Relative Relative Bearing Bearing

Estimation Estimation using using

Commodity Commodity Radios Radios

Karthik Dantu1

Prakhar Goyal2

Gaurav S.

Sukhatme1

1Dept of Computer Science University of Southern CaliforniaLos Angeles, CA - 90089-2905

2Dept of Computer Science and Engg.Indian Institute of Technology-Bombay

Mumbai - 400237

22/21/21

What is Relative Bearing?

A

B

AB

BA

33/21/21

Uses of Relative Bearing

• Robot Localization (Briechle 04, Chintalapudi 04, Das 02,

Martinelli 05, Niculsecu 03, Spletzer 01, Taylor 07)

• Navigation (Bekris 04, Ducatelle 08, O’Hara 08)

• Topology Control (Eren 03, Li 05, Poduri 08)

• Formation Control (Das 02, Mostagh 08, Spletzer 01)

• Pursuit-Evasion Games (Karnad 08, Maloy 95)

44/21/21

Measuring Relative Bearing

Directional sensor array

Transmitter array (acoustic, radio)

Vision

Bumper array

55/21/21

Radio as a Sensor

• Signal strength roughly

correlated with distance

between sender and receiver

• Most modern robots have

off-the-shelf radios

• Radio characteristics are well

studied

66/21/21

Large Scale Fading

• Radio behavior over

large distances (>> )

• Correlated to distance

• Modeling less reliable

for shorter distances

and very close to

transmitter

77/21/21

Small Scale Fading

Blue signal travels 1/2 farther than red to reach receiver, who receives purple

Sender Receiver

• Signal variability on the scale of

• Multipath effects dominate (reflection, refraction, diffraction, scattering)

• Mobility introduces Doppler effects

• ~ 12cm for 2.4 GHz

88/21/21

Large Scale Fading Models

• Free Space Model: Models signal strength on a clear

unobstructed link

LossdB=20log(d) + 20 log(f) + C

• Log Distance Path Loss Model: Logarithmic path loss

model with Path Loss Exponent () for the particular

medium

LossdB= PL(d0)+ 10log(d/d0) + XBg

• ITU Indoor Model: Takes into account the frequency of

transmission and floors between sender and receiver

LossdB= 20log(f) + Nlog(d) + Lf(n) + K

Introduction to RF Propagation, John S. Seybold, Wiley-Interscience.

99/21/21

Estimating Bearing Using Radio

• Consider only large scale fading effects

• Sample signal strength in the locality of robot

• Perform Principal Component Analysis (PCA)

• Primary component is the direction of maximum

variance of signal strength

• Relative bearing of robot is approximated to this

direction

1010/21/21

Bearing Estimation Algorithm

A

B

S - step sizeS

45° CCW

1111/21/21

Step Distance

• Step distance is a parameter

• Greater step distances improve signal gradient

but odometry error and area of deployment

are constraints

• From our signal strength measurements, for a

signal strength loss of 20dB step size is 6m

outdoors and 2m indoors

1212/21/21

Simulation Setup

• Simulated an area of 100m x 100m

• Two robots are randomly placed in the given

area

• Parameters

• Step distance

• Number of samples collected

• AWGN Noise added to samples collected

• Results are averaged over 100 trials

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Effect of Step Distance Variation

6m

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Effect of Number of Samples

100 samples

1515/21/21

Effect of Noise

1616/21/21

Experimental Setup

iRobot Create

~3 ft

Telos B Mote for ZigBee radio

Wi-Fi Antenna

E-box with Intel 800Mhz PC with 802.11 Wi-Fi card

1717/21/21

Bearing Error Outdoors

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Bearing Error Indoors

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Outdoor Multi-robot Experiments (5 robots)

Edge Actual

Angle

Estimated

Angle

Bearing

Error

1 120° 103.7 ° 12.3 °

2 135° 104.8° 30.2°

3 45° 58.8° 13.8°

4 -30° -11.8° 18.2°

5 -150° -130.7° 19.3°

6 0° 25.8° 25.8°

Average error over two trials was 19.1°

2020/21/21

Indoor Multi-robot Experiments (5 robots)

Edg

e

Actual Angle Estimate

d Angle

Estimatio

nError

1 5° 9.3° 4.3°

2 120° 148.1° 28.1°

3 -160° -147.2° 12.81°

4 170° 202.5° 32.5°

5 -30° -18.3° 11.7°

6 150° 172.1° 22.1°

Average error over 5 trials was 24.3°

2121/21/21

Conclusions

• Relative bearing can be estimated using commodity radios

• Tested algorithm in simulation and experiment

(ZigBee and Wi-Fi)

• Used this estimation as input for connectivity algorithm

• ZigBee radios perform better than Wi-Fi on average

• Average error is approximately 20° indoors and 25°

outdoors using ZigBee radios

• Future work: Exploit small scale effects

2222/21/21

Backup Slides

2323/21/21

Discussion

• Use

2424/21/21

Bearing Estimation Algorithm

A

B

S - step sizeS

2525/21/21

Bearing Estimation Algorithm

A

B

S - step sizeS

45 CCW