Transcript Document

Sound-based Techniques for
Navigation
Josh Markwordt
October, 24 2007
COMP 790-058
Overview
• Basics of Sound
• Active Sonar
• Passive Sonar
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Basics of Sound
• We perform motion planning and navigation
everyday
• In addition to sight, we use our other senses
including sound to aid our decisions making
• Our audio sense differs in a number of
beneficial ways from our sense of sight:
– Sound is omni-directional
– Sound can move around obstacles that completely
obscure line of sight
– Sound can be a good way to quickly estimate the
general direction of something
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What is Sound?
• Sound is a mechanical disturbance that
propagates through air as a wave
• Longitudinal wave, meaning motion of particles
is along the direction of propagation
• Compressions and rarefactions in air pressure
(or other medium the sound is being
transferred in)
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Properties of Sound
• Wavelength () is measured from crest to crest
• Frequency (f) refers to how many cycles pass by per
second at a given point
• Phase (): Measures the progression of pressure at a
point between a crest and a trough
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Diffraction
• Sounds with wavelengths similar to the dimensions of obstacles
diffract around those obstacles
• High frequency sounds, with short wavelengths, do not diffract
around most objects but are reflected or absorbed
• A sound shadow is created behind objects, which is perceived as a
decrease in the loudness of a sound
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Interference
• Resultant pressure is the linear
supposition of the two signals
• If they are in phase, the signal
will magnify the amplitude of
the wave resulting in
“constructive interference”
• Signals that are out of phase
produce “destructive
interference”
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Overview
• Basics of Sound
• Active Sonar
• Passive Sonar
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Active Sonar
• Creates a pulse of sound from a transmitter and
listens for reflections of the pulse
• Time from transmission of a pulse to reception
is measured to determine distance
• An array of sensors can be used to gain more
accurate information
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Probabilistic Occupancy Grid
• Number of difficulties with processing sonar
data, mainly due to the sensors themselves
– Low angular resolution
– Errors due to multiple reflections or specular
reflections away from the sensor
• This leads to a probabilistic approach to the
recovery of spatial information from sonar
range data
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Probabilistic Occupancy Grid
• Sonar reading R corresponds to a range value r
returned by a sensor
• Define a conditional probability function P(cell
C is occupied | sensor reading R)
• Informally measures our confidence that cells
inside the cone of the beam are empty
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Probabilistic Occupancy Grid
• Occupancy grids are 2D or 3D tesselations of
space into cells
• Each cell has probabilistic estimate of its
occupancy
• Each cell C has a state variable s(C ), a discrete
random variable with two states OCCUPIED and
EMPTY such that
P(s(C )  OCCUPIED)  P(s(C )  EMPTY)  1
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Bayesian Model for Updating
• Can avoid combinatorial explosion by assuming
– Each cell in the grid is independent
– The superposition of many readings will eventually
converge to the correct state of each cell
• Bayes’ Theorem tells how to update or revise
probabilities in light of new evidence
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Bayes’ Theorem
P( si ) P(e | si )
P( si | e) 
 P ( s j ) P (e | s j )
•
•
•
•
•
j
Where s i is one of n disjoint states being estimated
e is the relevant evidence
P( si ) is the a priori probability of the system being in state i
P(e | si ) is the probability that evidence e would be present given
that the system is in state
P(si | e) is what is needed for decision making, namely conditional
probability that the system is in state i in light of the evidence e
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Bayesian Model for Updating
• In our system, the evidence is sensor range
readings R
• Desired probabilities P(OCC |R) and P(EMP|R)
P(OCC | R) 
P(OCC) P( R | OCC)
P(OCC) P( R | OCC)  P( EMP) P( R | EMP)
• Since P(R|EMP) = 1 – P(R | OCC) we can write it
just in terms of one of the probabilities
P(OCC | R) 
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P(OCC) P( R | OCC)
P(OCC) P( R | OCC)  (1  P(OCC))(1  P( R | OCC))
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Bayesian Model for Updating
• This formula has several useful properties
– It is commutative and associative (data can be
incorporated in any order)
– Combining evidence E with the prior probability for
UNKNOWN (P(OCC) = 0.5), gives E as a result
– Conflicting measurements of the same strength
cancel (OCCUPIED +EMPTY = UNKNOWN)
• Initialize map by assigning equal probability of
P(OCC)=P(EMP)=0.5 (or UNKNOWN) to each
cell
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Probabilistic Occupancy Grid
• Graphic corresponds to reading taken by a sensor
positioned at the upper left pointing to the lower right
• The plane shows the
UNKOWN level
• Values above the plane
represent OCCUPIED
probabilities
• Values below represent
EMPTY probabilities
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Sonar Map Example
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Active Sonar Maps
• A single set of sonar readings
– provides substantial information
about empty space, but is weak in
recovering object shape
– Immediate motion decisions are
possible
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Active Sonar Maps
• Only through the composition of
several views is more spatial
structure recovered
• Wide angle of beam sometimes
precludes the detection of free
space between close objects
• Phantom obstacles can be
generated due to multiple
reflections
• But over several sets of readings
sonar is able to recover good
descriptions of surfaces
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Active Sonar Maps
• Resulting active sonar maps are very useful for
navigation
– Much denser than ones generated by previous
sparse stereo vision programs
– Computationally about an order of magnitude faster
to produce
• Autonomous navigation
system that uses an A*-based
path planner to obtain routes
in these maps
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Overview
• Basics of Sound
• Active Sonar
• Passive Sonar
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Passive Sonar
• Passive sonar listens without transmitting
• Must rely on the sound of the object being
detected
• Advantages
– Power consumption of passive sonar is very low
– Data can be used for target identification or to
pinpoint location of the emitting sound source
• Disadvantages
– Can be more difficult based on the amount of noise
or stealth of the object
– Need to identify an object by sound
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Beamforming
• Takes advantage of the distance from an object to each
receiver being different
• Each recording will be a phase-shifted replica of the
others
• Shift the signals in the opposite direction in order to get
them in phase
• Results in constructive interference to amplify the
desired signal
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Beamforming
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Beamforming Pseudocode
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Passive Sonar System
• EvBot II equipped with eight microphones
• Tested with various real-object sounds such as
helicopters, trucks and airplanes
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Passive Sonar System
• Able to effectively track a moving object
emitting a sound
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Conclusion
• Sonar maps are useful for localization in motion
planning tasks
• In combination with stereo vision can provide a
more complete view of the world to
autonomous robots
• Passive sonar can be used to track an object,
but it’s not as practical as active sonar
• Questions?
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References
• Sensor integration for robot navigation: Combining sonar and
stereo range data in a grid-based representation Alberto Elfes,
Larry Matthies 26th IEEE Conference on Decision and Control, Vol
26 1987.
• Beamforming: A versatile approach to spatial filtering Van
Veen, B.D., Buckley, K.M., IEEE ASSP Magazine Vol 5, Issue 2 1988.
• Passive sonar applications: target tracking and navigation of
an autonomous robot Mattos, L., Grant, E. IEEE International
Conference on Robotics and Automation Proceedings, Vol 5, Issue
26 2004.
• A sonar-based mapping and navigation system Elfes, A. IEEE
International Conference on Robotics and Automation
Proceedings, Vol 3 1986.
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