1

Planning

Chapters 11 and 12

Thanks: Professor Dan Weld, University of Washington

2

Planning

Input Description of initial state of world (in

some KR) Description of goal (in some KR) Description of available actions (in some

KR) Output

Sequence of actions Or, a partial order of actions

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Input Representation

Description of initial state of world Set of propositions: ((block a) (block b) (block c) (on-table a) (on-

table b) (clear a) (clear b) (clear c) (arm-empty)) Description of goal (i.e. set of desired worlds)

Logical conjunction Any world that satisfies the conjunction is a goal (:and (on a b) (on b c)))

Description of available actions

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How Represent Actions? Simplifying assumptions

Atomic time Agent is omniscient (no sensing necessary). Agent is sole cause of change Actions have deterministic effects

STRIPS representation World = set of true propositions Actions:

Precondition: (conjunction of literals) Effects (conjunction of literals)

a

aa

north11 north12

W0 W2W1

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STRIPS Actions Action = a function from world-state to world-

state Precondition says when function defined Effects say how to change set of propositions

aa

north11

W0 W1

north11precond: (and (agent-at 1 1)

(agent-facing north))

effect: (and (agent-at 1 2)

(not (agent-at 1 1)))

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Action Schemata

(:operator pick-up :parameters ((block ?ob1)) :precondition (and (clear ?ob1) (on-table ?ob1) (arm-empty)) :effect (and (not (on-table ?ob1))

(not (clear ?ob1)) (not (arm-empty))

(holding ?ob1)))

Instead of defining: pickup-A and pickup-B and …

Variables: ?x. For example, ?ob1 Define a schema:

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STRIPS vs ADL

Positive/Negative conditions Closed world assumption Negated Effects Quantified Effects Goals as conjunctions and disjunctions Conditional Effects (when …) Equality Predicate Typing

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Examples

Air Cargo Domain Spare Tire Problem The blocks world

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Planning as Search

Nodes

Arcs

Initial State

Goal State

World states

Actions

The state satisfying the complete description of the initial conds

Any state satisfying the goal propositions

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Forward-Chaining World-Space Search

AC

BCBA

InitialState Goal

State

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Backward-Chaining World-Space Search

DCBA

E

D

CBA

E

DCBA

E

* * *

Problem: Many possible goal states are equally acceptable.

From which one does one search?

AC

B

Initial State is completely defined

DE

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Backward Planning

Try out http://www.cs.ubc.ca/labs/lci/CIspace/Version4/planning/ at UBC which shows goal-directed planning

Shows blocks world planning Idea: find a first subgoal

Achieve it by selecting an action Regress to discover new subgoals from the

action’s preconditions Continue

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Planning as Search 2

Nodes

Arcs

Initial State

Goal State

Partially specified plans

Adding + deleting actions or constraints (e.g. <) to plan

The empty plan

A plan which when simulated achieves the goal

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Plan-Space Search and Partial Order Planning

pick-from-table(C)

pick-from-table(B)

pick-from-table(C)put-on(C,B)

How represent plans? How test if plan is a solution?

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Terminologies

Partial Ordering Linearization Ordering constraints Causal Links Achieves Conflicts Open Preconditions Consistent Plans

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Planning as Search 3

Phase 1 - Graph Expansion Necessary (insufficient) conditions for plan existence Local consistency of plan-as-CSP

Phase 2 - Solution Extraction Variables

action execution at a time point Constraints

goals, subgoals achieved no side-effects between actions

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Planning Graph

PropositionInit State

ActionTime 1

PropositionTime 1

ActionTime 2

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Constructing the planning graph…

Initial proposition layer Just the initial conditions

Action layer i If all of an action’s preconds are in i-1 Then add action to layer I

Proposition layer i+1 For each action at layer i

Add all its effects at layer i+1 Also allow propositions at layer i to persist

to i+1

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Mutual Exclusion (or Mutex)

Actions A,B exclusive (at a level) if A deletes B’s precond, or B deletes A’s precond, or A & B have inconsistent preconds (so they

cannot be executed at the same time) Propositions P,Q inconsistent (at a level)

if all ways to achieve P exclude all ways to achieve

Q

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Graphplan Create level 0 in planning graph Loop

If goal contents of highest level (nonmutex)

Then search graph for solution If find a solution then return and terminate

Else Extend graph one more level

A kind of double search: forward direction checks necessary

(but insufficient) conditions for a solution, ...

Backward search verifies...

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Searching for a Solution

For each goal G at time t For each action A making G true @t

If A isn’t mutex with a previously chosen action, select it If no actions work, backup to last G (breadth first search)

Recurse on preconditions of actions selected, t-1

PropositionInit State

ActionTime 1

PropositionTime 1

ActionTime 2

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Dinner Date

Initial Conditions: (:and (cleanHands) (quiet))

Goal: (:and (noGarbage) (dinner) (present))

Actions:(:operator carry :precondition

:effect (:and (noGarbage) (:not (cleanHands)))(:operator dolly :precondition

:effect (:and (noGarbage) (:not (quiet)))(:operator cook :precondition (cleanHands)

:effect (dinner))(:operator wrap :precondition (quiet)

:effect (present))

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Planning Graph noGarb

cleanH

quiet

dinner

present

carry

dolly

cook

wrap

cleanH

quiet

0 Prop 1 Action 2 Prop 3 Action 4 Prop

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Are there any exclusions? noGarb

cleanH

quiet

dinner

present

carry

dolly

cook

wrap

cleanH

quiet

0 Prop 1 Action 2 Prop 3 Action 4 Prop

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Do we have a solution? noGarb

cleanH

quiet

dinner

present

carry

dolly

cook

wrap

cleanH

quiet

0 Prop 1 Action 2 Prop 3 Action 4 Prop

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Extend the Planning Graph noGarb

cleanH

quiet

dinner

present

carry

dolly

cook

wrap

carry

dolly

cook

wrap

cleanH

quiet

noGarb

cleanH

quiet

dinner

present

0 Prop 1 Action 2 Prop 3 Action 4 Prop

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One (of 4) possibilities noGarb

cleanH

quiet

dinner

present

carry

dolly

cook

wrap

carry

dolly

cook

wrap

cleanH

quiet

noGarb

cleanH

quiet

dinner

present

0 Prop 1 Action 2 Prop 3 Action 4 Prop

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Planning Languages

PDDL Tutorials FF Planner

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Robot Architectures (page787)

Problem: low level action takes too long to reason about!

Function Based Architecture:

Task Planning and Learning

Vision Inferencing

Map based Navigation

Sensors and Actuators

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Behavior-based Robotics (page 788)

Rodney Brooks designed behavior-based robotics

Agent design should not be function based (I.e., should not be based on learning, task planning, sensing, etc).

Instead, it should be indepdent modules

Each has own sensing, inferencing, and acting

Higher level modules more intelligent, and can access sensors independently, and can modify outputs of lower-level modules

sensors actuatorsexplore

wonder

Avoid objects

vision

learn

Plan ahead

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Robot Insect Video

Rodney Brooks’ robots in a video http://www.youtube.com/watch?v=C9p8B7-

5MTI

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Summary Planning

Reactive systems vs. planning Planners can handle medium to large-

sized problems Relaxing assumptions

Atomic time Agent is omniscient (no sensing necessary). Agent is sole cause of change Actions have deterministic effects

Generating contingent plans Large time-scale Spacecraft control