Dr. John (Jizhong) Xiao

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Course Summary
Introduction to ROBOTICS

• Dr. John (Jizhong) Xiao
• Department of Electrical Engineering
• City College of New York
• jxiao_at_ccny.cuny.edu

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Mobile Robot
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Mobot System Overview
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Mobile Robot Locomotion
Locomotion the process of causing a robot to move

• Tricycle

• Differential Drive

Swedish Wheel

• Synchronous Drive

• Omni-directional

• Ackerman Steering

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Differential Drive
Property At each time instant, the left and
right wheels must follow a trajectory that moves
around the ICC at the same angular rate ?, i.e.,

• Kinematic equation

• Nonholonomic Constraint

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Differential Drive

• Basic Motion Control

R Radius of rotation

• Straight motion
• R Infinity VR VL

• Rotational motion
• R 0 VR -VL

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Tricycle

• Steering and power are provided through the front
  wheel
• control variables
• angular velocity of steering wheel ws(t)
• steering direction a(t)

d distance from the front wheel to the rear axle
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Tricycle
Kinematics model in the world frame ---Posture
kinematics model
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Synchronous Drive

• All the wheels turn in unison
• All wheels point in the same direction and turn
  at the same rate
• Two independent motors, one rolls all wheels
  forward, one rotate them for turning
• Control variables (independent)
• v(t), ?(t)

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Ackerman Steering (Car Drive)

• The Ackerman Steering equation

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Car-like Robot
Driving type Rear wheel drive, front wheel
steering
Rear wheel drive car model
forward velocity of the rear wheels
angular velocity of the steering wheels
non-holonomic constraint
l length between the front and rear wheels
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Robot Sensing

• Collect information about the world
• Sensor - an electrical/mechanical/chemical device
  that maps an environmental attribute to a
  quantitative measurement
• Each sensor is based on a transduction principle
  - conversion of energy from one form to another
• Extend ranges and modalities of Human Sensing

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Gas Sensor
Gyro
Accelerometer
Metal Detector
Pendulum Resistive Tilt Sensors
Piezo Bend Sensor
Gieger-Muller Radiation Sensor
Pyroelectric Detector
UV Detector
Resistive Bend Sensors
CDS Cell Resistive Light Sensor
Digital Infrared Ranging
Pressure Switch
Miniature Polaroid Sensor
Limit Switch
Touch Switch
Mechanical Tilt Sensors
IR Sensor w/lens
IR Pin Diode
Thyristor
Magnetic Sensor
Polaroid Sensor Board
Hall Effect Magnetic Field Sensors
Magnetic Reed Switch
IR Reflection Sensor
IR Amplifier Sensor
IRDA Transceiver
IR Modulator Receiver
Radio Shack Remote Receiver
Solar Cell
Lite-On IR Remote Receiver
Compass
Compass
Piezo Ultrasonic Transducers
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Sensors Used in Robot

• Resistive sensors
• bend sensors, potentiometer, resistive
  photocells, ...
• Tactile sensors contact switch, bumpers
• Infrared sensors
• Reflective, proximity, distance sensors
• Ultrasonic Distance Sensor
• Motor Encoder
• Inertial Sensors (measure the second derivatives
  of position)
• Accelerometer, Gyroscopes,
• Orientation Sensors Compass, Inclinometer
• Laser range sensors
• Vision, GPS,

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Motion Planning
Path Planning Find a path connecting an initial
configuration to goal configuration without
collision with obstacles

• Configuration Space
• Motion Planning Methods
• Roadmap Approaches
• Cell Decomposition
• Potential Fields
• Bug Algorithms

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Motion Planning

• Motion Planning Methodololgies
• Roadmap
• Cell Decomposition
• Potential Field
• Roadmap
• From Cfree a graph is defined (Roadmap)
• Ways to obtain the Roadmap
• Visibility graph
• Voronoi diagram
• Cell Decomposition
• The robot free space (Cfree) is decomposed
  into simple regions (cells)
• The path in between two poses of a cell can
  be easily generated
• Potential Field
• The robot is treated as a particle acting
  under the influence of a potential field U,
• where
• the attraction to the goal is modeled by
  an additive field
• obstacles are avoided by acting with a
  repulsive force that yields a negative field

Global methods
Local methods
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Full-knowledge motion planning
Cell decompositions
Roadmaps
visibility graph
exact free space represented via convex polygons
voronoi diagram
approximate free space represented via a quadtree
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Potential field Method

• Usually assumes some knowledge at the global
  level

The goal is known the obstacles sensed
Each contributes forces, and the robot follows
the resulting gradient.
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Mobile Robot Mapping
Introduction to ROBOTICS

• Dr. John (Jizhong) Xiao
• Department of Electrical Engineering
• City College of New York
• jxiao_at_ccny.cuny.edu

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Sonar sensing
The sponge
sonar timeline
0
.5s
75ms
the transducer goes into receiving mode and
awaits a signal...
a chirp is emitted into the environment
typically when reverberations from the initial
chirp have stopped
after a short time, the signal will be too weak
to be detected
Sonar (sound navigation and ranging) range
sensing using acoustic (i.e., sound) signal
Blanking time
Attenuation
Why is sonar sensing limited to between 12 in.
and 25 feet ?
Polaroid sonar emitter/receivers
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Using sonar to create maps
What should we conclude if this sonar reads 10
feet?
there isnt something here
there is something somewhere around here
10 feet
Local Map
unoccupied
no information
occupied
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Using sonar to create maps
What should we conclude if this sonar reads 10
feet...
10 feet
10 feet
and how do we add the information that the next
sonar reading (as the robot moves) reads 10 feet,
too?
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What is it a map of ?
Several answers to this question have been tried
cell (x,y) is unoccupied
cell (x,y) is occupied
oxy
oxy
Its a map of occupied cells. Its a map of
probabilities p( o S1..i ) p( o
S1..i )
pre 83
The certainty that a cell is occupied, given the
sensor readings S1, S2, , Si
83 - 88
The certainty that a cell is unoccupied, given
the sensor readings S1, S2, , Si
The odds of an event are expressed relative to
the complement of that event.
Its a map of odds.
evidence log2(odds)
probabilities
p( o S1..i )
odds( o S1..i )
The odds that a cell is occupied, given the
sensor readings S1, S2, , Si
p( o S1..i )
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Combining evidence
So, how do we combine evidence to create a map?
What we want --
the new value of a cell in the map after the
sonar reading S2
odds( o S2 ? S1)
What we know --
the old value of a cell in the map (before sonar
reading S2)
odds( o S1)
the probabilities that a certain obstacle causes
the sonar reading Si
p( Si o ) p( Si o )
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Combining evidence
p( o S2 ? S1 )
defn of odds
odds( o S2 ? S1)
p( o S2 ? S1 )
p( S2 ? S1 o ) p(o)
.
Bayes rule ()
p( S2 ? S1 o ) p(o)
p( S2 o ) p( S1 o ) p(o)
conditional independence of S1 and S2
.
p( S2 o ) p( S1 o ) p(o)
p( S2 o ) p( o S1 )
.
Bayes rule ()
p( S2 o ) p( o S1 )
previous odds
precomputed values
the sensor model
Update step multiplying the previous odds by a
precomputed weight.
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A Taste of Localization Problem
Introduction to ROBOTICS

• Dr. John (Jizhong) Xiao
• Department of Electrical Engineering
• City College of New York
• jxiao_at_ccny.cuny.edu

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Bayes Formula
If y is a new sensor reading
Prior probability distribution
?
Posterior probability distribution
?
Generative model, characteristics of the sensor
?
?
Does not depend on x
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Bayes Rule with Background Knowledge
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Markov assumption(or static world assumption)
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Markov Localization

• Measurement

• Action

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Measurement Update Phase
a
b
c
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Measurement Update Phase
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Recursive Bayesian Updating
Markov assumption zn is independent of
z1,...,zn-1 if we know x.
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Action Prediction Phase

• The robot turns its wheels to move
• The robot uses its manipulator to grasp an object
• Plants grow over time
• Actions are never carried out with absolute
  certainty.
• In contrast to measurements, actions generally
  increase the uncertainty.

• How can we incorporate such actions?

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Modeling Actions

• To incorporate the outcome of an action u into
  the current belief, we use the conditional pdf
• P(xu,x)
• This term specifies the pdf that executing u
  changes the state from x to x.

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Integrating the Outcome of Actions
Continuous case Discrete case
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Summary

• Measurement

• Action

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Bayes Filters Framework

• Given
• Stream of observations z and action data u
• Sensor model P(zx).
• Action model P(xu,x).
• Prior probability of the system state P(x).
• Wanted
• Estimate of the state X of a dynamical system.
• The posterior of the state is also called Belief

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Markov Assumption
Measurement probability
?
State transition probability
?

• Markov Assumption
• past and future data are independent if one knows
  the current state

• Underlying Assumptions
• Static world, Independent noise
• Perfect model, no approximation errors

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Bayes Filters
z observation u action x state
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Bayes Filters are Family

• Bayes rule allows us to compute probabilities
  that are hard to assess otherwise.
• Under the Markov assumption, recursive Bayesian
  updating can be used to efficiently combine
  evidence.
• Bayes filters are a probabilistic tool for
  estimating the state of dynamic systems.

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Thank you!
Next Thur (Dec. 8) Final Exam Time
645pm-845pm, Dec. 8, 2011, Coverage Mobile
Robot Close-book with 1 page cheat sheet, but Do
Not Cheat