Coverage and Fault Tolerance Maximization in Mobile Sensor Networks

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Coverage and Fault Tolerance Maximization in
Mobile Sensor Networks

• By
• Michael Portnoy

• June 06/2006

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Presentation Focus

• Survey of recent research on Mobile Sensor
  Networks (MSNs).
• Emphasize on how the coverage of an MSN may be
  maximized while maintaining fault tolerance?

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Mobile Sensor Network

• A wireless network of small, inexpensive,
  spatially distributed devices capable of passive
  or active sensing of their environment.
• Capable of autonomous deployment or redeployment.

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Fault Tolerance

• Property of the MSN which enables it to maintain
  proper operation and degrade gracefully given the
  failure of some of the nodes in the MSN.
• By degrade gracefully, we say that the reduction
  in quality is at most proportional to the size of
  the failure.

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Coverage Behaviors

• Gage GAG92 defines coverage as the
  maintenance of spatial relationship which adapts
  to specific local conditions to optimize the
  performance of some function
• Describes three coverage behavior types
• Blanket coverage
• Barrier coverage
• Sweep coverage
• Effectiveness of each coverage behavior depends
  on the context of the specified mission goal.

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Blanket Coverage

• Static arrangement of nodes that maximizes the
  detection rate of targets within the coverage
  area.

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Barrier Coverage

• Static arrangement of nodes that minimizes the
  probability of underdetected penetration through
  the barrier.

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Sweep Coverage

• Move a group of nodes across a coverage area so
  to maximize the number of detections per time and
  minimize the number of missed detections per area.

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Additional MSN Control Issues

• Formation Behaviors
• Deployment
• Group Navigation

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Scalable Control of Distributed Robotic
Macrosensors

• Brian Shucker and John K. Bennett (University of
  Colorado at Boulder) SHU04, SHU05a, SHU05b
• Problem Coordination and control of the
  activities of distributed robotic macrosensors
  presents a number of challenging problems
• scalability
• automatic operation
• starting state independence
• exploration
• coverage
• target tracking
• flexibility of deployment
• fault-tolerance
• extensibility
• security

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Scalable Control of Distributed Robotic
Macrosensors

• Solution Control algorithm for distributed
  robotic macrosensors (DRMs)
• Emergent behavior
• Addresses each of the previously mentioned
  challenges.

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Virtual Spring Mesh

• DRMs employ a virtual spring mesh (VSM) as the
  underlying control mechanism.
• Extension of virtual physics-based control.
• Goal Design virtual forces and rules of motion
  for desirable emergent behavior.

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Virtual Spring Mesh

• Graph analogy robots are vertices and
  connections are force transmitting edges (i.e.
  virtual springs).
• Force transmission occurs only between selected
  adjacent pairs of robots.
• Virtual spring force increases with error,
  resulting in desirable control properties.

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Spring Formation

• Robot R will create a spring connection with its
  neighbor S if for every other neighbor T, the
  interior angle RTS is acute.
• Zero-energy configuration produces a hexagonal
  lattice.
• Other formations possible (e.g. square).

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Spring Formation
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Exploration

• Goal Cover complex environments without the use
  of global information.
• Problem Spreading the robots out may not lead to
  a good solution in a complex environment.
• Solution Introduce an exploration force to draw
  robots towards areas that are visible and not
  occupied.

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Exploration
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Point Target Tracking
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Diffused Target Tracking

• Two Challenges
• Locate and bound all diffused targets in the area
  of interest (i.e. move robots entirely through or
  around the targets).
• Map the interior of the targets.

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Diffused Target Tracking
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Diffused Target Tracking

• Exploration force applies to edge robots.
• Initially was based on the local target gradient
  (i.e. drew edge nodes towards areas of high
  target concentration.
• Ineffective at bringing the mesh all the way
  through the target.

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Diffused Target Tracking

• Explore away from the other nodes, rather than
  into the target.
• Exploration force pulls edge robots away from the
  other robots in the mesh, along the bisector of
  the largest "sweep angle" in which there is no
  visible robots.
• Exploration force increases with the intensity of
  the target.

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Fault Tolerance

• Control is fully distributed and individual
  robots are nearly stateless.
• No single points of failure.
• Fast recovery
• Cost communication overhead

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Fault Tolerance
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Discussion

• Coverage is linearly scalable in the number of
  robots
• Complexity is independent of the total number of
  robots
• Coverage formation tailored to the mission
• Fault tolerant

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An Incremental Self-Deployment Algorithm for MSNs

• Andrew Howard, Maja J. Mataric, Gaurav S.
  Sukhatme (University of Southern California)
  HOW01, HOW02
• Problem Autonomous placement of MSNs in a
  complex space, with no prior knowledge and global
  positioning tools, in order to produce maximum
  coverage while maintaining a visibility
  constraint.
• Nodes are deployed one at a time, making use of
  the information gathered by the previously
  deployed nodes.

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Assumptions, Constraints, Performance

• Homogeneous nodes
• Static environment
• Model-free
• Localization
• Visibility constraint
• Coverage metric

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Obstruction Resolution
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Algorithm Overview

• 4 Phases
• Initialization
• Goal Selection
• Goal Resolution
• Execution

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Initialization

• Nodes are assigned one of three states waiting,
  active or deployed.

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Goal Selection

• Sensor data from the deployed nodes is combined
  to form a map of the environment.
• Map is analyzed to select the optimal deployment
  location for the next node.
• Since there is no prior model of the environment,
  use goal selection policies that rely on
  heuristics.

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Goal Selection

• Sensor data from deployed nodes is combined to
  form an occupancy grid (possible states free,
  unknown, occupied).
• Use a Bayesian technique to determine if cell is
  occupied, then threshold probability.
• Use a configuration grid (derived from occupancy
  grid) to ensure that the goal is both visible and
  reachable.

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Goal Selection

• Best policy heuristics
• Boundary heuristic nodes should deploy to the
  boundary between free and unknown space (i.e.
  minimum sensory overlap, maximum coverage).
• Coverage heuristic nodes should deploy to the
  location at which they will cover the greatest
  area of unknown space (i.e. greatest potential to
  increase coverage).

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Goal Resolution

• Assign the newly selected goal to a waiting node.
• Use recursive resolution algorithm
• Find nearest deployed or waiting node that can
  reach the goal.
• If waiting, assign goal to the node, change
  state.
• If deployed, assign goal to the node, change
  state, and call the resolution algorithm
  recursively to assign nodes current location to
  another node.

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Execution

• Active nodes are deployed to their goal
  locations.
• By default, deployment is sequential, in
  practice, concurrent deployment is better.
• Nodes navigate using potential fields
• Attractive force gradient of the distance
  transform
• Repulsive force obstacles

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Discussion

• Pros
• Proven to work in simulation and real-world
• Coverage is within 70 to 85 of the greedy (near
  optimal) value.
• Cons
• Relies on global localization mechanisms
• Greedy is the best result for incremental
  deployment.
• Poor scalability (localization errors)
• No fault tolerance

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Modeling Multiple Robot Systems for Area Coverage
and Cooperation

• Jindong Tan (Michigan Technological Univ.), Nig
  Xi (Michigan State Univ.), Weihua Sheng
  (Kettering Univ.), Jizhong Xiao (City College,
  CCNY) TAN04.
• Problem Fault tolerant algorithm for autonomous
  deployment, area coverage and cooperation among
  mobile sensors, utilizing a Voronoi diagram and
  Delaunay triangulation model.

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Model of MSN Problem
Formulation

• Relationship between neighboring nodes is defined
  by using two graphs
• Voronoi diagram
• Delaunay tessellation (triangulation)

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Model of MSNCoordinate Systems and Information
Sharing

• Delaunay graph provides a distributed definition
  of the relationship between any two robots in the
  network.
• A robot maintains its local coordinate system and
  their relationship with respect to its one-hop
  neighbors.

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Model of MSNCoordinate Systems and Information
Sharing
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Model of MSNCoverage Area

• Coverage is defined in terms of communication
  range gt sensing range.
• Voronoi regions are initially not closed, and
  depend on sensing range and obstacles.

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Model of MSNCoverage Area
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Sensor Deployment and CooperationContinuous
Deployment Algorithm

• Goal Maximize coverage area.
• Problem Initially, sensor node may not cover its
  Voronoi cell.
• Solution Move sensor node towards the direction
  of the geometric center (a.k.a. centroid) of its
  Voronoi cell.
• Note As nodes move, their relationship with
  their neighbors changes, changing the Voronoi
  diagram (i.e. centroids).

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Sensor Deployment and CooperationContinuous
Deployment Algorithm

• Algorithm summary
• Construct the Voronoi tessellation V for sensor
  nodes in open space.
• If V is an open set, close it based on the
  sensing range of sensor nodes.
• Compute the centroid for each V cell.
• Execute controller (i.e. move nodes towards the
  centroids) for a certain time period.
• Return to step 1.

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Sensor Deployment and CooperationContinuous
Deployment Algorithm
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Sensor Deployment and CooperationFault Tolerance
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Discussion

• Pros
• Adaptive and fault tolerant
• No central control
• No common reference frame
• Formal and provable
• Stable and uniform (good coverage)
• Cons
• Computationally complex ( O(MlogM to M2) where M
  is the number of visible neighbor nodes).
• Convex shape

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The Analysis of an Efficient Algorithm for Robot
Coverage and Exploration based on Sensor Network
Deployment

• Maxim A. Batalin, Gaurav S. Sukhatme (University
  of Southern California) BAT05
• Problem An efficient solution to the problem of
  coverage, exploration and sensor network
  deployment.

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Introduction

• Number of nodes to cover an unknown environment
  completely can not be determined in advance.

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Least Recently Visited (LRV) Algorithm

• Capable robot carries the network nodes as
  payload and emplaces them into the environment.
• Nodes self organize to form a network and emit
  navigation directions for the robot.
• Nodes compute navigation directions based on
  local frequency counts of which directions the
  robot has recently pursued (i.e. least recently
  visited directions).

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Theoretical Analysis Summary

• Modeled the steady state of the deployed network
  as a finite graph G.
• Proved the exploration time of LRV on G is finite
  (i.e. complete).
• For G(V,E) with max degree d
• if Cover Time O(f(V)), then
• Exploration Time dO(f(V))

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Theoretical Analysis Summary

• Proved that Exploration Time lt 2E
  (asymptotically optimal), for the special case
  where G is a tree.
• Proved that when G is a square lattice (i.e.
  directions bound to 2k, k2), cover and
  exploration time are lt V ln V.

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Special Graph Cases
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Fault Tolerance

• Emergent property of LRV
• Since LRV is complete, it is guaranteed to visit
  the same node over and over again.
• If a node malfunctions, there will be a
  communication gap, and a new node will be
  deployed by the robot.

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Discussion

• Pros
• LVR does not need a map and localization.
• Fast cover time, less then V log V, and faster
  for special cases.
• Fault tolerance through automated maintenance.
• May prove practical in a real scenario.
• Cons
• Slow deployment
• Slow network repair
• Single source of failure (i.e. robot)

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Conclusion

• Reviewed a number of recent techniques and
  algorithms for fault tolerant area coverage in
  MSNs.
• Many solutions exist, but effectiveness of each
  solution depends on the particular context of the
  specified mission goal.

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References

• BAT05 Maxim Batalin and Gaurav S. Sukhatme,
  "The Analysis of an Effiient Algorithm for
  Robot Coverage and Exploration based on Sensor
  Network Deployment," In IEEE International
  Conference on Robotics and Automation, pp.
  3489-3496, Barcelona, Spain, April 2005.
• GAG92 Gage, D.W. Command Control for
  Many-Robot Systems, Proceedings of AUVS-92,
  Huntsville, AL, 22-24 June 1992.
• HOW01 Howard, A., Mataric, M.J., Cover Me! A
  Self- Deployment Algorithm for Mobile Sensor
  Networks, Robotics Research Lab, USC, 2001.
• HOW02 Howard, A., Mataric, M.J., Sukhatme,
  G.S., An Incremental Self-Deployment
  Algorithm for Mobile Sensor Networks,
  Autonomous Robots, Special Issue on Intelligent
  Systems, 2002.

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References

• SHU04 Brian Shucker and John K. Bennett.
  "Scalable Control of Distributed Robotic
  Macrosensors." In Proceedings of 7th
  International Symposium on Distributed
  Autonomous Robotic Systems (DARS), 2004.
• SHU05a Brian Shucker and John K. Bennett.
  "Target Tracking with Distributed Robotic
  Macrosensors." In Proceedings of MILCOM 2005.
  Atlantic City, New Jersey. October, 2005.
• SHU05b Brian Shucker and John K. Bennett.
  "Virtual Spring Mesh Algorithms for Control of
  Distributed Robotic Macrosensors." University
  of Colorado Department of Computer Science,
  technical report CU-CS-996-05. May 2005.

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References

• TAN04 Jindong Tan, Ning Xi,Weihua Sheng, and
  Jizhong Xiao. Modeling multiple robot systems
  for area coverage and cooperation. In
  Proceedings of IEEE International Conference on
  Robotics and Automation, pages 25682573, New
  Orleans, LA, USA, 2004.

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Thank you.Questions?