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7/30/2019 Kostas Compass3 30
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Robotics and Sensor Networks:
Coverage, Localization and Mobility
Kostas Bekris
March 29, 2005COMPASS 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. CoverageArt-Gallery Problems
(Computational Geometry)
II. LocalizationDistributed Markov and Monte Carlo
(Machine Learning)
III. MobilityArtificial 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 ofn 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 themost realistic case of sensors with limited-range.
Decomposition methods
compute cells that can be
observed by limited range
guards.
[Cheong, Efrat, Har-Peled 2004]
[Kazazakis, Argyros 2002]
[Gonzalez-Banos, Latombe 2002]
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Robotic SN Deployment
[Howard, Mataric, Sukhatme 2002]
Incremental approach: select a node at a time to be
deployed in a new location, a second nodes replaces it
Build a centralizedrepresentation
while maximizing
network coverage
and retaining
line-of-sight
communication.
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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
[Bergamo,
Mazzini 2002]
Assume a subset of the nodes can self-localize(e.g. GPS) localize the rest relative to the beacons.
Trilateration Triangulation MLE
[Niculescu,
Nath 2003][Nasipuri, Li 2002]
[Savvides, Han,
Srivastava 2002]
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Uncertainty in Robotics
[Fox, Burgard, Kruppa, Thrun: A probabilistic approach
to collaborative multi-robot localization, 2000]
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
Probabilistic/bayesian techniques proven successful
in dealing with uncertainty and providing robustness.
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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:
(a) Odometry: at
(b) Sensing observations: ot
(c) Detections of other robots: rt
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Updating the distribution
The belief represents the posterior up to time t:
Belt(L) = Pr(Lt|dt)
Perception model:
Pr(ot|L)
Motion Model:
Pr(L|at,L)
Updates after:
(1) Sensing: Belt(L) = Pr(ot|L) Belt-1(L)
(2) Action: Belt
(L) = Pr(L|at
,L) Belt-1
(L) dL
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Multi-Robot Case
Independence assumption:
Pr(L1, , Ln|dt) = Pr(L1|d
t) Pr(Ln|dt)
Detections used to add additional constraints.
Assume robot m detects robot n:
Beltn(L) =
Belt-1n(L) Pr(Ln=L|rtm,Lm=L) Bel
t-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 ofKweighted particles:
S = { (Li,pi) | i=(1,,K) }
where: Li is a candidate position and
pi is a discrete probability pi=1
Sensing leads to re-weighting the set of samples so
as to agree with the measurements.
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An equivalent approach is to distribute thecomputation 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
More on Localization
[Roumeliotis, Bekey 2002]
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Providing location aware services in buildings thatare 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
Localization for RSN
[Hsieh, Kumar, Taylor 2004]
[Ladd, Bekris, Rudys, Marceau, Kavraki, Wallach 2002]
[Haeberlen, Flannery, Ladd, Rudys, Wallach, Kavraki 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
[Dantu, Rahimi, Shah, Babel,
Dhariwal, Sukhatme 2004]
Example Mobile Platform: Robomote
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Goal of navigation approaches
Navigational strategies for SN should not haveextensive sensing and computational requirements.
They should take advantage of the distributed natureof such networks.
Computationally or memory expensive approachesare also not appropriate.
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Navigation Functions
Many distributed navigation approaches are basedon navigation functions.
Construct a real-valued map: V:C
f R
with uniqueminimum 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 inducingan 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 ofmobile 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 adaptthe 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 typicalrobotic 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 withadaptive 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