Download CS 415 – A.I.

CS 415 – A.I.
Slide Set 2
Outline
• Last Time
– AI, an attempted definition
– Historical foundations
• Today
– Overview of application areas
– An introduction to representation and search
First Material Review
• Accurate Relative Localization
– See website for link to pdf
• Read by class on Tuesday
– 1 page summary report
• Full run-down of what the paper is about
• Any thoughts you had about the paper
Turing Test
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Attempts to give an objective notion of intelligence
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Abstracts out unanswerable questions
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Humanity is the best and only known standard
Avoids debate about “true” nature of intelligence
What is consciousness? Is the computer conscious?
Eliminates “bias” against machines
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Interrogator can’t see any evidence except text
Abstracts out specific intelligent processes
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No spinning disks, no artificial sounding voices, etc.
Lady Lovelace’s Objection
• Ada Lovelace
– After whom the programming language
Ada is named
• Computers can only do as they are
instructed, thus they are incapable
of original thought
– What is originality, but a rehashing of
the old
• Certainly, computers can do this
– Genetic Algorithms, etc.
– What is the fundamental difference between humans and
computers in this regard
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• What is the seat of human originality
• Humans only know what they’ve been taught – or – “ghost in the
machine”
Programs do not have to be strictly sequential
– Instead, AI programs can be built as rules that can be applied when it is
deemed by the computer to be necessary
Argument from Informality of Behavior
• “No set of instructions can prepare a computer for
behaving rationally in any possible previously
unknown situation.”
• Wrong
– Again, computers do not have to act sequentially to
perform tasks
– Nor, in fact, do computers have to be strictly discrete.
– Also, how flexible are humans to new environments and so
how flexible do computers need to be?
Other Theories and Approaches
• So far, only talked about rationalist theories
– Define intelligence according to mathematics and logical
consistency
• But, post-modernism is diametrically opposed to this
viewpoint
– Connectionist Theory
• Intelligence doesn’t have to be rational
– Humans don’t always act rationally
• Instead, lets model the biology of the brain
– Neural networks
– Genetic algorithms
» Knowledge and solutions morph unpredictably and are tested
against previous solutions
Emergent Knowledge
• Bakeries in New York
– Provide almost exactly the correct amount of bread to New
York
• no rationalizing on good information
• Stock Market
– Prices are set, but investors have little knowledge
• Universities
– Answers to hard problems are solved because people work
and interact, even seperately
• Web 2.0
– Wikipedia
– Data Mining
Agents
• How does the knowledge emerge?
– Agents that interact with other agents in simple
ways
• Each agent is autonomous, and each has a task that
isn’t based upon the system as a whole
• Each agent is sensitive to its own environment
• Agents form a “society”
• The society is structured in some way
– Each agent, working in its own sphere in the
society allows the society to produce emergent
knowledge
Overview of AI Application Areas
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2 Major Parts to AI
1. Knowledge Representation
2. Search
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Game Playing
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Not just for fun
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Well-structured rules, “easily” represented states
Show need for heuristics
Automated Theorem Proving
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Given any set of known facts and a possibly true
statement, is the statement in question implied?
PROLOG (Chapter 15)
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Expert Systems
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A system that focuses on “domain-specific knowledge”
2 parts
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Theoretical understanding of the problem
Set of heuristics that can be applied in certain situations
Expert systems are “loaded” with these two parts
Problems
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Difficult to capture “deep” knowledge in the field
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Not necessarily robust of flexible
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Sometimes the expert just knows what he/she knows
Can’t cross-apply knowledge from different fields like humans can
Can’t present deep explanations
Difficulty in verification
Aren’t flexible in the sense of being able to learn anything new
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Specialized systems only
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Understanding Natural Language
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Make my computer do what I mean, not strictly
what I say
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Programmer’s dream
But, there isn’t a consistent way to parse
language
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Meaning is often, if not always, a matter of context
and domain
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Modeling Human Performance
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Make computers act more and more like humans
Planning and Robotics
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Start with a robot that can perform certain atomic tasks
Now, build it so that it can plan and act in its
environment without previous knowledge of the
environment
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Hierarchical problem decomposition
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How does a robot enter a room and find an object
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Possible Step?
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Each step can be rationally decomposed
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Languages and Environments for AI
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Object-Oriented Programming
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LISP and PROLOG
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C++ and Java
Represent Knowledge Representation from the start
Support modular development and better ability for handling
complexity of heuristic search
Machine Learning
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Computers asked a question today, will, when asked tomorrow, take
the same steps to determine the same answer to the same question
Humans don’t have to do this
Need to have computers that remember results in meaningful ways
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Text-completion
Here are some RNA strands that are known to exist in nature, can this
one exist in nature?
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Neural Nets and Genetic Algorithms
 Neural Nets
 Based on biological nueron networks
 See pg 29
 Genetic Algorithms
 Solutions “evolve”
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AI and Philosophy
 Most of the theoretical questions we asked
earlier are also asked by philosophers
What it all means
• We cannot solve the unanswered questions that
have been asked for centuries
– Not in this class anyway
• However, we can look at the foundational
approaches that have gone in to the basics of AI and
Robotics
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Predicate Calculus
Search Methods
Knowledge Representation
Machine Learning
Reasoning
PROLOG
LISP
Representation and Search
• Representational System – function is to capture the
essential features of a problem domain and make the
information accessible
– Abstraction – being able to efficiently store the features of
the problem domain
• Note: the features will undoubtedly change
– Balance trade-offs between efficiency and expressiveness
Representation in Mobile Robotics
• Kinematics – basic study of how mechanisms
move
– Basic goal: given all the angles and movement,
what is you point in space at this time
– 2 Frames of Reference
• Global Frame of Reference
– Robot gets through layers of representations (maps, etc)
• Local Frame of Reference
– Don't know what the world looks like
– Remember how far I've traveled
• Given global frame of reference
– If the robot moves how do we keep up with where
we are in space
– Kinematic Equations
• A system of equations that determines our x,y position
and our rotation (angle Θ) after k control steps
• See second page of ARL paper
– Synchro Drive Robots
– Also exist for Differential Drive Robots
• Store as a matrix system
– Perform matrix operations to transform and solve
• Regardless, everyone should work in the same
frame of reference
– Homogenous Transform
• Do matrix operations to transform from one frame of
reference to another
How far has the robot moved?
• Apply power, robot moves, right?
– Power does not relate well to speed
• So, other options:
– Check the particular motor velocity (left/right)
– Some visual cue for how fast you're going
– Encode inside motor
• How many 'ticks' has the motor made as it rotated
• Use PID, proportional integral derivative
– Integral and derivative → smooths error/gives result
Mapping
• How do we abstract a map?
• Efficiency vs Expressiveness
– What are the tradeoffs
• Dealing with Errors
– Examples:
• Synchro Drive
• Differential Drive
Accurate Relative Localization Using
Odometry
• Drawing Maps
– Depends on relative localization
• Can't escape the use of odometry
– Have error built in
• Overcoming Error
1.Odometry error modeling
2.Error Parameters estimation
3.Covariance matrix estimation
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1 and 2 – systematic errors
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3 – non-systematic errors
Systematic Errors
• Define these for the robot based on the
appropriate error model for the drive type
– Differential Drive → given in the literature
• Borenstein paper
– Synchro Drive → given in this paper
• Major source: wheel misalignment
– Major source of distortion for theta (angular velocity): drag AND
rotate the robot
– Provable by geometric analysis of kinematic equation
Non-systematic Errors
• PC (POSTECH CMU)-method
– 1st get the error model
– 2nd use PC-method to generate error parameters
and covariance matrix
• Based on sensor-based navigation through the
Generalized Voronoi Graph (GVG)
– Voronoi extensively covered in literature
– Creates a well-understood path based on obstacles
– Robot drives it forward (FOP) and backward (BOP)
• 2 diff odom paths, same real-world path
• Give an initial CFOP and CBOP based on error
model and initial error parameters guess
• Then, find the error parameters that minimize
error between CFOP and CBOP
– Steepest descent method
• Now, build an error covariance matrix based on
3 assumptions and worst-case analysis
A little error, uncorrected, tends to
flourish
• See Fig 8
– Note: one possible approach, reset the odometry
before the error gets too bad
• See Fig 9
• See Fig 12
• See Fig 13
Representation/Search Considerations
• Real-time Systems
– Is it schedulable
• Has a lot to do with efficiency/expressiveness
– How are we storing things (fast to slow)
• I/O
• Memory
• Registers
• Cache
– What Language are we using (fast to slow)
• Assembly
• C
• C++
• Java
• Python
Other Forms of Representation
• Example: A robot might be stacking elements from a
table on top of one another
• Might give the following predicates (state facts about
our domain):
clear(c)
clear(a)
ontable(a)
ontable(b)
on(c,b)
cube(b)
cube(a)
pyramid(c)
• Might also define a set of rules
which relate to these predicates
For all X if there does not exist
any Y where on(Y,X) than this
implies clear(X)
Using Predicate Calculus
• Predicates can also be more advanced
hassize(bluebird,small)
hascovering(bird,feathers)
hascolor(bluebird,blue)
hasproperty(bird,flies)
isa(bluebird,bird)
isa(bird,vertebrae)
• Predicates are not functions in the sense of higher-level
languages, nor should you think of them in terms of
programming
– There is no set of predicate functions
– Any predicate can be defined
• They are strictly useful for representing knowledge in conjunction with
rules
Search
• What are the possible moves?
– The computer knows because of the knowledge
representation
• All moves are either stored or can be inferred from the
stored knowledge and set of rules.
• What is the best move?
– This is the domain of search
– Example: Tic Tac Toe
Limitations of State-Space Search
• Not sufficient to automate intelligent behavior
– How big is the state-space for chess?
• 10120 different board configurations
– Larger than # molecules in the universe
– Larger than the number of seconds since the “big bang”
– How big is the state-space for human language?
• Untold possibilities
• State-Space Representation and Search is an
important tool only
Exhaustive Search vs. Heuristic Search
• Exhaustive Search
– Brute force attempting all possible combinations
till an optimized solution is found
• Heuristic Search
– Humans don’t use exhaustive search
– Instead, we use rules of thumb based on what
seems most “promising”
– Heuristic – a strategy for selectively searching a
state space ---- Examples?