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Toimenpiteiden suunnittelu(Planning, 11.1-3)
Eero HyvönenHelsingin yliopisto
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Classical Planning Problem• Consider fully observable, deterministic, finite, static, and
discrete environments• Determine action sequences: initial state -> goal
– Search algorithms can be used• Dealing with large real world problems
– Ignoring irrelevant actions• Must be goal driven
– Finding good heuristics• By the agent itself?
– Exploiting problem structure• Planning at different levels of abstraction• Decomposable plans would be nice• Partial order plans can often be determined
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Language for Planning ProblemsClassical STRIPS language
• Representation of states– Conjunction of positive literals (ground, function free)
• At(Plane1, Helsinki) & At(Plane2, NewYrok) & …– Closed World Assumption made
• Representation of goals– As above: set of positive literals– A state s statisfies a goal g if g subsetOf s
• Representation of actions– Action schema:
• Actions are rules on states: Preconditions -> Effects• Action(Fly(p,from,to)),
PRECOND: At(p,from) & Plane(p) & Airport(from) & Airport(to)EFFECT: ¬At(p,from) & At(p,to)
• Effect can be specified also in terms of ”addlist” and ”delete list”– STRIPS assumption (cf. frame problem):
• Every literal not mentioned in the action remains unchanged• Solution = sequence of actions to the goal (possibly partial ordering)
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Extensions to STRIPS• Action Description Language ADL
– Also negative literals in states– Open world assumption– Quantified variables in goals– Disjunctions in goals– Equality predicate allowed– Variables can have types (e.g. p: plane)– …
• Planning Domain Definition Language (PDDL)– Contains e.g. STRIPS and ADL– For sharing problems
• Missing features– Ramification problem (side effects)– Qualification problem (exceptional effects causing failure)
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Example: Cargo Transportation
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Planning forward (progression) & backward (regression)
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• Progression: forward planning– Problem of irrelevant actions
• Regression: backward planning– Focuses in relevant actions– Predecessor must include preconditions– Subgoal not present in the predecessor
• Avoid loops– Actions not undo desired literals
• e.g. Load(C2, P1) negates At(C2,B)
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Heuristics
• Using relaxed problems -> admissibleheuristics– E.g. ignore preconditions– E.g. remove negative effects
• Assume independent subproblems– Can be optimistic (admissible)
• Negative interactions between subgoals– An achieved goal deleted by another subproblem
– Can be pessimistic (inadmissible)• Redundant work in subproblems
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Partial-Order Planning• Problems of forward/backward search: total order plans
– Strictly linear action sequences– Cannot exploit problem decomposition
• Working on several subgoals• Combining subplans together
• Least commitment strategy– Delaying unnecessary choices during search– Generally useful principle in AI!
• Partial planner– Can place two actions in a plan without specifying their mutual
ordering– -> multiple plan linearizations– Search in the space of partial plans, not in the actual state space
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Components of a Plan• A set of actions that make up the plan
– Empty plan: • Start: Preconditions={}; Effect=initial state• Finish: Preconditions=goal state; Effect={}
• A set of ordering constraints– Partial orderings: A < B– A < B and B < A would be a contradiction
• A set of causal links– A →p B, ”A achieves p for B”
• p is the effect of action A and a precondition of action B
• A set P of open preconditions– Planner tries to reduce P to {} without in introducing
contradictions
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Example: Putting Shoes On• Goal(RightShoeOn & LeftShoeOn)• Init()• Actions
– Action(RightSock, Effect: RightSockOn)– Action(LeftSock, Effect: LeftSockOn)– Action(RightShoe, Precond: RightSockOn, Effect: RightShoeOn)– Action(LeftShoe, Precond: LeftSockOn, Effect: LeftShoeOn)
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A Partial-order Plan
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The Components• Actions: {RightSock, RightShoe,
LeftSock, LeftShoe, Start, Finish}
Orderings:{RightSock<RightShoe,LeftSock<LeftShoe}
Links:{RightSock→RightSockOnRightShoe,LeftSock→LeftSockOnLeftShoe,RightShoe→RightShoeOnFinish, LeftShoe→LeftShoeOnFinish}
Open preconditions:{}
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• Consistent plan– No cycles in ordering constraints– No conflicts with the clausal links
• Solution = – consistent plan– open proconditions={}
• Plan execution– Any total ordering can be selected– Flexible in varying situations
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POP as a Search Problem• Initial plan:
– Actions:{Start, Finish}– Orderings:{Start<Finish}– Links:{}– Open precond. = proconditions of Finish
• Successor function– Pick an open procond. p and select an action for
achieving it: A →p B– Consistency enforcing
• Add A<B to plan (if needed, also Start<A, A<Finish)• If an action C has effect ¬p, reschedule B<C or C<A
• Goal test: Open precond. = {}
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Example
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• Pick the only precond. At(Spare,Axle)-> Action PutOn(Spare, Axle)
• Pick At(Spare,Ground)-> Action remove(Spare,Trunk)
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• Pick ¬At(Flat,Axle): action LeaveOvernight• Conflict -> Reschedule -> Conflict 2
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• At(Spare,Trunk) in conflict with LeaveOvernight-> LeaveOvernight cannot be chosen at all in the plan
• New try Remove(Flat, Axle) for precondition¬At(Flat,Axle) will lead to the solution
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Final Solution
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Complications
• Variables in actions– Delayed unification needed– Additional inequality contraints for consistency
can be used• Heuristics for successor function
– Harder to estimate how far the plan is from a solution
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Lähteet
• S. Russell, P. Norvig: Artificial Intelligence, a Modern Approach. Prentice-Hall, 2003.
• S. Russell, Tekoälykurssin kalvot Berkleynyliopistossa, 2004.