Introduction to RoboticsPerception I

CSCI 4830/7000February 7, 2010

Nikolaus Correll

Review: Kinematics and Control

• Concepts– Forward Kinematics– “Odometry”– Feed-back Control– Inverse Kinematics

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

More on robot kinematics (arms)

John CraigIntroduction to Robotics Mark Spong, Seth Hutchinson and M.Vidyasagar

Robot Modeling and Control

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

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

Today

• Perception: Basis for reasoning about the world

• Understand how a sensor works before using it

• Case studies

iRobot Roomba

• 4 Bumpers• 2 Floor sensors• 1 infrared distance

(side)• Infrared• Wheel encoders

PrairieDog

• Roomba• 5.6m, 240 degrees laser

scanner• Indoor localization

system• Camera• Microphone• 5 Position encoders

(arm)

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?

PR2 (WillowGarage)

Laser Range Scanner

• Measures phase-shift of reflected signal

• Example: f=5MHz -> wavelength 60m

Examples

2 D 3D (PR2 sweep)(after classification)

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

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

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

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

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

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

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

Homework

• Read section 4.1.7 (pages 117 – 145)• Questionnaire on CU Learn