Wireless Distributed Sensor
Challenge Problem: Demo of
Physical Modelling Approach
Bart Selman, Carla Gomes, Scott Kirkpatrick,
Ramon Bejar, Bhaskar Krishnamachari,
Johannes Schneider
Intelligent Information Systems Institute, Cornell
University & Hebrew University
Autonomous Negotiating Teams
C&D Meeting, June 27, 2002
Vanderbilt University, Nashville TN
Outline
Overview of our approach
 Movie conventions
 Computational cost (can be small)
 Phase diagram
Connections with distributed agents
 We demonstrate results of varying amounts of renegotiation
Enhancements and restrictions
 Reduce sector changes
 Scale to larger sensor arrays
Overview of Approach
We develop heuristics more powerful
than greedy, not compromising speed
Goal:
 Principled, controlled, hardness-aware systems
IISI, Cornell University
ANTs Challenge Problem
Multiple doppler radar sensors track moving
targets
Energy limited sensors
Constrained, fallible
communications
Distributed computation
Real time requirements
Physical model (and annealing)
Represent acquisition and tracking goals in terms of a
system objective function
Define such that each sensor, with info from its 1-hop
neighbors, can determine which target to track
“Energy” per target depends on # of sensors tracking
More on annealing
Target Cluster (TC) is >2 1-hop sensors
tracking the same target – enough to
triangulate and reach a decision on response.
Classic technique – Metropolis method
simulates asynchronous sensor decision,
thermal annealing allows broader search
(with uphill moves) than greedy, under
control of annealing schedule.
Moving targets, tracking and acquisition
100 sensors, t targets (t=5-30) incident on the array,
curving at random. Movies of 100 frames for each of
several values of (sensors in range)/target and (1hop neighbors)/sensor. Sensors on a regular lattice,
with small irregularities. Between each frame a
“bounce,” or partial anneal using only a low
temperature, is performed to preserve features of the
previous solution as targets move.
Physical Model as Distributed Agents
To compare with agent-based approaches:
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Our sensors are independent agents
At each time step, each chooses a target to track, based on
the energy function, and informs its neighbors.
At T=0, sensors optimize locally
T>0 is like renegotiation with reduced constraints, except
that “uphill moves” may occur at any point in the search, not
only when stuck.
As targets move, sensor re-allocation is done using “heat
bumps” – low T is restricted renegotiation, higher T allows
more extensive search for alternatives.
Moving Targets -- Movies
Conventions:
Targets
(blue pts)
Target range
(green circles)
Sensors (crosses)
 Sectors
active in a TC
are shown
Target Clusters
(red lines)
Fraction of
targets covered
(thermometer)
Introduce reduced connectivity
2.8 ngbrs/sensor
6.16 ngbrs/sensor
Analysis of physical model results
When t targets arrive at once, perfect tracking can
take time to be achieved.
Target is considered “tracked” when a TC of 3+
sensors keeps it in view continuously.
We analyze each movie for longest continuous period
of coverage of each target, report minimum and
average over all targets.
Analyzing the movies
Summary frames:
easy case (10 targets)
hard case (30 targets)
color code: red (1 TC), green (2 TCs), blue (3 TCs), purple (4TCs) , …
Additional summary information:
Total time tracked, max continuous time tracked
Computation can be speeded up
>100x without loss of quality
Determine Phase Boundary
Results with moving targets
Target visibility range and targets/sensor bounds seen:
Movies to show:
Results of pure agent, agents with
renegotiation, and “annealing”
operating points
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CR10 = 4 ngbrs on average
15 targets incident on the array
Cases: T0, T0.3, T3.0
15 targets, no renegotiation
15 targets, T=0.3 in iterations
15 Targets, T=3.0 in iterations
15 targets, no renegotiation
15 targets, T = 0.3 renegotiation
15 targets, T = 3.0
Results of renegotiation
Harder cases see bigger improvement, but effect of small amounts hard to control.
Control of sector assignment
Previous movies allowed sensor to sample all
sectors while choosing target. Now we make
that choice only at the outset of time step.
Problem is harder. We lose about 8% average
coverage, hold same continuous coverage.
An intermediate approach is desireable.
Phase boundary (or threshold of dif ficulty)
moves in.
Finding the phase boundary
Finding the phase boundary
Comparing coverage, 10 targets, CR10
Sectors fixed
Sectors varying
Comparing coverage, 10 targets, CR10
Varying sectors
Fixed sectors
How much can search be speeded up?
Conservative setting (100x) uses <10 msec/sensor/time step (850
MHz Pentium)
Further 10-100x reductions possible except near phase bndry.
As the problems get bigger…
Physical model effort, in principle, scales linearly, not
exponentially, as number of sensors managed grows.
In our model, biggest cost is the communications
cost of keeping cluster information (TC’s) current in a
well-connected model with few targets present. As
the problem gets uglier, this cost decreases because
TC’s get smaller!
Example – series of simulations with 400 sensors, 40120 targets incoming. One movie can be seen at
http://www.cs.huji.ac.il/~kirk/darpa/film.gif .
How often must sectors change?
Note that varying sectors change less often, and give better solution.
Fraction of sensors covering targets
Once targets spread, nearly all sensors contribute.
Fraction of sensors covering targets
Fixing sectors reduces available sensors ~12%.
Average # of TCs per target tracked
Not wasteful, >1 TC’s helps handoff as targets move.
Average # of sensors tracking a target
Excessive coverage of some targets. Can sensors
be freed up to improve detection, save power?
Ways to further improve big array
performance:
Explore restricted # of sector changes in a time step.
Reallocate sensors from overtracked targets, e.g. by
tuning the potential for high densities.
Introduce target-identity memory to reduce need for
continuous tracking. Create a derived MRF object,
like edge detection in image processing.
IISI, Cornell University
Summary
Graph-based physical models capture
the ANTs challenge domain
Results on the tradeoffs between:
Computation, Communication, Radar range,
and Performance are captured in phase
diagram.
Techniques handle realistic constraints, fast
enough for use in real distributed system.
IISI, Cornell University
The End