Download - Lecture 04
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Introduction to RoboticsSensors
CSCI 4830/7000September 20, 2010
Nikolaus Correll
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Review: Kinematics and Control
• Concepts– Forward Kinematics– “Odometry”– Feed-back Control– Inverse Kinematics
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Forward Kinematics
• How does the robot move in world space given its actuator speed and geometry?
• “Odometry”: forward kinematics for mobile platform
• Example: from exercise 3
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Proportional Control
N.B.: zero error neq correct position!
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More on robot kinematics (arms)
John CraigIntroduction to Robotics Mark Spong, Seth Hutchinson and M.Vidyasagar
Robot Modeling and Control
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Inverse Kinematics
• How do we need to control the actuators to reach a certain position?
• Inversion of forward kinematics• Examples: Differential wheel drive (Exercise 3)
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Feedback control
• Use error between reference and actual state to calculate next control input
• Change in speed proportional to error• Error zero -> speed zero• Problem: find stable controllers• Example: from exercise
K. OgataModern Control Engineering
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Today
• Perception: Basis for reasoning about the world
• Understand how a sensor works before using it
• Case studies
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iRobot Roomba
• 4 Bumpers• 2 Floor sensors• 1 infrared distance
(side)• Infrared• Wheel encoders
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PrairieDog
• Roomba• 5.6m, 240 degrees laser
scanner• Indoor localization
system• Camera• Microphone• 5 Position encoders
(arm)
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Nao
• 2 VGA cameras• 4 Microphones• 2-axis gyroscope• 3-axis accelerometer• 2 bumpers (feet)• Tactile sensors
(hands + feets)• Hall-effect encoders• 2 Sonar• 2 Infrared
Proprioceptive or Exteroceptive?
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PR2 (WillowGarage)
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Laser Range Scanner
• Measures phase-shift of reflected signal
• Example: f=5MHz -> wavelength 60m
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Examples
2 D 3D (PR2 sweep)(after classification)
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Sensor performance
• Dynamic range: lowest and highest reading• Resolution: minimum difference between
values• Linearity: variation of output as function of
input• Bandwidth: speed with which
measurements are delivered• Sensitivity: variation of output change as
function of input change• Cross-Sensitivity: sensitivity to
environment• Accuracy: difference between measured
and true value• Precision: reproducibility of results
Hokuyo URG
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Relation between sensor physics and performance (solutions)
• Dynamic range: – Range: limited by power of light and modulated frequency, smallest wave-length difference measurable– Angle: limited by physical setup / trade-off between bandwidth and angular resolution
• Resolution:– Range: Precision of phase-shift measurement– Angle: limited by bandwidth / encoder
• Linearity:– Range: phase shift is linear -> signal is linear, but: weak reception makes determination of phase harder– Angle: depends on motor implementation
• Bandwidth– Range: speed of light, calculating phase shift– Angle: motor speed
• Sensitivity:– Range: Doppler effect -> not relevant in robotics, Confidence in the range (phase/time estimate) is inversely proportional to the
square of the received signal amplitude– Angle: n.a.
• Cross-Sensitivity:– Range: Glass / reflection properties, 785nm light
• Accuracy:– Range: Precision of phase-shift measurement, strength of reflected light– Angle: motor quality
• Precision: range / variance
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Infra-red distance sensors
• Principle: measure amount of reflected light
• The closer you get, the more light gets reflected
• Digitized with analog-digital converter
Sharp IR Distance Sensor GP2Y0A02YK20-150cm
Miniature IR transceiver0-3cm
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Sensor performance
• Dynamic range: lowest and highest reading
• Resolution: minimum difference between values
• Linearity: variation of output as function of input
• Bandwidth: speed with which measurements are delivered
• Sensitivity: variation of output change as function of input change
• Cross-Sensitivity: sensitivity to environment
• Accuracy: difference between measured and true value
• Precision: reproducibility of results
Sharp IR Distance Sensor
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Relation between sensor physics and performance (solutions)
• Dynamic range: limited by power of light• Resolution: limited by ADC, e.g. 10bit -> 1024 steps• Linearity: highly non-linear (intensity decays
quadratically)• Bandwidth: limited by ADC bandwidth (sample&hold)• Sensitivity: varies over range due to resolution• Cross-Sensitivity: sun-light, surface properties• Accuracy: limited by ADC, varies over range• Precision: varies over range
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Infra-red distance sensors in Webots (Exercise 1)
• Color of the bounding object affects sensor
• Non-linear relation between distance and signal strength
• Distance-dependent resolution and noise
Software linearization
Noise
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Exercise
• Design a robot that can– Vacuum a room– Mow a lawn– Collect golf-balls on a range– Collect tennis balls on a court
• Address– Sensors– Algorithm– Mechanism
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Scratchboard
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Homework
• Read section 4.1.7 (pages 117 – 145)• Questionnaire on CU Learn
• Midterm: October 11 (during class)