This document summarizes session 28 of an Artificial Intelligence course which covered classical planning approaches and planning graphs. It defines planning graphs as a way to approximate the complete search tree of all possible actions and results. Planning graphs work for propositional planning problems and are organized into levels with nodes representing fluents and applicable actions. The document provides details on how to construct a planning graph by propositionalizing actions, adding levels for states and actions, and adding links between and within levels to represent mutex relationships. The next session will cover the GRAPH-PLAN algorithm.

1. ARTIFICAL INTELLIGENCE
(R18 III(II Sem))
Department of computer science and
engineering (AI/ML)
Session 28
by
Asst.Prof.M.Gokilavani
VITS
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2. TEXTBOOK:
• Artificial Intelligence A modern Approach, Third
Edition, Stuart Russell and Peter Norvig, Pearson
Education.
REFERENCES:
• Artificial Intelligence, 3rd Edn, E. Rich and K.Knight
(TMH).
• Artificial Intelligence, 3rd Edn, Patrick Henny
Winston, Pearson Education.
• Artificial Intelligence, Shivani Goel, Pearson
Education.
• Artificial Intelligence and Expert Systems- Patterson,
Pearson Education.
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3. Topics covered in session 28
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Planning
Classical Planning: Definition of Classical Planning,
Algorithms for Planning with State-Space Search,
Planning Graphs, other Classical Planning
Approaches, Analysis of Planning approaches.
Planning and Acting in the Real World: Time,
Schedules, and Resources, Hierarchical Planning,
Planning and Acting in Nondeterministic Domains,
Multi agent Planning.

4. Planning graphs
• Graph Plan is an algorithm based on planning
graph
• Planning graphs are also used as a source of
heuristics (an estimate of how many steps it
takes to reach the goal)
• Planning graph is an approximation of a
complete tree of all possible actions and their
results Planning graphs work only for
propositional planning problems—ones with no
variables.
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7. Planning graphs
Planning graph is organized into levels.
• Level S0: initial state, consisting of nodes
representing each fluent that holds in S0.
• Level A0: each ground action that might be
applicable in S0 Then alternate Si and Ai.
• Si contains fluent which could hold at time i,
(may be both P and ¬P); literals may show up
too early but never too late.
• Ai contains actions which could have their
preconditions satisfied at i.
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8. Mutex
• A mutex between two actions indicates that it
is impossible to perform these actions in
parallel.
• A mutex between two literals indicates that it
is impossible to have these both literals true at
this stage.
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9. Example
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Department of CSE (AI/ML)

10. Constructing a planning graph
• All action schemas must be propositionalized
• Generate all possible grounded actions so no
variables are left.
• Start with S0 = all initially true fluents
• Construct Ai = all actions whose preconditions are
satisfied by Si
• Construct Si = all fluents made true by the effects
of the actions in Ai-1
• All levels in Ai have the NO-OP action which
passes all true fluents in Si to Si+1.
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Department of CSE (AI/ML)

11. Add links:
• Between levels
– From fluents in Si to preconditions of actions in Ai
– From effects of actions in Ai to fluents in Si+1
• Within Levels (mutual exclusion)
– Action Mutex Link: Two actions compete for
resources
– State Mutex Link: Two fluents that cannot both be
true at the same time
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Department of CSE (AI/ML)

12. Rules for Constructing Mutex Links
Action Mutex:
• Inconsistent Effects: One action negates the effect of the
other (e.g., Eat(Cake) and Bake(Cake) )
• Interference: One of the effects of one action is the negation
of a precondition of the other (e.g., Eat(Cake) and the
persistence of Have(Cake))
• Competing Needs: One of the preconditions of one action is
mutually exclusive with a precondition of the other
• Depends on State Mutex links in previous level
State Mutex:
• One is the negation of the other.
• All pairs of actions that could make both true have Act on
mutex links between them.
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Department of CSE (AI/ML)

13. Example
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14. Topics to be covered in next session 29
• GRAPH-PLAN Algorithm
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Thank you!!!