unifying planning techniques

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Unifying Planning Techniques Jonathon Doran

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Unifying Planning Techniques. Jonathon Doran. The Planning Domain. A domain describes the objects, facts, and actions in the universe. We may have a box and a table in our universe. Fluents. There is a green box. The box is on the table. Propositions that are true or false at a point - PowerPoint PPT Presentation

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Page 1: Unifying Planning Techniques

Unifying Planning Techniques

Jonathon Doran

Page 2: Unifying Planning Techniques

The Planning DomainA domain describes the objects, facts, andactions in the universe.

We may have a box and a tablein our universe.

Page 3: Unifying Planning Techniques

Fluents

Propositions that aretrue or false at a pointin time.

There is a green box.The box is on the table.

The state of the universe is describedby a set of these fluents.

Page 4: Unifying Planning Techniques

Actions

A set of preconditionsA set of fluents to addA set of fluents to delete

STRIPS formalism

Our goal is to move the universefrom one state to another.

Actions change the universe’s state.

Page 5: Unifying Planning Techniques

Plans

The goal is typically a subset of a final state.

Actions imply state... plans are equivalently a list of states.

An initial state of the universe, and a list of actionsthat change the universe to some goal state.

Page 6: Unifying Planning Techniques

Plan Structure

We could look at a plan as an alternatingsequence of states and actions...

SASASAS ...

Plans are also recursive.

SA (S A (S A S))

Plans are not necessarilyunique.

Page 7: Unifying Planning Techniques

The State Space

Actions:

Up, Down, Left, Right

This space growsexponentially withthe number of variables!

Page 8: Unifying Planning Techniques

Complications

How do we plan a route?

We cannot reliably estimate our distance to the goal...

Page 9: Unifying Planning Techniques

Planning is NP-Complete

Abandon all hope

It gets worse:

Optimal planning is NP-Hard

Early planners did an exhaustive search.

Page 10: Unifying Planning Techniques

Some HopeBut we have seen techniques fordealing with NP-complete problems...

DPLL prunes the solution space. This works if we are

lucky.

Page 11: Unifying Planning Techniques

GraphPlanBlum and Furst1995

Represents solution spaceas a graph.

Able to prune this graphin polynomial time.

Able to build this graph in polynomial time.

Page 12: Unifying Planning Techniques

Graph Representation

Circles represent fluents.Squares represent actions.

Page 13: Unifying Planning Techniques

Mutual Exclusion

Mutually exclusive situations maybe identified and pruned.

Actions are mutex if no plan couldcontain both at the same time.

Page 14: Unifying Planning Techniques

Mutex ExamplesInterference: (one action deletes a precond of another)

I have $15, and can either buy a CD or a movie ticket.

Inconsistent Effects:

The effect of one action is the negation of another action.

I wish to paint the room entirely blue and entirely red.

Page 15: Unifying Planning Techniques

Mutex ExamplesCompeting Needs:

Two actions have preconditions that are mutex.

I wish to sleep and go to class.

Page 16: Unifying Planning Techniques

Fluent MutexesFluents are mutex if all ways of asserting them are mutex.

I am presently in Dallas and Denton.

What would it mean for some actions(but not all) to be mutex?

Or, if one fluent is the negation of another.

Page 17: Unifying Planning Techniques

Graph GrowthActions monotonically increase.

Fluents monotonically increase.

Fluent-mutexes monotonically decrease.

Action-mutexes monotonically decrease.

At some point the graph stops changing.

Page 18: Unifying Planning Techniques

Theorem

The size of the graph, and the time to create it are:

• polynomial in t (the number of levels)• polynomial in n (the number of objects)• polynomial in m (the number of actions)• polynomial in p (the number of fluents in the goal)

O(k(a+n)^2)

Page 19: Unifying Planning Techniques

SatPlanExpress the problem as a CSP (Boolean Sat for example)

UseAction(a1, t1) ^ UseAction(a2,t2)...

Holds(p1,t1) ^ Holds(p2,t2) ...

With appropriate constraints.

Run this through a Sat Solver

Page 20: Unifying Planning Techniques

Unifying GraphPlan and SatPlanCreate a planning graph, like GraphPlanfor k-levels.

Convert graph to a CNF wff

Run through a Sat Solver.

Increase graph to k+1 levels if needed

Page 21: Unifying Planning Techniques

A Good Idea?A wff from a graph is much smallerthan using STRIPS operators.

Random restarts used in implementations.

Restart threshold gradually increases.

SatPlan requires significantpreparation time.

Page 22: Unifying Planning Techniques

Results

Page 23: Unifying Planning Techniques

Rocket Example Problemtwo rockets: X1, X2locations: Earth, Mars, Venuspeople: Adam, Bettyboth rockets fueled, and at EarthAdam and Betty on Earth

Goal: Adam at Mars, Betty at Venus

Page 24: Unifying Planning Techniques

DomainPredicates: (at <X> <planet>) (in <X> <rocket>)

(fueled <rocket>)

Actions: (load <person> <rocket>)(unload <rocket> <planet>)(fly <rocket> <planet>)

Page 25: Unifying Planning Techniques

16 Level 1 Actions(load A 1) (load A 2) (load B 1) (load B 2)(F 1 E) (F 1 M) (F 1 V) (F 2 E) (F 2 M) (F 2 V)

Plus 6 no-op actions

Page 26: Unifying Planning Techniques

14 Level 1 Fluents(at A E) (in A 1) (in A 2)(at B E) (in A 1) (in A 2)(at X1 E) (at X1 M) (at X1 V)(at X2 E) (at X2 M) (at X2 V)(fueled 1) (fueled 2)

Page 27: Unifying Planning Techniques

ResearchDirectionsplanning with preferencescooperative planningdistributed planningprobabilistic planningplanning under uncertainty (SCM, POMDP)