Relative Bearing Estimation using Commodity Radios

1. Relative Bearing Estimation using Commodity Radios Karthik Dantu1 Prakhar Goyal2 Gaurav S. Sukhatme1 1Dept of Computer Science University of Southern California Los Angeles, CA - 90089-2905 2Dept of Computer Science and Engg.Indian Institute of Technology-Bombay Mumbai - 400237

2. What is Relative Bearing?  BA B AB A

3. 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)

4. Measuring Relative Bearing • Directional sensor array Transmitter array (acoustic, radio) Vision Bumper array

5. 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

6. Large Scale Fading • Radio behavior over large distances (>> ) • Correlated to distance • Modeling less reliable for shorter distances and very close to transmitter

7. Small Scale Fading Sender Receiver Bluesignal travels 1/2 farther thanred to reach receiver, who receivespurple • Signal variability on the scale of  • Multipath effects dominate (reflection, refraction, diffraction, scattering) • Mobility introduces Doppler effects •  ~ 12cm for 2.4 GHz

8. 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)+ 10log(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.

9. 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

10. S S - step size Bearing Estimation Algorithm B 45° CCW A

11. 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

12. 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

13. Effect of Step Distance Variation 6m

14. Effect of Number of Samples 100 samples

15. Effect of Noise

16. Experimental Setup Wi-Fi Antenna Telos B Mote for ZigBee radio ~3 ft E-box with Intel 800Mhz PC with 802.11 Wi-Fi card iRobot Create

17. Bearing Error Outdoors

18. Bearing Error Indoors

19. Outdoor Multi-robot Experiments (5 robots) Average error over two trials was 19.1°

20. Indoor Multi-robot Experiments (5 robots) Average error over 5 trials was 24.3°

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

22. Backup Slides

23. Discussion • Use

24. S S - step size Bearing Estimation Algorithm B A

25. S S - step size Bearing Estimation Algorithm B 45 CCW A