64-424 intelligent robotics - uni-hamburg.de...i ultrasonic waves require a medium like air or water...

University of Hamburg Department of Informatics

6 Distance 64-424 Intelligent Robotics

Outline1. Introduction2. Fundamentals3. Rotation / Motion4. Force / Pressure5. Frame transformations6. Distance

Physical principlesSensors for distance measurementLiterature

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6 Distance 64-424 Intelligent Robotics

Distance measurement

I Very important aspect of mobile robotic systemsI Use of infrared or ultrasonic sensors and laser range finders

I A few of the underlying physical principles are:I Time-of-flightI Phase di�erenceI Triangulation

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6.1.1 Distance - Physical principles - Time-of-flight 64-424 Intelligent Robotics

Time-of-flight

1. Emit impulse2. Measure the time until reception of the echo/reflection

Distance =measured time ⇥ speed in the medium

2

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Time-of-flight (cont.)

I Advantage: Emitter and receiver lie on the same axisI Diameter of the beam is specified as

Diameter = 2 ⇥ Distance ⇥ tan (angle of beam)

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Time-of-flight (cont.)

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6.1.2 Distance - Physical principles - Phase di�erence 64-424 Intelligent Robotics

Phase di�erence

I Alternative to time-of-flight: Measurement of the phasedi�erence between emitted and reflected beam of a transducer(e.g. laser)

I The emitted beam with a wavelength of � is split up using abeam splitter

I The so called reference beam is measured at distance L by ameasurement unit

I The second beam runs to the object’s surface and back intothe measurement unit

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Phase di�erence (cont.)

The distance traveled by the reflected beam is specified asD0 = L + 2D

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I If D = 0, then D0 = L and both beams reach the measurementunit simultaneously

I If D is increased, the reflected beam needs to run a longerdistance, resulting in a phase di�erence ✓ compared to thereference beam

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The following equation applies:

D0 = L +✓

360�

For ✓ = 360� the phase di�erence is 0, therefore one cannotdistinguish between D0 = L and D0 = L + n�, n = 1, 2, . . .I To receive a distinct result, ✓ < 360� respectively 2D < � need

to applyI Since D0 = L + 2D, one gets

D =✓

360

✓�

2

◆

as distance, if the wavelength is known253




I Since the wavelength of a laser is very small (e.g. 632.8 nm fora Helium-Neon laser), this direct approach is not usable in thefield of robotics

I A simple solution for this problem is the modulation of thebeam with a much longer wave (c = f �)

I A modulating sine wave with a frequency of f = 10 MHz has awavelength of about 30 m

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6.1.3 Distance - Physical principles - Triangulation 64-424 Intelligent Robotics

Triangulation

I Determination of the distance with the help of two visual pointsI Distance between the visual points needs to be knownI Distance is determined through the angles to the object at

both visual pointsI Two visual points may result in a variety of ways:

I Movement of a single sensorI Special design of the active sensorI Several sensors

I An active sensor emits a signal and receives the reflectionI A passive sensor receives environmental signals (e.g. stereo

vision)

255



Triangulation (cont.)

Distance = l2 =l1 sin(↵)

sin(⇥+ ↵)

256




257




Example: Okada’s optical distance meter (1982)

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6.2 Distance - Sensors for distance measurement 64-424 Intelligent Robotics

Outline6. Distance

Physical principlesSensors for distance measurementLiterature

259


6.2.1 Distance - Sensors for distance measurement - Infrared sensors 64-424 Intelligent Robotics

Infrared sensors

I Infrared sensors are the most simple type of non-contact sensorsI Are commonly used for obstacle detection in roboticsI Infrared sensors emit an infrared light signal

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Infrared sensors (cont.)

I The infrared light signal is reflected by objects in the vicinityI To be able to distinguish the emitted signal from other infrared

sources in the vicinity (e.g. fluorescent lamps or sunlight), it isusually modulated with a low frequency (e.g. 100 Hz)

I Assuming that all objects are equal in color and surface, thedistance to the objects can be determined

I The intensity of the reflected light is inversely proportional tothe squared distance

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I Issue: In realistic environments, surfaces are not equal in colorI Colored surfaces reflect di�erent amounts of lightI Black surfaces are practically invisibleI In fact, IR-sensors can only be used for object detection, but

not for exact distance measurementI If an IR-signal is received by the sensor, one can assume, that

there’s an object in front of of the sensorI Note: A missing IR-signal does not necessarily mean there’s an

object in front of the sensorI IR-sensors are used for short distances (50 to 100 cm)

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6.2.2 Distance - Sensors for distance measurement - Ultrasonic sensors 64-424 Intelligent Robotics

Ultrasonic sensors

In biology there are two inspiring examples for the application ofultrasonic sensing technology1. Dolphin

I LocalizationI NavigationI CommunicationI Tracking (Hunting)

2. BatI LocalizationI Navigation (e.g. in complete darkness)I Tracking (Hunting)

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Ultrasonic sensors (cont.)

Bats use various di�erent sound navigation and ranging (sonar)techniquesI Fixed frequenciesI Varying frequencies

Although artificial ultrasonic sensors are capable of creatingfrequencies similar to those in the animal world, the animalcapabilities remain unmatched

265




I Ultrasonic waves are di�erentiated from electromagnetic wavesbased on the following physical properties:I MediumI Speed (in medium)I Wavelength

I Ultrasonic waves require a medium like air or waterI Ultrasonic speed in air amounts to 331.6 + 0.6 ⇥ �C m/sI Time-of-flight measurement is possible for short distancesI The wavelength of an ultrasonic sensor driven with a frequency

of 50 kHz amounts to 6.872 mm

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I Reflection of ultrasonic waves from smooth (and flat) surfacesis well-defined

I Very rough structures lead to di�use reflection of ultrasonicwaves

I Note: A round rod produces a di�use reflection

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Piezoelectric ultrasonic transducer

I To produce ultrasonic waves, the movement of a surface isrequired, leading to a compression or expansion of the medium

I One possibility to generate ultrasonic waves is the use of apiezoelectric transducer

I Applied voltage causes a bending of the piezoelectric elementI Piezoelectricity is reversible, therefore incoming ultrasonic

waves produce an output voltage

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Piezoelectric ultrasonic transducer (cont.)

I Typically, piezoelectric transducers are operated in theproximity of their resonance frequency fr (usually 32 kHz)

I That’s where the ceramic element reacts with the highestsensitivity

269




I The piezoelectric transducer operates as a transmitter(motor-mode) and a receiver (passive-mode)

I It transforms electricity into sonic waves and the other wayaround (both due to mechanical stress)

I As a receiver, the transducer operates very much like anelectrostatic microphone

I The piezoelectric component is usually a solid material such asa specific ceramic or crystal

I The opening angle of the ultrasonic signal emitted by thetransducer amounts to roughly 15�

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Example: Pioneer platform equipped with 16 ultrasonic (sonar) sensors

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Ultrasonic precision

The minimum distance dmin which can still be measured, isspecified as:

dmin =12vtImpulse

v : Speed of the wave in the corresponding mediumtImpulse : Duration of the emitted impulse in seconds

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Ultrasonic precision (cont.)

The maximum distance dmax which can still be measured, isspecified as:

dmax =12vtInterval

v : Speed of the wave in the corresponding mediumtInterval : Time span between the single impulses

275




The distance resolution dResolution of a sonar sensor is specified as:

dResolution =dmax

q

q: Quantization steps available for distance encodingdmax : Maximum range (distance) of the sensor

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I Measurements with sonar sensors are subject to severalinaccuracies

I The precise position of the object usually remains unknown dueto the cone-shape of the sensitivity area of the emitted impulse

I An object perceived at a distance of d may be located at anarbitrary position within the sonar cone on the arc at a distanceof d

I Mirror and total reflections cause flawed measurementsI 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

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I If several sonar sensors are used simultaneously, specificallyencrypted signals need to be used, because otherwise crosstalkmay occur

I Since the measurement depends on the temperature of themedium, a change in air temperature will introducemeasurement errors (e.g. a di�erence of 16�C will cause ameasurement error of 30cm over a distance of 10m)

I Though such an error has no influence on simplesensor-motor-behavior like obstacle avoidance, it may lead toimprecise area maps during map creation

278




Measuring principle

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Resolution280




Measurement error

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Invisible wall

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Invisible corner283




Corner error284



Applications of ultrasonic sensors

I Motion detectionI Level detectionI Expansion measurementI Sorting, SelectionI Approaching, positioning and object detection

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6.2.3 Distance - Sensors for distance measurement - Laser range finders 64-424 Intelligent Robotics

Laser range finders

I Laser range finders (LRF) measure thedistance, speed and acceleration ofrecognized objects

I Functional principle similar to that ofa sonar sensor

I Instead of a short sonic impulse, ashort light impulse is emitted fromthe laser range finder

I The time span between emission andreception of the reflected impulseis used for distance measurement(time-of-flight)

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Laser range finders (cont.)

I The wavelength lies in the range of infrared light (700nm –1mm)

I It is significantly smaller compared to that of a sonar impulseI The likelihood of symmetric reflection from a smooth surface is

a lot smaller) fewer mirror reflections

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LRF - Functional principle

I A pulsed laser beam is emitted from the LRFI If the laser beam hits an object, it is reflected and registered by

the receiver within the LRFI The time span between emission and reception of the impulse

is directly proportional to the distance between the LRF andobject

I Using the internal mirror, the pulsed laser beam is deflected andthe environment is scanned in a fan-shaped area ("laser radar")

I Using the order of the received impulses, the shape of theobject can be calculated

I The measured values are usually available for analysis at theinterface in real-time

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LRF - Functional principle (cont.)

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LRF - Functional principle (cont.)

I Within its field (plane) of view the LRF emits a light impulse(spot) with a typical resolution of 0.25�, 0.5� or 1�

I Due to the geometry of the beam and the diameters of thesingle spots, they overlap on the measured object up to acertain distance

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LRF - Remission

The range of the laser range finders depends on the remission(reflectivity) of the object and the transmitting power

Material RemissionCardboard, black 10 %Cardboard, grey 20 %Wood (fir raw, dirty) 40 %PVC, grey 50 %Paper, white dull 80 %Aluminum, black 110...150 %Steel, stainless glossy 120...150 %Steel, high-gloss 140...200 %Reflectors >2000 %

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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, andApplications, chapter 7.5, pages 314–316.Springer New York, 4. edition, 2010.

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