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Robotics & Future Technology

Robotics & Future Technology

Future of Intelligent SystemsFuture of Intelligent Systems

Ray Kurzweil futurist A Long Bet Robot Soccer

BBC News - What happened to the Robotic Age?

Robotic Dance?

Ray Kurzweil futurist A Long Bet Robot Soccer

BBC News - What happened to the Robotic Age?

Robotic Dance?

REVIEW of some important

concepts to remember…

REVIEW of some important

concepts to remember…

CHAPTER 5 CHAPTER 5

Incremental Problem Formulation

(The N-Queens Problem)

Incremental Problem Formulation

(The N-Queens Problem)

Constraint Satisfaction Constraint Satisfaction A constraint satisfaction problem (CSP) is a problem composed of

variables and constraints. The objective is to assign values to variable in such a way that all of the constraints are satisfied.

A CSP can be more formally viewed as a triple <D,X,C> where:

D represents a set of n domains X represents a set of n variables, each variable xi takes it value from Di C represents a set of constraints.

A constraint satisfaction problem (CSP) is a problem composed of variables and constraints. The objective is to assign values to variable in such a way that all of the constraints are satisfied.

A CSP can be more formally viewed as a triple <D,X,C> where:

D represents a set of n domains X represents a set of n variables, each variable xi takes it value from Di C represents a set of constraints.

Two types of CSPsTwo types of CSPs

Finite domain CSPs Queens, Domains, Boolean

Infinite Domain CSPs If Job1 takes 5 days, then Job3 will start Job1 +5 < Job3

Finite domain CSPs Queens, Domains, Boolean

Infinite Domain CSPs If Job1 takes 5 days, then Job3 will start Job1 +5 < Job3

thrashingthrashingWasteful” backtracking is known asWasteful” backtracking is known as

Variable & Value OrderingVariable & Value Ordering

Variable order selection seldom results in the most efficient search

One efficient strategy Minimum Remaining Value (MRV) which

chooses the value with the fewest legal values

A.K.A “Most Constrained Value” A.K.A “Fail-First” Heuristic because it is the

most likely to cause failure first

Variable order selection seldom results in the most efficient search

One efficient strategy Minimum Remaining Value (MRV) which

chooses the value with the fewest legal values

A.K.A “Most Constrained Value” A.K.A “Fail-First” Heuristic because it is the

most likely to cause failure first

Propagating through constraintsPropagating through constraints

When every variable X is assigned, the forward checking process looks at each unassigned variable Y AND Deletes from Y’s domain any value that is inconsistent with the value chosen for X.

When every variable X is assigned, the forward checking process looks at each unassigned variable Y AND Deletes from Y’s domain any value that is inconsistent with the value chosen for X.

Forward Checking is a better use of constraints

Forward Checking is a better use of constraints

Think of Forward Checking as a way to incrementally compute the info needed for MRV to do its job

Think of Forward Checking as a way to incrementally compute the info needed for MRV to do its job

Arc ConsistencyArc Consistency nother backtrack-based algorithm that is even

more efficient is called the maintaining arc consistency (MAC) algorithm.

Arc Consistency provides fast method of constraint propagation stronger than forward checking.

Arc Consistency can be provided as preprocessing step (just as forward checking can be used to preprocess).

nother backtrack-based algorithm that is even more efficient is called the maintaining arc consistency (MAC) algorithm.

Arc Consistency provides fast method of constraint propagation stronger than forward checking.

Arc Consistency can be provided as preprocessing step (just as forward checking can be used to preprocess).

MAC Algorithm p146MAC Algorithm p146

Rather than just revising each domain corresponding with the value of each instantiated variable MAC makes the network arc-consistent with respect to the instantiated variables (all arcs must be consistent).

MAC is applied repeatedly until no more inconsistencies remain.

Node Consistency 1- consistency means that each individual variable by itself is

consistent (node consistency) 2- consistency is arc consistency

3- consistency means that any pair of adjacent variables can always be extended to a third neighboring variable (i.e. path consistency or AC-3)

AC-3 uses a queue to keep track of nodes that need to be checked for inconsistency

Rather than just revising each domain corresponding with the value of each instantiated variable MAC makes the network arc-consistent with respect to the instantiated variables (all arcs must be consistent).

MAC is applied repeatedly until no more inconsistencies remain.

Node Consistency 1- consistency means that each individual variable by itself is

consistent (node consistency) 2- consistency is arc consistency

3- consistency means that any pair of adjacent variables can always be extended to a third neighboring variable (i.e. path consistency or AC-3)

AC-3 uses a queue to keep track of nodes that need to be checked for inconsistency

Intelligent backtracking: looking backward

Intelligent backtracking: looking backward

Chronological backtracking: a policy for when a branch of the search fails by backing up to the preceding variable and try a different value for it

Chronological uses the more recent decision point to revisit

Chronological backtracking: a policy for when a branch of the search fails by backing up to the preceding variable and try a different value for it

Chronological uses the more recent decision point to revisit

Things that cause a failureThings that cause a failure

The conflict set

Backjumping backtracks to the most recent variable in the conflict set

The conflict set

Backjumping backtracks to the most recent variable in the conflict set