Coverage, Connectivity and Mobility in Wireless Mobile Sensor Robots Youn-Hee Han [email protected] Korea University of Technology and Education Laboratory.

Coverage, Connectivity and Mobility in Wireless Mobile Sensor Robots

Youn-Hee [email protected]

Korea University of Technology and EducationLaboratory of Intelligent Networks

http://link.kut.ac.kr

Introduction

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Review: Sensor Node ArchitectureSystem architecture of a typical wireless sensor node

i) a computing subsystem consisting of a microprocessor or microcontroller ii) a communication subsystem consisting of a short range radio for wireless

communication iii) a sensing subsystem that links the node to the physical world and consists

of a group of sensors and actuators iv) a power supply subsystem, which houses the battery and the dc-dc

converter, and powers the rest of the node.

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Mobile Sensors

Mobile Sensor Capabilities [1,2] SensingSensing CommunicationCommunication ComputationComputation LocomotionLocomotion

Self-deploy functionSelf-deploy function

Mobile Robots with Sensors

[Eight Legged Robot of LEGO mindstorm] [www.thinkbotics.com]

Static Sensor’ Capabilities

[Similar to a Tank]

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Mobile Sensor Robots

Mobile Sensor Robots: Distributed Multi-Robots with Sensing

Capability

Single Sensor vs. Distributed Multiple Sensors

Single Robot vs. Distributed Multi-Robots

Issues in Distributed Multi-Robots [3] Biological Inspirations

Use of the local control rules of biological societies, such as ants, bees, and birds to the development of similar behaviors in multi-robot systems.

behavior-based robotics robot architectures are built on activity-generating

building blocks rather than on centralized representations and deductive logic.

Communication Network robotics and Inter-robot interaction How to handle non-deterministic time delays in

communications and achieve robust performance in faulty communication environment

E.g., the remote tele-operation of space exploration robots Connectivity Issues

What Issues in Mobile Robots?

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Issues in Distributed Multi-Robots [3] Localization, Mapping, and Exploration

Enables robot team members to track positions of autonomously moving objects

Navigate between places of interest in an initially unknown environment

Motion Coordination Multi-robot path planning, formation generation

Reconfigurable Robotics Architecture, Task Allocation, and Control Object Transport and Manipulation

What Issues in Mobile Robots?

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Then, what issues in Mobile Sensor Robots ? Environmental Robotics

the deployment of distributed sensors and supported mobile sensor robots to observe, monitor, and assess the state of complex environmental processes.

It involves many different types of distributed sensing in land, sea, and air, and the coordination of mobile sensors through adaptive redeployment and adaptive sampling of environmental phenomena.

Coverage Issues

What Issues in Mobile Sensor Robots?

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[2004 WTEC ROBOTICS WORKSHOP]

Mobile Sensor Robots

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[ 조선일보 2008-09-22]떼지어 군사작전 ' 로봇 ' 나왔다정찰 · 독성물질 탐지 수행… 英 내년 상용화

벌이나 개미처럼 무수한 소형로봇들이 하나의 군사작전을 수행하는 ' 로봇떼 (swarm of robots)' 가 곧 현실화한다 . 영국 국방부가 16~18 일 영국 솔즈베리에서 개최한 , 새 군사 기술의 경연대회인 ' 그랜드 챌린지 ' 에서 특히 ' 소형로봇떼 ' 개념이 떠오르는 신기술로 주목을 받았다고 BBC 방송이 보도했다 . 전체 11 개 팀 중에서 3 개 팀이 ' 로봇떼 ' 를 선보였다 . 작은 곤충로봇들이 땅에서 움직이는 ' 마인드시트(Mindsheet)', 날아다니는 비행로봇들의 집단인 ' 로커스트 (Locust)', 그리고 미니 헬리콥터 8 개가 나는 ' 아울스 (Owls)' 등이다 . 영국 국방부는 ' 아울스 ' 의 기술을 참가 팀들 중 ' 가장 혁신적인 아이디어 ' 로 선정했다 . 아울스는 8 개의 소형 헬리콥터 로봇이 한 팀이 돼 움직인다 . 로봇 1 개당 프로펠러 4 개가 달려 있고 무게는 1 ㎏ 미만 . 이 로봇떼는 다양한 각도에서 고해상도의 영상을 찍어 적의 위협을 감지한다 . 대기에 뿌려진 독성물질을 탐지할 수도 있다 . 8 개 중 일부가 파괴되거나 고장 나도 , 나머지 로봇들이 없어진 로봇들의 임무를 대신하도록 프로그램 돼 있다 . 내년에 ' 새떼 ' 의 움직임을 모방한 알고리즘까지 아울스에 내장된다 . 영국 일간지 가디언은 " 아울스는 내년쯤 상용화해 영국군에 배치될 전망 " 이라고 보도했다 . 이 밖에 , 현재 미군이 개발 중인 ' 마이크로 자동 시스템기술 (MAST)' 프로그램은 병사 1 명에게 하나의 로봇떼를 제공하는 것이 목표다 . MAST 의 로봇떼는 시가전 ( 市街戰 ) 상황에서 건물이나 모퉁이 너머로 몰래 다가가 적의 동태를 살피는 ' 정찰병 ' 역할을 수행한다 .

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Change of Research Issues in Sensor Networks

Hardware (2000) CPU, memory, sensors, etc.

Protocols (2002) MAC layers Routing and transport protocols

Applications (2004) Localization and positioning applications

Management (2005) Coverage and connectivity problemsCoverage and connectivity problems Power managementPower management Etc.Etc.

From Dr. Yu-Chee Tseng(Associate Dean),

College of Computer Science, National Chiao-

Tung University

From Dr. Yu-Chee Tseng(Associate Dean),

College of Computer Science, National Chiao-

Tung University

Coverage Problem In general, determine how well the sensing field is

monitored or tracked by sensors.

Objectives of the problem Determine the coverage hole (or targets) Minimize the number of sensors deployed Make the whole area covered by three or more sensors

Location determination by “Triangulation” Maximize the network lifetime

[Def.] Sensor Network Lifetime The time interval that all points (or targets) in the given area is

covered by at least one sensor node. Etc.

Study of Coverage Problem

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Review: Art Gallery ProblemVictor Klee (1973)

Place the minimum number of cameras such that every point in the art gallery is monitored by at least one camera

Chvátal's art gallery theorem (1975) guards (cameras) are always sufficient

and sometimes necessary to guard

a simple polygon with vertices

3

n

n

42 vertices upper bound:42

123

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Review: Power SavingMake the sensor node sleep!!! [13]

Modes

* 2Mb/s IEEE 802.11 Wireless LAN

TxRx

Idle

Sleep

En

erg

y C

on

sum

pti

on

• Rockwell’s WINS Nodes Tx Rx Idle Sleep

0.38 ~ 1 W 0.75 W 0.72 W 0.4 W

• Medusa II Nodes Tx Rx Idle Sleep

22 ~ 24 mW

22 mW 6 mW 0.02 mW

http://www.inf.ethz.ch/personal/kasten/research/bathtub/energy_consumption.html

It is highly recommended to “schedule” the wireless sensor nodes to alternate between active (Tx, Rx, Idle) and sleep mode

Review: Power SavingMake the sensor node intelligent!!! [13]

The ratio of the energy spent in sending one bit of information to the energy spent in executing one instruction.

1500~2700 for Rockwell’s WIN nodes 220~2900 for the MEDUSA II nodes 1400 for the WINS NG 2.0

So, local data processing, data fusion and data compression are highly desirable.

Algorithm Characteristics 1) Centralized 2) Distributed 3) Self-*

Self-determination free choice of one’s own acts without external

compulsion Self-organization (Self-configuration)

a process of evolution where the effect of the environment is minimal, i.e. where the development of new, complex structures takes place primarily in and through the system itself

Self-healing For example, a mobile sensor can move to an area with a

coverage hole or routing void and significantly improve network performance.

Problem Design Methodology

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Coverage

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Sensor Deploy Method Deterministic (planned) vs. Random

Coverage Types Area coverage vs. Target (Point) coverage

Problem Design Criteria (1/2)

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6

54

3

2

1

7

8 R

S2

S1

S4S3

t3

t1

t2

Coverage Modeling Binary Model vs. Probability Model

Communication Range ( ) & Sensing Range ( ) vs. vs. Homogeneous vs. heterogeneous?

Problem Design Criteria (2/2)

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Binary, unit disc sensing model Probabilistic sensing model

CR SR

C SR R C SR R C SR R

Coverage ModelingBinary Model [1]

Each sensor’s coverage area is modeled by a disk Any location within the disk is perfectly monitored by the

sensor located at the center of the disk; otherwise, it is not monitored by the sensor.

Probability Model [2] An event happening in the coverage of a sensor is either

detected or not detected by the sensor depending on a probability distribution

Hence even if an event is very close toa sensor, it may still by missed by the sensor.

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Binary Model: K-coverage in 2-DK-coverage (only within Binary Model)

[Definition] covered A location in an area is said to be covered by if it is within 's

sensing range. [Definition] k-covered (location or area)

A location in an area is said to be k-covered if it is within at least K sensors' sensing ranges.

“k” is called coverage level

Why K>1? Fault-tolerance in case of the dismissal of some sensors Power saving and enlarge network lifetime Triangulation: getting location of a targeted object Uplift the confidence level on gathering information

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Binary Model: K-coverage in 2-DProblems about K-coverage [1]

[Definition] k-NC problem Given a natural number k, the k-Non-unit-disk Coverage (k-

NC) problem is a decision problem whose goal is to determine whether all points in an area are k-covered or not.

[Definition] k-UC problem Given a natural number k, the k-Unit-disk Coverage (k-UC)

Problem is a decision problem whose goal is to determine whether all points in an area are k-covered or not, subject to the constraint that r1 = r2 = · · · = rn.

21/50k-NC (k=1) k-UC (k=1)

So this area is not 1-covered!

1-covered means

that every point in

this area is covered by at least 1 sensor

2-covered means

that every point in

this area is covered by at least 2 sensors

This region is not covered by any

sensor!

Is this area 1-covered?

This area is not only 1-covered, but also 2-

covered!

What is the coverage level of

this area?

Coverage level = k means that this area

is k-covered

Binary Model: K-coverage in 2-D

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Binary Model: K-coverage in 2-DAlgorithm to determine coverage level, k, in a given sensor network? [1]

[Definition] k-perimeter-covered Consider any two sensors si and sj. A point on the perimeter of si

is perimeter-covered by sj if this point is within the sensing range of sj

[Theorem] An area A is k-covered iff

each sensor in A is k-perimeter-covered.

2 차원 문제를 1 차원 문제로 바꾸어 해결

Partially self-determination, but a central node determines the coverage level (k) finally.

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Binary Model: Coverage Configuration in 2-D

Coverage Configuration Protocol (CCP) [3] 1) a coverage level (k) is allocated to all sensors 2) all sensors are deployed randomly at the target area 3) Each sensor makes itself sleep or active to achieve the

coverage level [Theorem]

A given area is “k-covered” if the following conditions are satisfied

1) All intersection points between each pair of sensors are "k-covered"

2) All intersection points between each sensor and boundary of the area are "k-covered”

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Active nodes

Intersection points

Binary Model: Coverage Configuration in 2-D

Coverage Configuration Protocol (CCP) [3] A node becomes “sleep” if all intersection points inside its

coverage is already K-covered by other active nodes in its neighborhood.

A node becomes “active” if there exists an intersection point inside its sensing circle that is not K-covered by other active nodes.

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Active nodes

Sleeping nodes

Intersection points

active?

Binary Model: K-coverage in 3-DK-coverage in 3-D [4]

[Definition] k-BC Problem Given a natural number k, the k-Ball-Coverage (k-BC) Problem is

a decision problem whose goal is to determine whether all points in a 3-D cuboid sensing area are k-covered or not.

How to determine k? (3D2D) Determine whether the sphere of a sensor is

sufficiently covered (2D1D) Determine whether the circle of each spherical cap of

a sensor intersected by its neighboring sensors is covered

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Probability ModelWhy Probability Coverage Model? [2]

Quality of sensor surveillance may be much affected by sensing distances, signal propagation characteristics, obstacles, and environmental factors.

Probability coverage model may be more realistic!

Methodology Simple Model [5] Signal-strength-based Model [2]

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임의의 센서와 가까운 지역이 특수한 요인 (장애물 ) 에 의하여 센싱이 되지 않을 수 있거나 그 센서와 먼 지역이 특수한 요인 ( 다수의 센서의 감지 ) 에 의하여 센싱이 될 수도 있다 .

Probability ModelSimple Model [5]

: the probability that a sensor can sense a event happened at a location

: the detection probability contributed by the sensors

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kisiPr

5, 3er r

NPr

Coverage and Scheduling

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SchedulingBasic Policy

Sensor should be active or sleep? Scheduling (related to the coverage issue)

An interval: is active Another interval: is active So, the battery power can be saved

6S

7S

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7S

SchedulingScheduling Type

Centralized1) All sensors send “their location information” to the

centralized sink node.2) The sink node performs “its scheduling algorithm” for the

sensors3) The sink node broadcasts “the scheduling information” to

all sensor nodes4) Each sensor becomes active or sleep according to the

information

Distributed Each sensor self-determies its scheduling time # of messages reduced

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Centralized SchedulingMDSC (Maximum Disjoint Set Covers) [9]

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[Definition] Maximum Disjoint Set Covers Problem

Centralized SchedulingMDSC (Maximum Disjoint Set Covers) [9]

For example, C={S1, S2, S3, S4}, TARGETS={t1, t2, t3} A sensor’s battery lifetime: 1 Network Lifetime without any scheduling: 1 By MDSC Scheduling

Two Set Covers, C1 and C2 C1={S1, S2} with active time=1 C1={S3, S4} with active time=1

So that, network lifetime: 2

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s2

s1

s4s3

t3

t1

t2

s1

s2

s3

s4 t3

t2

t1

Centralized SchedulingMSC (Maximum Set Covers) [10]

MDSC

MSC

MDSC problem is a special case of MSC problem.!

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[Definition] Maximum Set Covers Problem

removed!

Centralized SchedulingMSC (Maximum Set Covers) [10]

For Example, By MSC Scheduling

Network Lifetime: 2.5

35/76active time=0.5 active time=0.5 active time=0.5 active time=1

s2

s1

s4s3

t3

t1

t2

Centralized SchedulingMSC (Maximum Set Covers) [10, 11]

Existing Algorithms Linear Programming [10] Greedy [10]

(Complexity: ) Branch-and-Bound [11]

2( )O im n i: # of set covers, m: # of targets, n: # of sensors

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Centralized SchedulingMSC (Maximum Set Covers) [10, 11]

Existing Algorithms Linear Programming [10] Greedy [10]

(Complexity: ) Branch-and-Bound [11]

2( )O im n

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i: # of set covers, m: # of targets, n: # of sensors

Distributed Scheduling1-Coverage Preserving Scheduling (1-CP) [12]

For Example

The set of intersection points within ‘s area

The set of sensorscovering the target p

Trnd=20

Ref1=2, Ref2=9, Ref3=11

Init Phase: 1) Each sensor exchange its location and Ref. value 2) Each sensor get its schedule (active) time

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is

Distributed Scheduling1-Coverage Preserving Scheduling (1-CP) [12]

2

911

5.5

16.5

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Connectivity

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ConnectivityWhy Connectivity?

Any sensing data should be sent to gateway (sink, base station) node

Multi-hop routing

Base Station

Sink

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K-ConnectivityConnected Graph of Sensor Networks

Vertex: each sensor nodes Edge: direct communication path for pairs of sensors

there exists an edge between two vertices iff the distance between them is less or equal to the transmission range r.

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K-Connectivity[Definition] k-connectivity

The network will remain connected after removing any arbitrary k-1 sensors from network.

It is also called “vertex k-connectivity” (not “edge k-connectivity”)

k-connected: any pair of nodes are connected by k indep. paths

Independent paths:

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K-ConnectivityExamples

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2-connected

4-connected

K-Edge-Connectivity[Definition] k-edge-connectivity

The network will remain connected after removing any arbitrary k-1 edges from network.

k-edge-connected: any pair of nodes are connected by k disjoint paths

disjoint paths:

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Min-Power Connectivity ProblemConnectivity & Transmission Power

Nodes in the network correspond to transmitters More power larger transmission range More Edges

More Connectivity transmitting to distance r requires r power

Battery operated power conservation critical

[Definition] Min-Power Connectivity Problems Find min-power range assignment so that the resulting

communication network satisfies prescribed properties (k-connectivity)

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Min-Power Connectivity Problem

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b

a

c

d

g

f

e

a

b

d

g

f

e

c

Range assignment Communication network

K-Connectivity & K-CoverageRelation between K-Coverage and K-Connectivity [3]

Communication Range: Sensing Range:

[Theorem] If the given region is continuous and ,

“The region is k-covered” means “The region is k-connected”

For example, k=1 Assume that the requested coverage level, k, is one and If The sensors covers the whole region completely, then Any sensing data produced by a sensor can be delivered to

the sink node.

CR

SR

2C SR R

2C SR R

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Sensing and Communication RangesReal Products’ Ranges [7]

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Self-deployment I

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Self-deploy using Potential Field [4] Problem Definition

How to maximize the sensor coverage in a model-free environment

Assumption each node is equipped with a sensor that allows it to

determine the range and bearing of both nearby nodes and obstacles

sensors can be constructed using “scanning laser range-finder”, “supersonic” or “omni-camera”.

Procedure Summary

Potential Field-based Strategy

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Determine “the virtual forces” from nodes and obstacles

convert “the virtual forces” into a control vector to be sent to its motors.

Deploy the sensor nodes randomly

Potential Fields and Forces [4]

Potential Fields generated by Obstacles and Boundary [5]

Potential Field

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The force vectors in the potential field generated by “AvoidObstacle” behavior

Force Vectors Force Vector due to obstacles

: coordinate of the current sensor node : coordinate of obstacle : distance from obstacle and the node : constant describing the strength of the field

Force Vector due to other sensors : coordinate of other sensor : distance from sensor and the node : constant describing the strength of the field

The compound force vector by the two components

Force Vectors from Potential Field

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0 2

1 i

oi i i

o nF k

r r

iioir

n

ok

2

1 i

s si i i

s nF k

r r

i

iisiir

sk

o sF F F

From Force Vectors to next location Next Acceleration

: mass of the node : friction force ( 마찰력 )

: viscosity coefficient : current velocity of node

Next Velocity : unit time

Next Location

: current location of the node

How to determine the next position?

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currentDnext

F vF Fa

m m

m

DF

D currentF v currentv

next current nextv v a t t

21

2next current next nextl l v t a t

currentl

Example

Example

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j i(2,0) (9/2,0)

Performance Evaluation

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Proto-typical deployment experiment for a 100-node network.

(a)Initial network configuration. (b)Final configuration after 300

seconds.(c) Occupancy grid generated for the

final configuration; visible space is marked in black (occupied) or white (free); unseen space is marked in gray.

Performance Evaluation

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Performance

Self-deployment II

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Self-deploy using Coverage Hole [7] Problem Definition

How to maximize the sensor coverage with minimal time and minimal movement distance in an obstacle-less model-free and finite environment

Procedure Summary

Coverage hole-based Strategy

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Discover the coverage hole (the area not covered by any sensor)

Calculate the target positions of the moving sensors

Deploy the sensor nodes randomly

Voronoi DiagramVoronoi polygon

: Voronoi polygon of sensor node O is the set of Voronoi vertices of O is the set of Voronoi edges of O

: the set of Voronoi neighbors of O

example

All positions inside are closer to the node O than to any other nodes

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Voronoi DiagramWhy Voronoi diagram?

All positions inside a Voronoi partition are closer to the generating node than to any other nodes

So, each sensor is responsible for the sensing task only within its Voronoi partition

One partition is small area to be monitored by one sensor Each sensor just examine the coverage hole locally

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Coverage holeHow to find the coverage hole?

After constructing the Voronoi polygons, each sensor intersects it with the sensing circle of the containing sensor.

If it is found, next? If any coverage hole exists in its Voronoi partition, the

generating sensor decide where to move to eliminate it or reduce its size.

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Movement protocolsThree movement protocols

VEC (VECtor-based) pushes sensors away from a densely covered area

VOR (VORonoi-based) pulls sensors to the sparsely covered area

Minimax moves sensors to their local center area

Features Distributed Self-deployment protocols

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VEC (VECtor-based)Strategy

To find the overall virtual force as the vector summation of virtual forces from the boundary and all Voronoi neighbors.

The virtual force will push sensors from the densely covered area to the sparsely covered area.

Terms : the distance between two sensors ( , ) : the distance between a sensor and boundary : the average distance between two sensors

when the sensors are evenly distributed in the target area It should be calculated beforehand

avgd

avgd

avgdavgd

/ 2avgd Final goalInitial

Deployment

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VEC (VECtor-based)E.g.) Vector Summation of the sensor s1

3 12 1 1

1

1 21 3 1

1 2 1 3 1

( )( ) ( )( , )( , ) ( )

2 ( , ) ( , ) 2 ( , )s ss s s bavg avgnext

s avg b

l ll l l ld d s s dl d d s s d s

d s s d s s d s b

1s

2s3s

센서 s1 과 s2 모두 자신의 Voronoi Partition 을 Cover 하고 있지 못하므로 둘 다 전체 평균 거리에 그들 사이의 거리를 뺀 것에 대해 절반의 거리씩 이동

센서 s3 는 자신의 Voronoi Partition 을 Cover 하고 있으므로 센서 s3 는 이동하지 않고 센서 s1 만 전체 평균 거리에서 그들 사이의 거리를 뺀 거리를 이동

Boundary b

Boundary 로 부터 센서 s1까지의 거리는 전체 센서들의 평균 거리의 절반으로 유지해야 한다 .

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VEC (VECtor-based)The execution of VEC

35 sensors / 50m x 50m / random deployment Coverage : 75.7% -> 92.2% -> 94.7%

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VOR (VORonoi-based)Strategy

Pull sensors to their local maximum coverage holes Sensors move toward its farthest Voronoi vertex ( )

In the above figure, Sensor si’s target location is B is equal to the sensing range

It is a greedy algorithm

farV

farV

( , )d A B

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VOR (VORonoi-based)The execution of VOR

Coverage : 75.7% -> 89.2% -> 95.6%

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MinimaxStrategy

Choose the target location as the point inside the Voronoi polygon whose distance to the farthest Voronoi vertex ( ) is minimized

The target location is called “Minimax point ( )” It reduces the variance of the distances to the Voronoi

vertices, resulting in a more regular shaped Voronoi polygon

It considers distances to all the Voronoi vertices, rather than only to the farthest vertex.

farV

mo

farVVOR

Minimax mo

Circumcircle of 3 Voronoi vertices

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Minimax

VOR vs. Minimax

Si

u

v

Sa

Sb

Sc

Sd

Se

(a) VOR strategy

Si

u

v

(b) Minimax strategy

| | suv r Minimax point.

So, how to find it?

최소 크기를 가지는 외접원의 중심

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MinimaxTerms

: Minimax point (target point) : Minimax circle centered at the minimax point ,

with radius

: Circumcircle of three points : Circumcircle of three points

Algorithm 1) Find all the circumcircles of any 2 and any 3 Voronoi

vertices. 2) Among these circles, select the one having the minimum

radius and covers all the vertices as the Minimax circle for that polygon.

3) The center of the selected circle is the Minimax point

mO

( , )m m mC O r mO( , )m m farr d O V

( , , )m u v wC V V V , ,u v wV V V

( , )m u vC V V ,u vV V

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MinimaxThe execution of Minimax

Coverage : 75.7% -> 92.7% -> 96.5%

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Performance EvaluationCoverage

Minimax performs best, VEC the worst. Minimax fully utilizes the Voronoi polygon VEC does not consider holes nor Voronoi polygon structure

when choosing target location Minimax better than VOR

since it considers more information.

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Performance EvaluationCoverage vs. Communication Range

Performance is reduced when communication range is reduced.

This is because most sensors do not know all the neighbors, thus construct inaccurate Voronoi polygons.

Consequently get incorrect coverage holes and target locations. VEC is least affected, since it does not use the Voronoi polygon

to determine target location.

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Performance EvaluationMoving Distance

Minimax moves longer distance than VOR, since not only fixes holes but tries to reach more regular shaped polygons.

For VEC, moving distance is similar under different sensor densities.

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Innercenter vs. Circumcenter vs. Centroid

[Centroid vs. Center of Gravity]- 도심 (Centroid) 와 무게중심 (Center of Gravity) 은 일반적으로 동의어로 쓰인다 . - 하지만 , 도심의 계산은 기하학적인 모양에만 관련이 된다 .- 만약 물체가 균질하다면 (homogeneous) 즉 , 일정한 밀도를 가졌다면 무게중심과 도심은 일치한다 .

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