Robotics and Sensor Networks:

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Robotics and Sensor Networks Coverage,
Localization and Mobility
Kostas Bekris
March 29, 2005 COMPASS project meeting
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What is the relation?

• Robotics and Sensor Networks are typically
• considered two unrelated fields.
• But
• Robots can provide mobility to Sensor Networks.
• Sensor Networks can provide rich sensing
• information to Robots.
• and most importantly
• The two fields are facing many similar
  challenges.

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Robots for Sensor Networks

• Mobile nodes can be used to
• Re-deploy and calibrate sensors,
• React to sensor failures and
• Deliver power.

Corke, Hrabar, Peterson, Rus, Saripalli,
Sukhatme, 2004
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Sensor Networks for Robots
A network offers detailed sensing information to
a robot that is not possible to acquire
otherwise. Distributed computation over the
network. Robots can form mobile sensor networks.
Batalin, Sukhatme, Hattig, 2004
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Similar challenges

• Many of the problems are the same
• Decision inference based on multiple sensing
  inputs
• Sensor fusion
• Location awareness
• Coordination
• Task allocation
• Workspace or sensor field coverage
• Compression of data
• Uncertainty
• Mobility

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Topics to cover

• I. Coverage
• Art-Gallery Problems
• (Computational Geometry)
• II. Localization
• Distributed Markov and Monte Carlo
• (Machine Learning)
• III. Mobility
• Artificial Potential Functions
• Formation Control
• (Control Theory)

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I. Coverage
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Coverage in Sensor Networks

• Very important for deployment
• Under-deployment might result in communication
• failures or failures in the sensing task
• Over-deployment can significantly increase the
  cost
• Typical Measure in
• Sensor Networks
• Path Exposure

Meguerdichian, Koushanfar, Potkonjiak,
Srivastava 2001
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Art-Gallery Problem
The original art gallery problem Find the
smallest number of point guards g(n) necessary to
cover any polygon of n vertices. According to
the art gallery theorem the necessary number is
g(n) ?n/3? Finding minimum set of guards
NP-hard
Conversation between Klee and Chvatal 1972
Chvatal 1975
Aggarwal 1984
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Heuristic Solution

• Greedy approach for map building in robotics
• Place the first guard at the point of
• maximum visibility
• Next guard is placed where it sees the maximum
• area not visible to the first and so on
• The sub-problem of finding the next guard of
• maximum visibility is called
• the Next-Best-View problem

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Various approaches
Randomized algorithms compute the
optimal location up to a constant factor
approximation. Sampling-based techniques can be
used for the most realistic case of sensors with
limited-range. Decomposition
methods compute cells that can
be observed by limited range guards.
Cheong, Efrat, Har-Peled 2004
Gonzalez-Banos, Latombe 2002
Kazazakis, Argyros 2002
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Robotic SN Deployment
Incremental approach select a node at a time to
be deployed in a new location, a second nodes
replaces it Build a centralized representation wh
ile maximizing network coverage and
retaining line-of-sight communication.
Howard, Mataric, Sukhatme 2002
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II. Localization
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Data for SN self-localization

• Received Signal Strength for known transmission
• power, the propagation loss is measured to
  estimate
• the distance based on a propagation model.
• Time-of-arrival or time-difference-of-arrival
  The
• propagation time can be directly translated
  into
• distance based on signal propagation speed.
• Angle-of-arrival Systems estimate the angle at
• which signals are received.

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Localization Approaches
Assume a subset of the nodes can
self-localize (e.g. GPS) localize the rest
relative to the beacons. Trilateration
Triangulation MLE
Bergamo, Mazzini 2002
Niculescu, Nath 2003
Savvides, Han, Srivastava 2002
Nasipuri, Li 2002
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Uncertainty in Robotics
Robots, like nodes of sensor networks, have to
be aware of their location. Typical sensors in
robotics sonar, laser, cameras. Problem
inherent uncertainty in sensor measurements Proba
bilistic/bayesian techniques proven successful in
dealing with uncertainty and providing robustness.
Fox, Burgard, Kruppa, Thrun A probabilistic
approach to collaborative multi-robot
localization, 2000
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Markov Localization

• Each robot maintains a belief for its position at
  time t
• Belt(L)
• where L is the robots configuration (e.g.
  x,y,?).
• Initially, Bel0(L) follows a uniform
  distribution.
• Each robot collects data dt
• Odometry at
• Sensing observations ot
• Detections of other robots rt

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Updating the distribution

• The belief represents the posterior up to time t
• Belt(L) Pr(Ltdt)
• Perception model
• Pr(otL)
• Motion Model
• Pr(Lat,L)
• Updates after
• Sensing Belt(L) ? ? Pr(otL) ? Belt-1(L)
• Action Belt(L) ?Pr(Lat,L) ? Belt-1(L) ?
  dL

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Multi-Robot Case
Independence assumption Pr(L1, , Lndt)
Pr(L1dt) ? ? Pr(Lndt) Detections used to
add additional constraints. Assume robot m
detects robot n
Beltn(L) Belt-1n(L) ? ?Pr(LnLrtm,LmL) ?
Belt-1m(L) ? dL
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Monte-Carlo Localization
Representation issue with the storage of
distributions Monte Carlo approach A
distribution is a set of K weighted
particles S (Li,pi) i(1,,K)
where Li is a candidate position and pi is
a discrete probability ?pi1 Sensing leads to
re-weighting the set of samples so as to agree
with the measurements.
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More on Localization

• An equivalent approach is to distribute the
• computation of a centralized Kalman filter to
• separate Kalman filters.
• More difficult problem SLAM (Simultaneous
• Localization and Mapping)
• Incrementally generate a maximum likelihood
• map
• Probabilistically estimate the robots position

Roumeliotis, Bekey 2002
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Localization for RSN

• Providing location aware services in buildings
  that
• are equipped with wireless infrastructure
• Build radio signal strength maps with multiple
  robots
• For a pair of locations return the expected
• signal strength
• Sample the environment and build the map for the
• samples

Ladd, Bekris, Rudys, Marceau, Kavraki, Wallach
2002 Haeberlen, Flannery, Ladd, Rudys, Wallach,
Kavraki 2004
Hsieh, Kumar, Taylor 2004
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III. Mobility
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Why mobility?

• Synoptic sensing implies either over-deployment
• (impractical you cannot have sensor
  everywhere)
• or mobility
• Mobility allows the system to focus sensing
  where
• it is needed, when it is needed
• The initial deployment of static nodes cannot
  deal
• with all possible changes in the environment

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Energy Considerations
Example Mobile Platform Robomote
Dantu, Rahimi, Shah, Babel, Dhariwal, Sukhatme
2004
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Goal of navigation approaches
Navigational strategies for SN should not have
extensive sensing and computational
requirements. They should take advantage of the
distributed nature of such networks. Computationa
lly or memory expensive approaches are also not
appropriate.
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Navigation Functions
Many distributed navigation approaches are
based on navigation functions. Construct a
real-valued map V Cf ? R with unique minimum
at the goal and is maximal over Cf boundary.
Rimon, Koditschek 1992
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Navigation Functions
Then the robot at position p can move according
to where d is an arbitrary dissipative
vector-field. Under additional requirements NFs
guide the robot to the goal without hitting local
minima. In the multi-robot case, each robot can
act as an obstacle in the potential function of
other robots.
?(p,p) -?V(p) d(p,p)
Dimarogonas, Zavlanos, Loizou, Kyriakopoulos
2003
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Source Gradient Climbing
A mechanism in the environment may be inducing an
environmental gradient field (light, sound
source). APFs are used for locating the source
with multiple robots. If a robot measures the
gradient only in the direction of motion then it
can only find minima along a line. An APF
enforces the team to stay close and eventually
the source will be found.
Ogren, Fiorelli, Leonard 2004
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Formation Control
Another possibly desirable behavior with a team
of mobile systems is to move the entire team in
formation. Alternatives such as (l-?) or (l-l)
control have been considered as basic motion
primitives for formations.
Desai, Ostrowski, Kumar 2001
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Conclusion
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Our interest
Interested in networks that have the ability to
adapt the location of their nodes - not
necessarily with autonomous mobility to solve
problems that might require node relocation Do
not assume mobility is easily available and
inexpensive as it is typically considered in
robotics Take into account the cost of mobility
and apply it only when it is necessary for the
application
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Sampling-Based Motion Planners
An improvement over potential functions in
typical robotic applications. They sample the
configuration space of robots and construct
lower-dimensional representations (e.g. graph
structures). They solve path planning problems
on the graph structures.
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Issues to consider

• Can we apply the SBMP framework to deal with
• adaptive sensor network problems?
• Can we have distributed SBMP?
• Can SBMP plan not just for motion but for other
  tasks,
• such as sensing and communication?
• Can we take into consideration the fact that
  different
• tasks have different energy costs?

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Questions??
THE END