APPLI LICATION ON DOM OMAIN: N: SENS NSOR OR NE NETWOR ORKS - - PowerPoint PPT Presentation

APPLI LICATION ON DOM OMAIN: N: SENS NSOR OR NE NETWOR ORKS KS

SENSOR NETWORK AS A CONTROL SYSTEM

Position/Move to optimize detection prob.

TARGET DETECTION DATA COLLECTION

Localize targets Update event density information Position/Move to optimize data collection quality

Know nothing - must deploy resources (how many? where?)

• Cooperate but operate autonomously
• Manage Communication, Energy

COVERAGE: persistently look for new targets ⇒ spread nodes out and search DATA COLLECTION:

• ptimize data quality

⇒ congregate nodes around known targets

Christos G. Cassandras

CODES Lab. - Boston University

• Model for
• ptimization

COVERAGE

Data fusion, build prob. map of target locations (static) or trajectories (dynamic) Know everything - must deploy resources to maximize benefit from interacting with data sources (targets): track, get data

• Manage Communication, Energy

TRADEOFF: Control node location to optimize COVERAGE + DATA COLLECTION

Christos G. Cassandras

CODES Lab. - Boston University

• COVERAGE CONTROL

Deploy sensors to maximize “event” detection probability – unknown event locations – event sources may be mobile – sensors may be mobile

Perceived event density (data sources) over given region (mission space)

5 10 2 4 6 8 10 10 20 30 40 50

Ω

R(x) (Hz/m2)

? ? ? ? ? ? ? ? ?

• Meguerdichian et al, IEEE INFOCOM, 2001
• Cortes et al, IEEE Trans. on Robotics and

Automation, 2004

• Cassandras and Li, Eur. J. of Control, 2005
• Ganguli et al, American Control Conf., 2006
• Hussein and Stipanovic, American Control

Conf., 2007

• Hokayem et al, American Control Conf., 2007

COVERAGE: PROBLEM FORMULATION

§ Sensing attenuation: pi(x, si) monotonically decreasing in di(x) ≡ ||x - si|| § Data source at x emits signal with energy E § N mobile sensors, each located at si∈R2 § Signal observed by sensor node i (at si ) § SENSING MODEL: ] ), ( | by Detected [ ) , (

i i i

s x A i P s x p ≡ ( A(x) = data source emits at x ) Christos G. Cassandras

CODES Lab. - Boston University

Ω

R(x) (Hz/ m2)

? ? ? ? ? ? ? ? ?

§ Joint detection prob. assuming sensor independence ( s = [s1,…,sN] : node locations)

[ ]

∏

=

− − =

N i i i

s x p x P

1

) , ( 1 1 ) , ( s

§ OBJECTIVE: Determine locations s = [s1,…,sN] to maximize total Detection Probability:

) , ( ) ( max dx x P x R

∫

Ω

s

s

COVERAGE: PROBLEM FORMULATION Christos G. Cassandras

CODES Lab. - Boston University

Perceived event density Event sensing probability

CONTINUED

DISTRIBUTED COOPERATIVE SCHEME § Set

[ ] dx

x p x R s s H

N i i N

∫ ∏

Ω =

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − − =

1 1

) ( 1 1 ) ( ) , , ( …

Christos G. Cassandras

CODES Lab. - Boston University

§ Maximize H(s1,…,sN) by forcing nodes to move using gradient information:

[ ]

dx x d x s x d x p x p x R s H

k k k k N k i i i k

∫ ∏

Ω ≠ =

− ∂ ∂ − = ∂ ∂ ) ( ) ( ) ( ) ( 1 ) (

, 1

k i k k i k i

s H s s ∂ ∂ + =

+

β

1

Desired displacement = V·Δt

CONTINUED

DISTRIBUTED COOPERATIVE SCHEME … has to be autonomously evaluated by each node so as to determine how to move to next position:

CONTINUED

Ø Use truncated pi(x) ⇒ Ω replaced by node neighborhood Ø Discretize pi(x) using a local grid Christos G. Cassandras

CODES Lab. - Boston University Cassandras and Li, EJC, 2005

[ ]

dx x d x s x d x p x p x R s H

k k k k N k i i i k

∫ ∏

Ω ≠ =

− ∂ ∂ − = ∂ ∂ ) ( ) ( ) ( ) ( 1 ) (

, 1

k i k k i k i

s H s s ∂ ∂ + =

+

β

1

CONTINUED

EXTENSION: POLYGONAL OBSTACLES

• Constrain the navigation of mobile nodes
• Interfere with sensing:

( , ) if is visible from ˆ ( , )

• therwise

i i i i i

p x s x s p x s ⎧ = ⎨ ⎩

Christos G. Cassandras

CODES Lab. - Boston University

Visibility Region

CONTINUED

GRADIENT CALCULATION WITH OBSTACLES

[ ]

( ) ( )

1 1,

ˆ ( , ) ˆ ( ) 1 ( , ) ( ) ( )

i i

Q s N i i i k k j j k k i i i i V s

p x s s x H R x p x s dx A s d x d x

= = ≠

∂ − ∂ = − + ∂ ∂

∑ ∏ ∫

visible ˆ invisible

i i

p p ⎧ = ⎨ ⎩

New term captures change in visibility region of si

Christos G. Cassandras

CODES Lab. - Boston University

Q(si): # of occluding corner points

Mathematically: use extension of Leibnitz rule for differentiating integral where both integrand and integration domain are functions of the control variable

OPTIMAL COVERAGE WITH OBSTACLES Christos G. Cassandras

CODES Lab. - Boston University

http://codescolor.bu.edu/coverage

Zhong and Cassandras, 2008

DEMO: OPTIMAL DISTRIBUTED DEPLOYMENT WITH OBSTACLES – SIMULATED AND REAL

Christos G. Cassandras

CODES Lab. - Boston University

Recall tradeoff: MODIFIED DISTRIBUTED OPTIMIZATION OBJECTIVE: collect info from detected data sources (targets) while maintaining a good coverage to detect future events

H s, t R x P x, s dx

u D t S u F u, s

COVERAGE: persistently look for new targets ⇒ spread nodes out DATA COLLECTION:

• ptimize data quality

⇒ congregate nodes around known targets TRADEOFF: Control node location to optimize COVERAGE + DATA COLLECTION

Christos G. Cassandras

CODES Lab. - Boston University

• COVERAGE + DATA COLLECTION

Dt : set of data sources, estimated based on sensor observations S(u) : data source value F(u,s) : joint data collection quality at u (e.g., covariance)

Christos G. Cassandras

CODES Lab. - Boston University

• DEMO: REACTING TO EVENT DETECTION

Important to note: There is no external control causing this

• behavior. Algorithm

includes tracking functionality automatically