Spatial Sound Localization for Robots

1. Spatial Sound Localization for Robots Nikunj Raghuvanshi University of North Carolina at Chapel Hill

2. Motivation • Humans do complex motion planning everyday • Our sound sensing is omni-directional • Sounds can get to places where light cannot • Sound tells us where to look for something, approximately • Vision tells us where something is exactly University of North Carolina at Chapel Hill

3. Culled Culled Culled Motivation • A robot first needs a target specification • In a real-life scenario, when a global map is not available, this may be difficult • Idea: Use sound to provide approximate direction in addition to visual clues • Reduces the search space drastically, no need to do a random search and map thewhole environment Target B A University of North Carolina at Chapel Hill

4. Overview • Background on Sound • Sound localization in humans • Sound localization for robots • Results University of North Carolina at Chapel Hill

5. What is Sound? • Sound: Tiny fluctuations of air pressure • Carried through air at 345 m/s (770 m.p.h) as compressionsand rarefactions in air pressure wavelength compressed gas rarefied gas University of North Carolina at Chapel Hill

6. Longitudinal vs. Transverse Waves • Sound is a longitudinal wave, meaning that the motion of particles is along the direction of propagation • Transverse waves—water waves, light—have things moving perpendicular to the direction of propagation University of North Carolina at Chapel Hill

7. p/2 Properties of Waves Wavelength() pressure • Wavelength () is measured from crest-to-crest • For traveling waves (sound, light), there is a speed (c) • Frequency (f) refers to how many cycles pass by per second at a given point • These three are related: f = c • Phase (q): Measures the progression of pressure at a point between a crest and a trough. Distance p 2p Phase(q) 3p/2 University of North Carolina at Chapel Hill

8. Interference A • The resultant pressure at P due to two waves is simply their linear superposition • Phase is very important in interference P B out of phase:cancel in phase: add signal A signal B A + B University of North Carolina at Chapel Hill

9. Diffraction • A wave bends around obstacles of size approx. its wavelength, i.e. when ~ s • P will have appreciable reception only if there is a good amount of diffraction • This is the reason sound can get to places where light cannot  s  P s University of North Carolina at Chapel Hill

10. Overview • Background on Sound • Sound localization in humans • Sound localization for robots • Results University of North Carolina at Chapel Hill

11. Before we start… • Sound localization: Finding the direction to the sound source • Two versus multiple receivers? • The localization performance of humans shows that two ears are sufficient • The work I discuss is the first one to effectively use two sensors to perform accurate sound localization University of North Carolina at Chapel Hill

12. Sound Localization The sound localization facility at Wright Patterson Air Force Base in Dayton, Ohio, is a geodesic sphere, nearly 5 m in diameter, housing an array of 277 loudspeakers. Listeners in localization experiments indicate perceived source directions by placing an electromagnetic stylus on a small globe. University of North Carolina at Chapel Hill

13. Sound Localization: ILD • Idea: A sound source on the right will be perceived to have more intensity at the right ear • Head casts an acoustical or sound shadow • The difference of the intensities at the two ears is the Interaural Level Difference (ILD) University of North Carolina at Chapel Hill

14. Sound Localization: ILD • The ILD depends on the angle as well as frequency • Different frequencies diffract differently • In general, higher frequencies diffract less, leading to a sharper shadow and higher ILD • Assume head has dia ~ 17 cm • ILD becomes useless for f<500 Hz (=69 cm) • Accurate for f>3000 Hz University of North Carolina at Chapel Hill

15. Sound Localization: ITD • Idea: Sound has longer path for farther ear (d), and hence takes more time to reach it • This too depends on both the angle and frequency of sound • Measured as the Interaural Time Difference (ITD) d University of North Carolina at Chapel Hill

16. ITD: Range of usefulness • If the signal is periodic (eg. Pure tone), ITD is useless if the path difference is much greater than the wavelength • For human head size, ITD is useful for f<1000 Hz a). Peak 1 arrives properly in sequence at the two ears and there’s no confusion. b). Peak 1 and 2 arrive closely at the ears and cause confusion University of North Carolina at Chapel Hill

17. Finding the ITD • Use a pattern matcher to check position of MAXIMUM similarity • Independent sound signals g(t) & h(t) are ‘slid’ across each other (Sliding Window) • Correlation vector is returned showing delay between the signals g(t) & h(t) i.e. the ITD University of North Carolina at Chapel Hill

18. Front-back ambiguity • The theory of humans using only ITD and ILD has a big flaw. The formulation has inherent symmetry which creates front-back ambiguity (points 2 and 3 in figure) • ITD and ILD for 2 and 3 will be identical (right?) University of North Carolina at Chapel Hill

19. Front-back ambiguity • There is a simple way to break this symmetry: move the head! • This approach is used in the paper I discuss later • Interestingly, a moving source alone may not be enough to break the ambiguity, its important to move the head • But humans can do it without even moving, how? University of North Carolina at Chapel Hill

20. The HRTF • There is no symmetry in reality because of the structure of the external ear and scattering by the shoulders and head • The Head Related Transfer Function (HRTF) measures the amounts by which different frequencies are amplified by the head for different source positions • This thing works well only when the sound is broad-band University of North Carolina at Chapel Hill

21. Summary • Sound provides two cues: ILD and ITD • ILD measures the intensity difference between the two ears at a given point in time • ITD measures the difference in arrival time for the same sound at the two ears • ILD is useful for frequencies >3000 Hz • ITD is useful for frequencies <1000 Hz • There is a front-back ambiguity using ITD and ILD alone which head motion resolves University of North Carolina at Chapel Hill

22. Overview • Background on Sound • Sound localization in humans • Sound localization for robots • Results University of North Carolina at Chapel Hill

23. Sound Localization for robots • The papers I will discuss: • A Biomimetic Apparatus for Sound-source Localization. Amir A. Handzel, Sean B. Andersson, Martha Gebremichael and P.S. Krishnaprasad. IEEE CDC 2003 • Robot Phonotaxis with Dynamic Sound-source Localization. Sean B. Andersson, Amir A. Handzel, Vinay Shah, and P.S. Krishnaprasad. IEEE ICRA 2004 University of North Carolina at Chapel Hill

24. Sound Localization The “head” • As discussed, to resolve front-back ambiguity, we have two options: • Use a spherical head, and use head motion to resolve front-back ambiguity • Use an asymmetric head and compute the HRTF and use that, like humans • The first approach is much simpler and is the one used in this paper University of North Carolina at Chapel Hill

25. Sound Localization Start End University of North Carolina at Chapel Hill

26. A simple ITD-based method • A very simple method commonly in use • Consider a distant source so that impinging wave is nearly planar • Path difference between left and right is given by l(ABC), which is, • By correlating the left and right sound signal, suppose the ITD is found, then a = c*ITD • Solve for using above equation University of North Carolina at Chapel Hill

27. The IPD-ILD algorithm • Solve for scattering from a hard spherical head. This is a more realistic physical model • Two microphones at the poles ( ) • Wave equation is given by, • Where c=344 m/s is the speed of sound, is the velocity potential and is the laplacian University of North Carolina at Chapel Hill

28. Mathematical Formulation • Basic idea for solution: Solve in spherical coordinates. The solution is well known, using separation of variables • The only place where scattering from a hard sphere is invoked is to satisfy the following equation: • In the above, and are the incident potential (from source) and scattered potential (from sphere) respectively • The solution has the following important properties: • Dependent only on the angle between source and receiver • Independent of source distance: can localize only the direction University of North Carolina at Chapel Hill

29. Mathematical Formulation • It is assumed that the sound source, the center of the head and the ears are in the same plane, i.e. localization is performed only in the horizontal plane • The pressure p, measured at a microphone is given by: • In the above, is the geometry and frequency-dependent phase-shift, and is the angular frequency ( ) • Its important to note that both A and depend on the frequency, , due to differential scattering University of North Carolina at Chapel Hill

30. The IPD and ILD • The Interaural Phase Difference (IPD) is the same concept as the ITD, except it measures the phase difference rather than the time difference. Specifically, • The IPD and ILD can be computed as, • At given source angle , using these theoretical formulas, we may calculate IPD( ) and ILD( ) • Our job is to invert this operation, given the IPD and ILD at different frequencies, we need to find University of North Carolina at Chapel Hill

31. Localization Metric • Sample and store the values of IPD( , ) in a table • Collect data from microphones and try to find closest theoretical curve • Apply FFT to gather ILD and IPD values for different • Distance metric: L2 norm distance between predicted and observed IPD and ILD curves • Final distance, • Minimize over , to get source direction University of North Carolina at Chapel Hill

32. Resolving front-back ambiguity • Even though IPD and ILD are the same for any two angles and , their derivatives with respect to , IPD’ and ILD’ are not • Since IPD and ILD are theoretically known, their derivatives may be calculated, sampled and stored just like the IPD and ILD values • The observed difference between the IPD values for two consecutive samples provides an approximation for IPD’ • Define a similar L2-norm metric for IPD’ and ILD’ • Augmented distance function to minimize: University of North Carolina at Chapel Hill

33. Overview • Background on Sound • Sound localization in humans • Sound localization for robots • Results University of North Carolina at Chapel Hill

34. Results: Accuracy of theoretical ILD • Curve: Theoretically computed ILD • Dots: Actual values measured from microphones University of North Carolina at Chapel Hill

35. Results: Accuracy of theoretical IPD • Much more accurate than ILD University of North Carolina at Chapel Hill

36. Localization Performance • Sharp minima at small angles, not so sharp at large angles University of North Carolina at Chapel Hill

37. Localization Performance IPD/ILD Algorithm Simple ITD-based algorithm University of North Carolina at Chapel Hill

38. Front-back ambiguity resolution Without ambiguity resolution With ambiguity resolution Symmetric University of North Carolina at Chapel Hill

39. Conclusion/Discussion • IPD/ITD is a much stronger clue than ILD. That’s why the simple ITD algorithm also gives decent performance • Overall this work is the first one to demonstrate a real working robot with good sound localization, so presumably this works well in practice • The method is theoretically well-motivated, and shows that good localization can be achieved with just two isotropic microphones • It is also claimed that it works well in a laboratory environment with some noise (CPU fans etc.) and reflections from the walls etc. University of North Carolina at Chapel Hill

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43. Thanks • Questions? University of North Carolina at Chapel Hill

44. Summary • Reflective environments, the precedence effect University of North Carolina at Chapel Hill