www.epa.gov
hazardous chemicals
Work in the controls literature by Zhang and
Leonard, Susca et al, Clark and Fierro, Barat and
Rendas, and others.
UUV-gas algorithm
*M. Kemp, A Bertozzi, D. Marthaler, 2004, Multi-UUV perimeter surveillance ,
Autonomous Underwater Vehicles, 2004 IEEE/OES, 17-18 June 2004
Single vehicle UUV-gas: Assuming that only a binary
state sensor is available, the vehicle travels around an arc
in a clockwise direction when inside the region of interest
and counterclockwise when outside the region of interest.
The behavior is described by the following:
d  

dt  
inside boundary
outside boundary
Where θ is the heading of the
vehicle and ω is the angular rate of
change.
Dm
r
Multiple vehicles – spaced according to gas law.
Rb
Caltech Multi-Vehicle Wireless Testbed
boundary tracking implementation
Chung H. Hsieh, Zhipu Jin, D. Marthaler, B. Q. Nguyen, D. J. Tung,
ALB, and R. Murray
Proc. American Control Conference, 2005
Testbed implementation without sensor noise.
Kelly vehicle with 700 Mhz laptop, two ducted
fans, 3 casters, gyro, barcoded hat, and
body frame.
Overhead positioning system tracks in real
time and sends information back to
vehicles.
Boundary Search Result
Individual path of (A) Vehicle 1,
(B) Vehicle 2, (C) Vehicle 3 while
cooperatively searching the
boundary.
The square, diamond, circle, and
triangle represent 1, 40, 80, 120
seconds respectively of each
vehicle’s path.
(D) Union of boundary crossing
point from the three vehicles
over 160 seconds (1 lap). The
axes are measured in meters.
•Only works with
clean sensor data.
•Large circular
motions are
inefficient
Zhipu Jin and ALB IEEE CDC 2008
Advanced
Control Law
Time-corrected algorithm:
 next
~
 0.5  ( t   2 ref ) if outside boundary
  previous  
~

0
.
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(
t   2 ref ) if inside boundary
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Includes time difference between
crossing points on boundary,
Uses a reference angle, ref
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CUSUM Filter for noisy sensor data
0
k 0

Upper U (k )  
min(max( 0, z (k )  B  cu  U (k  1)), U ) k  0
0
k 0

Lower L(k )  
max(min( 0, z (k )  B  cl  L(k  1)), L )k  0
Zhipu Jin and ALB IEEE CDC 2008
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Hidden Markov Model for Time
Dependent Boundary
Boundary W(k) is determined by parameters s(k)
W(k) = g(s(k))
where s evolves according to a Markov chain.
We observe the vehicles’ positions as
yi (k) = xi (k) + wi (k)
where i ϵ{1, · · · ,N}. Actually, there exist an offset d(k) between
xi and the real boundary.
Recursive Bayesian method: the distribution p(s(k)|Y(k)) is
predicted from p(s(k −1)|Y(k −1)) and p(s(k)|s(k −1)), and then
corrected by the measurement likelihood p(Y(k))|s(k)).
Zhipu Jin and ALB IEEE CDC 2008
.
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Solve as an Optimization Problem
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2D Boundary Simplification
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Matrix P
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Discussion and Future Work
Current problem
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Needs a good initial guess
Slow convergence to real parameters
More accurate P.
Future Work
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Using more sophisticated model to approximate boundary
Algorithm for updating P
Motion patterns of individual vehicles (d(k)) and possible approximation
of the distribution p(Y(k)|s(k)).
Realistic models for environmental tracers in air/ocean.
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Testbed implementation fixed boundary
IR onboard sensors
Vehicle with IR sensor
Raw output from sensor (top)
Kalman filtered output (bottom)
Car on teal tape
3<t<6 and 9<t<12
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CUSUM Filtering algorithms without/with
Kalman Prefliter
Without Kalman prefilter
With Kalman prefilter
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Comparison Bang-bang controller vs.
Zhipu
Bang-bang controller, no
prefilter
Time-correction controller, no
prefilter
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Comparison, without/with Kalman
prefilter
No Kalman prefilter, with time
correction
Kalman prefilter, with time
correction
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Boundary Tracking with Noise
UCLA testbed implementation, single vehicle
•Processor will decide state
based on noisy sensor data
•Vision system no longer
necessary to track boundary
•Useful if occlusions block
vehicle from cameras or if
GPS unavailable.
•Hidden Markov model for
changing boundary and
multiple vehicles
Thanks to Trevor Ashley
Harvey, Mudd College, Rick
Huang UCLA
Three car alogrithm
Three car algoritm
Lead car position
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Gradient Free Boundary Tracking in Images
Zhong Hu, Todd Wittman, Victor Mejia, ALB
We want to segment a region of interest in a (hypespectral)
image.
Classical gradient-based segmentation methods like active
contours and snakes look at all pixels in the image.
Ideally, the number of pixels checked would be proportional to
the length of the boundary.
The solution is to “walk” the boundary.
We propose a gradient-free boundary tracking algorithm
inspired by the robotic vehicle tracking algorithm developed by
(Kemp-Bertozzi-Marthaler 2004).
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Gradient free summary
Useful method for both high resolution/low SNR images and
robotics applications with noisy sensors
Time corrected algorithm improves efficiency while still
adequately tracking boundary
In very high SNR prefiltering of data can be useful
Multiple cooperative trackers can perform tasks such as
independent tracking and convoy control
Possible use for HSI imagery where pixel identification
applications sometimes involve cumbersome lookup tables or
computationally intensive manifold learning (e.g. bathymetry
calculations from remote sensing – C. Bachmann et al IEEE
2002-2007).
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