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
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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)
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Measuring Relative Bearing
Directional sensor array
Transmitter array (acoustic, radio)
Vision
Bumper array
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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
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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
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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.
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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
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Bearing Estimation Algorithm
A
B
S - step sizeS
45° CCW
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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
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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
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Effect of Noise
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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
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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°
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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
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Backup Slides
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Discussion
• Use
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Bearing Estimation Algorithm
A
B
S - step sizeS
2525/21/21
Bearing Estimation Algorithm
A
B
S - step sizeS
45 CCW