Robotics and Sensor Networks:

Coverage, Localization and Mobility

Robotics and Sensor Networks:

Coverage, Localization and Mobility

Kostas Bekris

March 29, 2005COMPASS project meeting

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.

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]

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]

Similar challenges

Many of the problems are the same:

• Decision inference based on multiple sensing inputs

• Sensor fusion

• Location awarenessLocation awareness• Coordination

• Task allocation

• Workspace or sensor field coverageWorkspace or sensor field coverage• Compression of data

• Uncertainty

• MobilityMobility

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)

I. Coverage

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]

Art-Gallery Problem

The original art gallery problem:

Find the smallest number of point

guards g(n)g(n) necessary to cover any

polygon of nn vertices.

According to the art gallery theorem the necessary

number is: g(n) = g(n) = n/3n/3

Finding minimum set of guards: NP-hard

[Conversation between Klee and Chvatal 1972]

[Chvatal 1975]

[Aggarwal 1984]

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

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]

[Kazazakis, Argyros 2002]

[Gonzalez-Banos, Latombe 2002]

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 centralized

representation

while maximizing

network coverage

and retaining

line-of-sight

communication.

II. Localization

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.

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]

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.

Markov Localization

Each robot maintains a belief for its position at time t

BelBeltt(L)(L)where L is the robot’s configuration (e.g. {x,y,}).

Initially, BelBel00(L)(L) follows a uniform distribution.

Each robot collects data ddtt:

(a) Odometry: aatt

(b) Sensing observations: oott

(c) Detections of other robots: rrtt

Updating the distribution

The belief represents the posterior up to time t:

BelBeltt(L) = Pr(L(L) = Pr(Ltt|d|dtt))

Perception model:

Pr(oPr(ott|L)|L)Motion Model:

Pr(L|aPr(L|att,L’) ,L’)

Updates after:

(1) Sensing: BelBeltt(L) = (L) = Pr(o Pr(ott|L) |L) Bel Belt-1t-1(L)(L)

(2) Action: BelBeltt(L) = (L) = Pr(L|aPr(L|att,L’) ,L’) Bel Belt-1t-1(L’) (L’) dL’ dL’

Multi-Robot Case

Independence assumption:

Pr(LPr(L11, …, L, …, Lnn|d|dtt) = Pr(L) = Pr(L11|d|dtt) ) … … Pr(L Pr(Lnn|d|dtt) )

Detections used to add additional constraints.

Assume robot mm detects robot nn:

BelBelttnn(L) = (L) =

BelBelt-1t-1nn(L) (L) Pr(LPr(Lnn=L|r=L|rtt

mm,L,Lmm=L’) =L’) Bel Belt-1t-1mm(L’) (L’) dL’ dL’

Monte-Carlo Localization

Representation issue with the storage of distributions

Monte Carlo approach:

A distribution is a set of KK weighted “particles”:

S = { (LS = { (Lii,p,pii) | i=(1,…,K) } ) | i=(1,…,K) }

where: LLii is a candidate position and

ppii is a discrete probability ppii=1=1

Sensing leads to re-weighting the set of samples so

as to agree with the measurements.

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

More on Localization

[Roumeliotis, Bekey 2002]

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

Localization for RSN

[Hsieh, Kumar, Taylor 2004]

[Ladd, Bekris, Rudys, Marceau, Kavraki, Wallach 2002]

[Haeberlen, Flannery, Ladd, Rudys, Wallach, Kavraki 2004]

III. Mobility

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

Energy Considerations

[Dantu, Rahimi, Shah, Babel,

Dhariwal, Sukhatme 2004]

Example Mobile Platform: Robomote

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.

Computationally or memory expensive approaches

are also not appropriate.

Navigation Functions

Many distributed navigation approaches are based

on “navigation functions”.

Construct a real-valued map: V: V: CCff RR with unique

minimum at the goal and is maximal over CCff boundary.

[Rimon, Koditschek 1992]

Navigation Functions

Then the robot at position pp can move according to:

where dd 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’) = -(p,p’) = -V(p) + d(p,p’)V(p) + d(p,p’)

[Dimarogonas, Zavlanos, Loizou, Kyriakopoulos 2003]

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]

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]

Conclusion

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

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.

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?

Questions??

THE END