University of Hamburg
6 Distance
Department of Informatics
64-424 Intelligent Robotics
Outline
1.
2.
3.
4.
5.
6.
Motivation
Fundamentals
Transformations
Rotation / Motion
Force / Pressure
Distance
Fundamentals
Sensors
Literature
7. Scan processing
8. State estimation
9. Vision systems
10. Fuzzy logic
Jianwei Zhang / Eugen Richter
222
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Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Measurement of distance
The ability to measure distance plays a crucially important role in
the field of robotics - it is particularly important for mobile robots
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Obstacle detection/avoidance
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Localization
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...
Several sensors can be used do determine the distance
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Infrared/Ultrasonic sensor
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Laser rangefinder
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"Vision system"
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...
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223
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6.1 Distance - Fundamentals
Department of Informatics
64-424 Intelligent Robotics
Measurement of distance (cont.)
The predominant underlying physical principles for measurement of
distance using sensor devices are:
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Time-of-flight (TOF)
! Time required for a signal to travel through a medium
Phase shift/difference
! Difference in phase as a property of the reflected signal
Triangulation
! A geometric approach
Jianwei Zhang / Eugen Richter
224
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Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Time-of-flight
Measurement of distance using the time-of-flight principle is a
straightforward process
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Emit signal (impulse)
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Measure time ( t) until reception of the echo/reflection
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Determine distance (D) using knowledge about the speed (v )
of the signal
D=
Jianwei Zhang / Eugen Richter
t ·v
2
225
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Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Time-of-flight (cont.)
Example: Distance measurement using light impulses
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Signal: Light impulse
Medium: Air
Measured time: 65 ns
Assuming v = c, where c is the speed of light (299792458 m/s)
and a value of 65 ns for t the resulting distance is
9.74 m ⇡
Jianwei Zhang / Eugen Richter
0.000000065 s · 299792458 m/s
2
226
University of Hamburg
6.1 Distance - Fundamentals
Department of Informatics
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Time-of-flight (cont.)
Example: Distance measurement using an ultrasonic sensor
Jianwei Zhang / Eugen Richter
227
University of Hamburg
Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Time-of-flight (cont.)
Advantages:
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Compact size of the system
! Emitter can be placed in close proximity to the receiver
Emitter and receiver could even be lying on the same axis
! Ultrasonic sensor
Computationally efficient calculation of the distance
(e.g 2D sensors)
Disadvantages:
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Sensitive to ambient light
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False measurements due to multiple reflections
Jianwei Zhang / Eugen Richter
228
University of Hamburg
Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Phase shift/difference
As an alternative to time-of-flight, the phase shift approach is also
very straightforward
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Emit signal (impulse) modulated with a given frequency (fmod )
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Feed the received echo/reflection of the signal into a
phasemeter
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Determine distance (D) based on the phase shift ( ✓) between
the reflected signal and the emitted signal
D=
Jianwei Zhang / Eugen Richter
1
✓
·
·
2 2⇡
=
1
✓
c
·
·
2 2⇡ fmod
229
University of Hamburg
Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Phase shift (cont.)
The distance traveled by the reflected beam is specified as
Dactual = L + 2D
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230
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6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Phase shift (cont.)
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If D = 0, then Dactual = L and both beams reach the
phasemeter simultaneously
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If D is increased, the reflected beam needs to run a longer
distance, resulting in a phase difference ✓ compared to the
reference beam
Jianwei Zhang / Eugen Richter
231
University of Hamburg
Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Phase shift (cont.)
Example: Distance measurement using light impulses
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Signal: Light impulse
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Medium: Air
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Frequency: 10 MHz
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Measured phase shift: 275
Assuming c the speed of light (299792458 m/s) and a value of
4.78 rad for ✓ the resulting distance is
11.45 m ⇡
Jianwei Zhang / Eugen Richter
1 4.78 299792458 m/s
·
·
2 2⇡
10000000 s 1
232
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6.1 Distance - Fundamentals
Department of Informatics
64-424 Intelligent Robotics
Phase shift (cont.)
The advantages and disadvantages of distance measurement based
on phase shift/difference are very similar to those of the
time-of-flight approach
Caution:
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For ✓ = 360 the phase difference is 0!
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Impossible to distinguish between Dactual = L and
Dactual = L + n , n = 1, 2, . . .
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To receive a distinct result, constraints ✓ < 360 and 2D <
need to apply
Jianwei Zhang / Eugen Richter
233
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Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Phase shift (cont.)
Direct use of a signal source is not possible
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Example: The wavelength of a laser emitter is very small (e.g.
632.8 nm for a Helium-Neon laser)
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A general solution for this problem is obtained through
modulation of the emitted signal with a much longer wave
( = c/fmod )
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A modulation frequency of fmod = 10 MHz results in a
wavelength of about 30 m
Jianwei Zhang / Eugen Richter
234
University of Hamburg
Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Triangulation
Triangulation is the process of calculation of distance to a point
using knowledge about viewing angles
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Use two viewing points with the distance between them
(baseline) known
Align both "viewers" looking towards the point in question
Determine the angles of both "viewers" to the baseline
Calculate the distance using basic trigonometry
Two viewing points may be obtained in a number of ways:
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Movement of a single sensor
Special design of the sensor
Multiple sensors
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235
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Department of Informatics
6.1 Distance - Fundamentals
64-424 Intelligent Robotics
Triangulation (cont.)
D = l2 =
Jianwei Zhang / Eugen Richter
l1 sin(↵)
sin(↵ + ⇥)
Dbaseline =
l1 sin(↵) sin(⇥)
sin(↵ + ⇥)
236
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6.1 Distance - Fundamentals
Department of Informatics
64-424 Intelligent Robotics
Triangulation (cont.)
Jianwei Zhang / Eugen Richter
237
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Outline
6. Distance
Fundamentals
Sensors
Literature
Jianwei Zhang / Eugen Richter
238
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
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Infrared sensors
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Infrared sensors are the most simple type of non-contact sensors
Are commonly used for obstacle detection in robotics
Infrared sensors emit a signal in the infrared spectrum
Jianwei Zhang / Eugen Richter
239
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Department of Informatics
6.2 Distance - Sensors
64-424 Intelligent Robotics
Infrared sensors (cont.)
Reflection of the emitted signal by objects in the vicinity:
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To be able to distinguish the emitted signal from other infrared
sources in the vicinity (e.g. fluorescent lamps or sunlight), it is
usually modulated with a low frequency (e.g. 100 Hz)
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Assuming that all objects are equal in color and surface, the
distance to the objects can be determined with usable accuracy
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The intensity of the reflected light is inversely proportional to
the squared distance
Jianwei Zhang / Eugen Richter
240
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6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Infrared sensors (cont.)
Problem: In realistic environments, surfaces are not equal in color
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Colored surfaces reflect different amounts of light
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Black surfaces are practically invisible
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In fact, IR-sensors can only be used for object detection, but
not for exact distance measurement
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If an IR-signal is received by the sensor, one can assume, that
there’s an object in front of of the sensor
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Note: A missing IR-signal does not necessarily mean there is
no object in front of the sensor
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IR-sensors are usually used for short distances (50 to 100 cm)
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241
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6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Infrared sensors (cont.)
Measured sensor output based on different object surfaces
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242
University of Hamburg
6.2 Distance - Sensors
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Ultrasonic sensors
Ultrasonic sensor have two inspiring examples in the field of biology
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Dolphin
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Localization
Navigation
Communication
Tracking (Hunting)
Bat
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Localization
Navigation (e.g. in complete darkness)
Tracking (Hunting)
Jianwei Zhang / Eugen Richter
243
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Ultrasonic sensors (cont.)
Bats use various different sound navigation and ranging (sonar)
techniques
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Fixed frequencies
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Varying frequencies
Note: Although artificial ultrasonic sensors are capable of creating
frequencies similar to those in the animal world, the animal
capabilities remain unmatched
Jianwei Zhang / Eugen Richter
244
University of Hamburg
Department of Informatics
6.2 Distance - Sensors
64-424 Intelligent Robotics
Ultrasonic sensors (cont.)
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Ultrasonic waves are differentiated from electromagnetic waves
based on the following physical properties:
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Medium
Speed (in medium)
Wavelength
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Ultrasonic waves require a medium like air or water
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Ultrasonic speed in air amounts to 340.29 m/s + 0.6 ⇥ C
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Time-of-flight measurement is possible for short distances
The wavelength of an ultrasonic sensor driven with a frequency
of 50 kHz amounts to ⇡ 6.872 mm
Jianwei Zhang / Eugen Richter
245
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Ultrasonic sensors (cont.)
Reflection of ultrasonic waves from smooth (and flat) surfaces is
well-defined
However:
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Very rough structures lead to diffuse reflection of ultrasonic
waves
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Note: A round rod produces a diffuse reflection
Jianwei Zhang / Eugen Richter
246
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Ultrasonic sensors (cont.)
Piezoelectric ultrasonic transducer:
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To produce ultrasonic waves, the movement of a surface is
required, leading to a compression or expansion of the medium
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One possibility to generate ultrasonic waves is the use of a
piezoelectric transducer
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Applied voltage causes a bending of the piezoelectric element
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Piezoelectricity is reversible, therefore incoming ultrasonic
waves produce an output voltage
Jianwei Zhang / Eugen Richter
247
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Ultrasonic sensors (cont.)
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Typically, piezoelectric transducers are operated in the
proximity of their resonance frequency fr (usually 32 kHz)
That’s where the ceramic element reacts with the highest
sensitivity
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248
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Department of Informatics
6.2 Distance - Sensors
64-424 Intelligent Robotics
Ultrasonic sensors (cont.)
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The piezoelectric transducer operates as a transmitter
(motor-mode) and a receiver (passive-mode)
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It transforms electricity into sonic waves and the other way
around (both due to mechanical stress)
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As a receiver, the transducer operates very much like an
electrostatic microphone
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The piezoelectric component is usually a solid material such as
a specific ceramic or crystal
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The opening angle (beam angle) of the ultrasonic signal that is
emitted by the transducer, can be up to 30 wide
Jianwei Zhang / Eugen Richter
249
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Ultrasonic sensors (cont.)
Jianwei Zhang / Eugen Richter
250
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6.2 Distance - Sensors
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Piezoelectric ultrasonic transducer (cont.)
Signal propagation and damping
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251
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6.2 Distance - Sensors
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Piezoelectric ultrasonic transducer (cont.)
Example: Pioneer platform equipped with 16 ultrasonic (sonar) sensors
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252
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6.2 Distance - Sensors
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Ultrasonic precision
The minimum distance dmin which can still be measured, is
specified as:
1
dmin = vtImpulse
2
v : Speed of the wave in the corresponding medium
tImpulse : Duration of the emitted impulse in seconds
The maximum distance dmax which can still be measured, is
specified as:
1
dmax = vtInterval
2
v : Speed of the wave in the corresponding medium
tInterval : Time span between the single impulses
Jianwei Zhang / Eugen Richter
253
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Ultrasonic precision (cont.)
Measurements with sonar sensors are subject to several inaccuracies
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The precise position of the object usually remains unknown due
to the cone-shape of the sensitivity area of the emitted impulse
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An object perceived at a distance of d may be located at an
arbitrary position within the sonar cone on the arc at a distance
of d
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Mirror and total reflections cause flawed measurements
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If the sonar beam hits a smooth object in a flat angle, the
signal will usually be deflected and no echo will reach the sensor
Jianwei Zhang / Eugen Richter
254
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Ultrasonic precision (cont.)
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If several sonar sensors are used simultaneously, specifically
encrypted signals need to be used, because otherwise crosstalk
may occur
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Since the measurement depends on the temperature of the
medium, a change in air temperature will introduce
measurement errors (e.g. a difference of 16 C will cause a
measurement error of 30cm over a distance of 10m)
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Though such an error has no influence on simple
sensor-motor-behavior like obstacle avoidance, it may lead to
imprecise area maps during map creation
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255
University of Hamburg
Department of Informatics
6.2 Distance - Sensors
64-424 Intelligent Robotics
Ultrasonic precision (cont.)
Measuring principle
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Ultrasonic precision (cont.)
Resolution
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Ultrasonic precision (cont.)
Measurement error
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Ultrasonic precision (cont.)
Invisible wall
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Ultrasonic precision (cont.)
Invisible corner
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Ultrasonic precision (cont.)
Corner error
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261
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Laser range finders
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Laser range finders (LRF) measure the
distance, speed and acceleration of
recognized objects
Functional principle similar to that of
a sonar sensor
Instead of a short sonic impulse, a
short light impulse is emitted from
the laser range finder
The time span between emission and
reception of the reflected impulse
is used for distance measurement
(time-of-flight)
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262
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Laser range finders (cont.)
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263
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Laser range finders (cont.)
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The wavelength lies in the range of infrared light (700nm –
1mm)
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It is significantly smaller compared to that of a sonar impulse
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The likelihood of symmetric reflection from a smooth surface is
a lot smaller
) fewer mirror reflections
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264
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
64-424 Intelligent Robotics
Laser range finders (cont.)
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A pulsed laser beam is emitted from the LRF
If the laser beam hits an object, it is reflected and registered by
the receiver within the LRF
The time span between emission and reception of the impulse
is directly proportional to the distance between the LRF and
object
Using the internal mirror, the pulsed laser beam is deflected and
the environment is scanned in a fan-shaped area ("laser radar")
Using the order of the received impulses, the shape of the
object can be calculated
The measured values are usually available for analysis at the
interface in real-time
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265
University of Hamburg
6.2 Distance - Sensors
Department of Informatics
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Laser range finders (cont.)
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Within its field (plane) of view the LRF emits a light impulse
(spot) with a typical resolution of 0.25 , 0.5 or 1
Due to the geometry of the beam and the diameters of the
single spots, they overlap on the measured object up to a
certain distance
Jianwei Zhang / Eugen Richter
266
University of Hamburg
Department of Informatics
6.2 Distance - Sensors
64-424 Intelligent Robotics
Laser range finders (cont.)
The range of the laser range finders depends on the remission
(reflectivity) of the object and the transmitting power
Material
Cardboard, black
Cardboard, grey
Wood (fir raw, dirty)
PVC, grey
Paper, white dull
Aluminum, black
Steel, stainless glossy
Steel, high-gloss
Reflectors
Jianwei Zhang / Eugen Richter
Remission
10 %
20 %
40 %
50 %
80 %
110...150 %
120...150 %
140...200 %
>2000 %
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Department of Informatics
6.3 Distance - Literature
64-424 Intelligent Robotics
Literature list
[1] Gregory Dudek and Michael Jenkin.
Computational Principles of Mobile Robotics, chapter 4.4, 4.5,
4.7, pages 90–100.
Cambridge University Press, 2. edition, 2010.
[2] Jacob Fraden.
Handbook of Modern Sensors: Physics, Designs, and
Applications, chapter 7, pages 279–326.
Springer New York, 4. edition, 2010.
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