Wireless Sensor Networks: Modeling and Analysis for Estimation and Control

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Wireless Sensor NetworksModeling and Analysis
for Estimation and Control

• Prof. Sastrys Nest Group
• April 16, 2004

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Questions

• A driving example
• How to route in Ad hoc networks?
• What are the control theoretic implications of
  using WSNs within the control loop?
• How can we track multiple object?
• Pursuit Evasion Games (PEG) with WSN?

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PEG Set-up
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What pursuers really see
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Sensor net increases visibility
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Strategy Planner
Map Builder
Vehicles coordination layer
Pursuers communication infrastructure
Tactical Planner Regulation
Vehicle-level sensor fusion
Control Signals to pursuer
Single vehicle estimation and control layer
WSN
vision
GPS
Sensor information layer
Physical Platform
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Distributed Pursuit Evasion Games (DPEGs)
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Questions

• A driving example
• How to route in Ad hoc networks?
• What are the control theoretic implications of
  using WSNs within the control loop?
• How can we track multiple object?
• Pursuit Evasion Games (PEG) with WSN?

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Routing with sporadic long links
Massimo Franceschetti Tanya Roosta Shankar Sastry
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Lets look at some real data
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Absence of sharp threshold
What we are used to
What we observe in practice
Can we exploit sporadic long links for routing ?
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Building the routing table
Links in the routing table
How do we build a routing table
with links at the right scale lengths
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Objective scale invariance
Z
r2
r1
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Objective scale invariance
Z
r2
r1
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Objective scale invariance
Z
r2
r1
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Objective scale invariance
Z
r2
r1
Slow close to destination
Slow far from destination
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Bottom line
T
e
d
S
Build networks where the density of neighbors
scales as 1/x2 to obtain efficient routing at
all distance scales
Want to balance the number of short and long
links Build small world networks!
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Questions

• A driving example
• How to route in Ad hoc networks?
• What are the control theoretic implications of
  using WSNs within the control loop?
• How can we track multiple object?
• Pursuit Evasion Games (PEG) with WSN?

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Can we use classical control theory?
Classical control design
Plant
Sensor
Controller
State estimator
Networked control in Sensor Networks
Wireless Sensor Network
Aggregate Sensor
Plant
Controller
State estimator
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Can we use classical control theory?
Classical control design

• Availability of data when needed
• Instantaneous communication
• Fixed delays

Plant
Sensor
Controller
State estimator
Networked control in Sensor Networks
Wireless Sensor Network
Plant
Aggregate Sensor

• Data dropped or randomly delayed in the
  communication

Controller
State estimator
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A priori analysis of performance

• Consider an application involving a large
  deployment of a WSN over a long period of time
• Given the application specs, want to know a
  priori how to design and deploy a network which
  will do the job
• Allocate the optimal amount of resources and
  guarantee successful outcome

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Estimation
Control
Sensors observations
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Observations travel through a network
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Lossy network
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Estimator Block Diagram View
System
z-1
M
Kalman Filter


-

z-1
M
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Main Result
l
l


C. the estimator is unstable

I.

some

and

0
for

c
l
l

lt
the estimator had bounded error

I.C.
any

and

1
for
c
1
l
l
l



-

1



c
s


max
i
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Typical estimation result below and above
critical value
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Extensions

• Close the loop

Wireless Sensor Network
Plant
Aggregate Sensor
Controller
State estimator
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Design Guidelines

• Estimation control problem
• Characterize the reliability of your channel
• Find your
• Model the dynamical phenomenon you want to
  observe (linearize if necessary)
• Observe the eigenvalues of the system
• If your estimate will have bounded
  covariance on average
• Else
• slow down dynamics (change eigenvalues) if you
  have control over them
• or increase the reliability of the channel

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How to get network parameters

• Want to extract the parameter ? from the WSN.
• ? is a lumped parameter that indicates the
  average success rate for a transmission
• Modeling we choose a Bernoulli process to model
  arrival of a packet.
• In order to identify the parameter, well use a
  data set from the real network.
• Average over all the nodes transmitting between
  all possible source and destination
  configurations.
• Test the result on an independent data set

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Our Plan an instrumented platform

• Need to extract internal state of each node for
  analysis of the global state of the network
• Routing level
• Average path length
• Delay distribution
• Packet loss process
• Sensing/Data Aggregation examples
• How does node density affect the precision of
  sensing?
• Number of observations aggregated per reading
  reported, variance of observations that were
  aggregated
• Every node will have an Ethernet connection to
  the base station
• Enable monitoring of the network without
  interfering with it

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Diagram of Testbed Physical Setup
Ethernet cable to the ceiling
Pulley
Emote
6m
1.5m
3m
Courtesy of Tanya Roosta
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Testbed Mote
eMote Connector
Base
Top View
Battery Holder
Battery Holder
Mote Stack
Distance??
Reset Switch
Battery Disconnect Switch
Ultrasound Ranging Board
Mica2Dot
Side View
eMote Pin-out and Switch Board
Magnetometer Board
Power Board
Batt
base
Courtesy of Phoebus Chen
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Toward a semantic definition of capacity for
control within WSNs

• What can you do with a sensor network?
• Literature provides key asymptotic results
• We are interested in answer different semantic
  questions, e.g.
• At the algorithmic level
• How much packet loss can a tracking algorithm
  tolerate?
• At the network level
• How many objects can a particular sensor network
  reliably track?
• At the control level
• How many plants can you control within a certain
  WSN?

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Communication and control in WSNs

• Consider PEGs
• Given capture time Tc as a metric we can explore
  fundamental tradeoff between density of pursuers
  ? and amount of information
• We expect that the amount of global information
  needed will decrease as the density of nodes
  increases.
• We need to formally define and order information,
  based on local vs. global

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Fundamental questions to answer

• What is the maximum density of nodes we can
  control, given a communication model
• This will answer some of our questions
• How many evaders can a specific WSN control and
  catch within a certain time bound?
• We expect a transition where Tc-gt8

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Closing the Loop AroundSensor Networks

• Formal framework
• Controller design
• Estimator design
• Test bed simulator
• PEG demo discussion
• Design
• Problems
• Solutions
• Lessons learned

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• Research Challenge
• Point navigation control for a vehicle
• Sensor Network is the only sensor
• Robust to
• network lag
• mote failures
• aperiodic, noisy sensor readings
• Time stamps for sensor readings
• Noisy
• Non-existent
• Dynamic system parameters

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• Design Methodology
• Develop vehicle and sensor network models
• Identify key system parameters
• Develop a parameterized point navigation
  controller
• Develop a state and parameter estimator
  exploiting knowledge of control scheme
• Simulate and implement design
• Evaluate designs performance

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• Control Scheme
• Many control schemes exist
• Start with simple controller
• Geometric controller is simple and will highlight
  bad estimation schemes
• First, turn as sharply as possible
• Then, go straight
• If point is within turning radius, first drive
  straight until point is outside turning radius

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• Estimation
• Develop probabilistic models based on knowledge
  of sensor network, vehicle dynamics, and chosen
  control scheme
• Using most recent data from sensor network,
  estimate the parameters and state of the vehicle
• Maximize the log likelihood over the
  parameter space given a set of data (sensor
  readings) using the following
  model

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Evader Position Estimate
Sensor Network
Evader Dynamics
?
Pursuer Dynamics
Controller
Estimator
Pursuer Position Estimate
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Turning Radius Estimator
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Velocity Estimator
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• Test bed
• 10 foot by 10 foot grid
• Camera with color tracking software estimates
  position of vehicle
• Automatic camera calibration scheme
• Pursuer estimates sent to Matlab
• Control computed in Matlab
• Control values broadcast to vehicle

Matlab
user supplied navigation point
Camera
Pursuer
Controller
Estimator
Pursuer Position Estimate
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Testbed Intel Labs, Berkeley
Testbed Vehicles COTS-BOTS
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Simulation
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Simulation
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Questions

• A driving example
• How to route in Ad hoc networks?
• What are the control theoretic implications of
  using WSNs within the control loop?
• How can we track multiple object?
• Pursuit Evasion Games (PEG) with WSN?

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Multiple Target Tracking in Sensor Networks
Requirements
Our approach

• Autonomous
• Unknown number of targets
• Track initiation/termination
• Low computation and memory usages
• Robust against failures and delays
• Scalable
• Low communication load

• MCMC data association
• Can track unknown number of targets
• Can initiate and terminate tracks
• Low memory requirement
• Outperforms MHT
• Hierarchy
• Local data fusion

• MCMC data association
• Optimization algorithm (stochastic search)
• Solution space constrained partitions of
  observations
• Search for a partition with maximum posterior

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Questions

• A driving example
• How to route in Ad hoc networks?
• What are the control theoretic implications of
  using WSNs within the control loop?
• How can we track multiple object?
• Pursuit Evasion Games (PEG) with WSN?

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Pursuit-Evasion Algorithms with Imperfect
Information Characterizing the Performance of
Regions in the Sensor Network and Incorporating
this Performance Metric into the Pursuit Strategy

• Phoebus Chen

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Pursuit Evasion with Imperfect Information

• Sensor Networks are inherently lossy and
  imperfect
• How does this change a pursuit evasion problem?
• We have pockets in the network where
• Readings of an evaders position are more
  accurate
• Evader position readings have a lower probability
  of being lost
• Evader position readings can arrive at certain
  spots in the network faster
• The Pursuer does not have a perfect view of the
  world
• Pursuit Evasion Algorithms should account for
  irregularities in the network
• In the case of active evasion by the evader, the
  pursuer can exploit better regions in the
  network by chasing the evader away from poor
  performing regions.
• Pursuit strategy may change depending on
  speed/accuracy or position reports.
• ex. Fast, Accurate readings predict evaders
  next position and head off.
• Slow, Inaccurate readings greedy
  pursuit

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Metrics at Each Abstraction Level

• Pursuer Algorithm cares about
• Sensor Accuracy, Latency, Missing Data, False
  Alarm Rate, etc.
• Quality of data stream from the Base Station
  depends on
• Network Congestion, Node Density, Power
  Consumption Constraints, Physical Distance, etc.
• Is this the right abstraction? Pursuer can
  Change the Environment!

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Sensor Network Characteristics and Algorithm
Input-Data Characteristics

• We need to understand how
• Latency is related to physical distance and
  network congestion
• Also, is the actual distribution of reports over
  time important, or just the average latency?
• The Accuracy of reading reports is related to
  Localization Error (which can in turn be a
  function of many other factors), the number of
  nodes reporting (node density)
• Missing Data is related to the power level of the
  nodes (and hence sensor range), dropped packets
  from an overly congested network
• False Alarm Rate is related to the physical
  environment the nodes are deployed in
• Can we use machine learning to characterize this
  before the evaders arrive?
• Once we understand this relationship, we can
  begin characterizing pockets in the network as
  good/bad, better/worse.
• Probably more akin to a potential field than
  discrete regions

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Sample Scenario Evader hiding in a non-uniform
sensor network
Goal
Nodes low on power

• If the pursuer doesnt know of potential gaps in
  the network (ex. Sensors are lower on power, so
  sensing range is reduced), the evader may hide in
  those regions until the pursuer leaves.

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Other Potential Pursuer Strategy Changes

• Pursuer periodically patrols/test sensitivity of
  regions that are low on batteries, etc.
• At the sensor network level Network shuts up
  certain regions from reporting back to the
  pursuers when the network is too congested.
• These quite regions move with the evader and
  start reporting again when the network is less
  congested.
• In the future?
• Pursuers patching the network by dropping
  sensors
• Moving around mobile nodes?

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DyMNDRobust Adaptive Coordination in Dynamic
Meshes of Networked Devices

• Luca Schenato
• Joint project with Lockheed Martin Space Systems

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Multiple vehicles tracking and coordination using
sensor networks
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Control Unit Architecture
Control inputs to pursuer thrusters
PATH PLANNER
Assign evader to pursuer
CONTROLUNIT
PURSUER-to-EVADER ASSIGMENT
Position/velocity of each evader
EVADERS POSITION ESTIMATION
Sensor network data
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Simulation
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Issues

• Evader position estimation
• False alarm and missing observations
• Variable time delay of packets
• Data association and disambiguation
• Real-time (complexity constrained)
• Pursuer assignments
• Robust model predictive control
• Definition of time-to-capture and its estimation
• Optimization of multi-objective function
• Centralized vs decentralized
• Real-time (complexity constrained)
• Path planning
• Coordinated vs distributed
• Object collision avoidance predictive vs
  reactive
• Feedback vs feedforward
• Real-time (complexity constrained)