artificial intelligence planning system

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L. Manevitz Lecture 6 1

Artificial IntelligencePlanning System

L. Manevitz



Components of a Planning System

• Chose the best rule to apply next based on the best available heuristic information.

• Apply the chosen rule to compute the new problem state that arises from its application.

• Detect when a solution has been found.



Components of a Planning System cont.

• Detect dead ends so that they can be abandoned and the system’s effort directed in more fruitful directions.

• Detect when an almost correct solution has been found and employ special techniques to make it totally correct.



The Blocks World

• Operators:– UNSTACK(A,B) – Pick up block A from its

current position on block B. The arm must be empty and block A must have no blocks on top of it.

– STACK(A,B) – Place block A on block B. The arm must already be holding A and the surface of B must be clear.



The Blocks World cont.

– PICKUP(A) – Pick up block A from the table and hold it. Te arm must be empty and there must be nothing on top of block A.

– PUTDOWN(A) – Put block A down on the table. The arm must have been holding block A.




• Predicates:– ON(A,B) – Block A is on block B.– ONTABLE(A) – Block A is on the table.– CLEAR(A) – There is nothing on top of

block A.– HOLDING(A) – The arm is holding block

A. – ARMEMPTY – The arm is holding nothing.




• Inference rules:– [ x : HOLDING(x)] ARMEMPTY

– x : ONTABLE(x) y : ON(x,y)

– x : [ y : ON(y,x)] CLEAR(x)



A Simple Blocks World Description

BB

AA

ON(A,B,S0)

ONTABLE(B,S0)

CLEAR(A,S0)



STRIPS – Style Operate for the Blocks World

STACK(x,y)

P: CLEAR(y) HOLDING(x)

D: CLEAR(y) HOLDING(x)

A: ARMEMPTY ON(x,y)

UNSTACK(x,y)

P: ON(x,y) CLEAR(x) ARMEMPTY

D: ON(X,Y) ARMEMPTY

A: HOLDING(x) CLEAR(y)



STRIPS – Style Operate for the Blocks World cont.

PICKUP(x)

P: CLEAR(x) ONTABLE(x) ARMEMPTY

D: ONTABLE(x) ARMEMPTY

A: HOLDING(x)

PUTDOWN(x)

P: HOLDING(x)

D: HOLDING(x)

A: ONTABLE(x) ARMEMPTY



A Simple Search Tree

1

2

3

UNSTACK(A,B)

PUTDOWN(A)

Global database at this point

ONTABLE(B) CLEAR(A)

CLEAR(B) ONTABLE(A)



A Very Simple Blocks World Problem

AA

BB

CC DD AA DD

BBCC

Start: ON(B,A)

ONTABLE(A)

ONTABLE(C)

ONTABLE(D)

ARMEMPTY

Goal: ON(C,A)

ON(B,D)

ONTABLE(A)

ONTABLE(D)



Goal Stack Planning

1) Initial goal stack:

ON(C,A) ON(B,D) ONTABLE(A) ONTABLE(D)



Goal Stack Planning cont.

2) Choose to work on ON(C,A) before ON(B,D):

ON(C,A) ON(B,D) OTADON(B,D)ON(C,A)




3) Achieve ON(C,A) with STACK(C,A):

ON(C,A) ON(B,D) OTADON(B,D)ON(C,A)STACK(C,A)




4) Add STACK’s preconditions:

ON(C,A) ON(B,D) OTADON(B,D)STACK(C,A)

HOLDING(C)CLEAR(A)

CLEAR(A) HOLDING(C)




5) Achieve CLEAR(A) with UNSTACK(B,A):


HOLDING(C)CLEAR(A) HOLDING(C)

UNSTACK(B,A)ON(B,A) CLEAR(B) ARMEMPTY

ON(B,A)CLEAR(B)ARMEMPTY

CLEAR(A)




6) Pop satisfied predicates:


HOLDING(C)CLEAR(A) HOLDING(C)

UNSTACK(B,A)ON(B,A) CLEAR(B) ARMEMPTY

ON(B,A)CLEAR(B)ARMEMPTY




7) Achieve HOLDING(C) with UNSTACK(C,x):


HOLDING(C)CLEAR(A) HOLDING(C)UNSTACK(C,x)ON(C,x) CLEAR(C) ARMEMPTY

ON(C,x)CLEAR(C)ARMEMPTY




8) Achieve ON(C,x) by STACK(C,x):

ON(C,A) ON(B,D) OTADON(B,D)STACK(C,A)CLEAR(A) HOLDING(C)UNSTACK(C,x)ON(C,x) CLEAR(C) ARMEMPTY

ON(C,x)CLEAR(C)ARMEMPTY

STACK(C,x)CLEAR(x) HOLDING(C)HOLDING(C)CLEAR(x)




9) Terminate path because HOLDING(C) is duplicated.

ON(C,A) ON(B,D) OTADON(B,D)STACK(C,A)CLEAR(A) HOLDING(C)UNSTACK(C,x)ON(C,x) CLEAR(C) ARMEMPTY

CLEAR(C)ARMEMPTY

STACK(C,x)CLEAR(x) HOLDING(C)HOLDING(C)CLEAR(x)




10) Achieve HOLDING(C) with PICKUP, not UNSTACK:

ON(C,A) ON(B,D) OTADON(B,D)STACK(C,A)CLEAR(A) HOLDING(C)PICKUP(C)ONTABLE(C) CLEAR(C) ARMEMPTY

CLEAR(C)ARMEMPTY

ONTABLE(C)




11) Pop ONTABLE(C) and CLEAR(C), and achieve ARMEMPTY by STACK(B,D):

ON(C,A) ON(B,D) OTADON(B,D)STACK(C,A)CLEAR(A) HOLDING(C)PICKUP(C)ONTABLE(C) CLEAR(C) ARMEMPTY

CLEAR(C)ARMEMPTY

ONTABLE(C)

STACK(B,D)CLEAR(D) HOLDING(B)HOLDING(B)CLEAR(D)




12) Pop entire stack, and return plan:i. UNSTACK(B,A).

ii. STACK(B,D).

iii. PICKUP(C).

iv. STACK(C,A).



A Slightly Harder Blocks Problem

AA

CC

BB CC

BB

AA

Start: ON(C,A)

ONTABLE(A)

ONTABLE(B)

ARMEMPTY

Goal: ON(A,B)

ON(B,C)



Goal Stack Planning

• There are two ways to begin solving:

21

ON(A,B) ON(B,C)ON(B,C)ON(A,B)

ON(A,B) ON(B,C)ON(A,B)ON(B,C)




• Let’s choose alternative 1.we will eventually produce this goal stack:

ON(A,B) ON(B,C)ON(B,C)STACK(A,B)CLEAR(B) HOLDING(A)PICKUP(A)CLEAR(A) ARMEMPTY

CLEAR(C)

ARMEMPTYUNSTACK(C,A)

ARMEMPTYCLEAR(C) ARMEMPTY

ON(A,B)

HOLDING(A)

CLEAR(A)




• We can pop off the stack goals that have already been satisfied:

ON(A,B) ON(B,C)ON(B,C)STACK(A,B)CLEAR(B) HOLDING(A)PICKUP(A)CLEAR(A) ARMEMPTY

CLEAR(C)

ARMEMPTYUNSTACK(C,A)

ARMEMPTYCLEAR(C) ARMEMPTY

PUTDOWN(C)HOLDING(C)

To satisfy ARMEMPTY we need to PUTDOWN(C).




• We can continue popping:

ON(A,B) ON(B,C)ON(B,C)STACK(A,B)CLEAR(B) HOLDING(A)PICKUP(A)CLEAR(A) ARMEMPTYPUTDOWN(C)HOLDING(C)




• The current state is:

• The sequence of operators applied so far is:1. UNSTACK(C,A)2. PUTDOWN(C)3. PICKUP(A)4. STACK(A,B)

CC BB

AAONTABLE(B)

ON(A,B)

ONTABLE(C)

ARMEMPTY




• Now we can begin to work on ON(B,C).

We need to stack B on C. To do that we need to unstack A from B. By the time we have achieved the goal ON(B,C), and popped it off the stack, we will have executed the following additional sequence of operators




• The sequence of operators :5. UNSTACK(A,B)

6. PUTDOWN(A)

7. PICKUP(B)

8. STACK(B,C)

• The problem state will be:

CC

BB

AA

ON(B,C)

ONTABLE(A)

ONTABLE(C)

ARMEMPTY




• But now when we check the remaining goal on the stack:

we discover that it is not satisfied.We have undone ON(A,B) in the process of achieving ON(B,C).

• The sequence of operators we need to add:9. PICKUP(A)10. STACK(A,B)

ON(A,B) ON(B,C)




The complete plan that has been discovered is:1. UNSTACK(C,A)

2. PUTDOWN(C)

3. PICKUP(A)

4. STACK(A,B)

5. UNSTACK(A,B)

6. PUTDOWN(A)

7. PICKUP(B)

8. STACK(B,C)

9. PICKUP(A)

10. STACK(A,B)

Although this plan will achieve the desired goal, it does not do so very efficiently.

The same would have happened if we had chosen the second alternative.




• There are two approaches we can take to the question of how a good plan could be found:

1. Look at ways to repair the plan we already have – look for places in the plan where we perform an operation and then immediately undo it. We can eliminate both the doing and the undoing steps from the plan.

2. Use a plan-finding procedure that could construct efficient plans directly – the Nonlinear Planning.



Repairing the First Plan

1. UNSTACK(C,A)2. PUTDOWN(C)3. PICKUP(A)4. STACK(A,B)5. UNSTACK(A,B)6. PUTDOWN(A)7. PICKUP(B)8. STACK(B,C)9. PICKUP(A)10. STACK(A,B)

1. UNSTACK(C,A)2. PUTDOWN(C)3. PICKUP(B)4. STACK(B,C)5. PICKUP(A)6. STACK(A,B)



The Nonlinear Planning

• Begin work on the goal ON(A,B) by clearing A, thus putting C on the table.

AA CCBB

CC



Nonlinear Planning cont.

• Achieve the goal ON(B,C) by stacking B on C.

AA CCBB

BB



Nonlinear Planning cont.

• Complete the goal ON(A,B) by stacking A on B.

AA CC

BB

AA



Backwards Non-Linear Planner

• Finds “Last Operator” recursively

• Uses theorem prover to prune paths



The Problem Solving System NOAH

• NOAH plans by developing a hierarchy of subgoals.

• The procedural net contains several levels of representation of a plan, each level more detailed than the previous one.

• For example: the node representing the abstract goal make coffee may be expanded to : grind coffee, boil water, put the coffee in a filter, pour the water through it.



NOAH cont.

• We’ll use NOAH to solve the blocks problem.• The operators used in this example are slightly

different from those we have been using .• STACK – will put any object on any other

(including the table), provided that both objects are clear. It includes the picking up of the object to be moved.



The Blocks Problem

• A reminder of the problem :

AA

CC

BB CC

BB

AA

Start: ON(C,A)

ONTABLE(A)

ONTABLE(B)

ARMEMPTY

Goal: ON(A,B)

ON(B,C)



NOAH Solution

• The initial state of the problem solver:

(ON(A,B) ON(B,C)) Level 1



NOAH Solution cont.

• The first thing that it does is to divide the problem into two subproblems:

ON(A,B)

Level 2

ON(B,C)

S J

Split Join



NOAH Solution cont.

• At the third level the preconditions of STACK are considered – the two blocks involved must be clear.

CLEAR(A)

Level 3: before criticism

CLEAR(B)S J

CLEAR(B)

CLEAR(C)S J

S

STACK(A,B)

STACK(B,C)

J

1

2

4

56

3



NOAH Solution cont.

• Now NOAH employs a set of critics to examine the plan and detect interactions among the subplans.

• Each critic is a little program that makes specific observations about the proposed plan.



The Resolve Conflicts critic

• The Resolve Conflicts critic – constructs a table that lists all the literals that are mentioned more than once in the plan.

CLEAR(B): asserted: node 2 “Clear B”

denied: node 3 “Stack A on B”

asserted: node 4 “Clear B”

CLEAR(C): asserted: node 5 “Clear C”

denied: node 6 “Stack B on C”



The Resolve Conflicts critic cont.

• Constraints on the ordering of operation arise when a given literal must be true before one operation can be performed but will be undone by another.

CLEAR(B): denied: node 3 “Stack A on B”

asserted: node 4 “Clear B”



The Resolve Conflicts critic cont.

• Conclusion:

Since putting A on B could undo the preconditions for putting B on C, putting B on C needs to be done first.



NOAH Solution cont.

• The third level after criticism to resolve conflicts:

CLEAR(A)

Level 3

CLEAR(B)S J

CLEAR(B)

CLEAR(C)S J

S

STACK(A,B)

STACK(B,C)



Eliminate Redundant Preconditions

• Can be invoked to eliminate the redundant specification of subgoals. In this case CLEAR(B) appears twice and is only denied by the last step of the plan.



NOAH Solution cont.

• The third level after all criticism:

CLEAR(A)Level 3

J

CLEAR(B)

CLEAR(C)S J

SSTACK(A,B)

STACK(B,C)



NOAH Solution cont.

• To clear A, C must be removed from A. in order to do that C must be clear :

CLEAR(C)Level 4: before criticism

J

CLEAR(B)

CLEAR(C)S J

S STACK(A,B)

STACK(B,C)

STACK(C,x)



The Resolve Conflicts critic

• The critic observes that putting B on C will make CLEAR(C) false, so everything that depends on C being clear will have to be done before B is put on C.



NOAH Solution cont.

• The Resolve Conflicts critic is employed:

CLEAR(C)

Level 4: after criticism to resolve conflicts

CLEAR(B)

CLEAR(C)S

J

S

STACK(A,B)STACK(B,C)

STACK(C,x)



Eliminate Redundant Preconditions

• It notices that CLEAR(C) is required twice.

• Since putting C somewhere must occur before putting B on C, and both require C being clear then we know that when we get to putting B on C, C will be clear.

• CLEAR(C) can be eliminated from the lower path.



NOAH Solution cont.

• The Eliminate Redundant Preconditions critic is called:

CLEAR(C)

Level 4: after all criticism

CLEAR(B) J

S

STACK(A,B)STACK(B,C)

STACK(C,x)



NOAH Solution cont.

• The system observes that the remaining goals , CLEAR(C) and CLEAR(B), are true in the initial state.

• Therefore the final plan is:

Final plan

STACK(A,B)STACK(B,C)STACK(C,x)

artificial intelligence planning system

Documents

xholdi manevitz lecture

xholdingc manevitz lecture

goal stack planning

blocks world cont

b block

block b

planning system cont

ontablea block