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

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Outline of Talk

Prior Work

Local Boundary Tracking Algorithm

Formulation for Boundary Estimation

Formulation and Optimization

Simulation Results

Testbed Results

Cooperative boundary tracking with unmanned vehicles

Such general problems are of current interest for unmanned vehicle operations with specific applications of tracking coastal algae blooms chemical plumes adaptive ocean sampling oil spills hazardous chemicals Work in the controls literature by Zhang and Leonard,

Susca et al, Clark and Fierro, Barat and Rendas, and others.

Image of Exxon oil spill from http://www.epa.gov

UUV-gas algorithm

boundary outside

boundary inside

dt

d

Where θ is the heading of the vehicle and ω is the angular rate of

change.

Dm

r Rb

*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:

Multiple vehicles – spaced according to gas law.

Caltech Multi-Vehicle Wireless Testbedboundary tracking implementation

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.

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.

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.

Boundary Search Result

•Only works with clean sensor data.•Large circular motions are inefficient

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Advanced Control Law

Time-corrected algorithm:

Includes time difference between

crossing points on boundary,

Uses a reference angle, ref

boundary inside if

boundary outside if

)2~(5.0

)2~(5.0

ref

refpreviousnext

t

t

Zhipu Jin and ALB IEEE CDC 2008

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CUSUM Filter for noisy sensor data

Upper

Lower

0

0

) )),1()(,0min(max(

0)(

k

k

UkUcBkzkU

u

0)

0

)),1()(,0max(min(

0)(

k

k

LkLcBkzkL

l

Zhipu Jin and ALB IEEE CDC 2008

Hidden Markov Model for Time Dependent Boundary

Boundary (k) is determined by parameters s(k)

(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 (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)).

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Zhipu Jin and ALB IEEE CDC 2008

Solve as an Optimization Problem

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2D Boundary Simplification

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Matrix

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Discussion and Future Work

Current problem Needs a good initial guess Slow convergence to real parameters More accurate .

Future Work Using more sophisticated model to approximate boundary Algorithm for updating 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

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Raw output from sensor (top)Kalman filtered output (bottom)

Car on teal tape 3<t<6 and 9<t<12

Vehicle with IR sensor

IR onboard sensors

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 prefilterTime-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 NoiseUCLA 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 ImagesZhong 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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