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### CS344 : Introduction to Artificial Intelligence

Pushpak BhattacharyyaCSE Dept., IIT Bombay

Lecture 17- Robotic Planning mainly discussed the search issues

Example : Blocks World

- STRIPS : A planning system – Has rules with precondition deletion list and addition list

Robot hand

Robot hand

A

C

B

A

B

C

START

GOAL

Sequence of actions :

Grab C

Pickup C

Place on table C

Grab B

Pickup B

6. Stack B on C

- Grab A
- Pickup A
- Stack A on B

Example : Blocks World

- STRIPS : A planning system – Has rules with precondition deletion list and addition list

Robot hand

Robot hand

A

C

B

A

B

C

START

GOAL

on(B, table)

on(A, table)

on(C, A)

hand empty

clear(C)

clear(B)

on(C, table)

on(B, C)

on(A, B)

hand empty

clear(A)

Rules

- R1 : pickup(x)

Precondition & Deletion List : handempty, on(x,table), clear(x)

Add List : holding(x)

- R2 : putdown(x)
- Precondition & Deletion List : holding(x)
- Add List : handempty, on(x,table), clear(x)

Rules

- R3 : stack(x,y)

Precondition & Deletion List :holding(x), clear(y) Add List : on(x,y), clear(x), handempty

- R4 : unstack(x,y)
- Precondition & Deletion List : on(x,y), clear(x),handempty
- Add List : holding(x), clear(y)

Plan for the block world problem

- For the given problem, Start Goal can be achieved by the following sequence :
- Unstack(C,A)
- Putdown(C)
- Pickup(B)
- Stack(B,C)
- Pickup(A)
- Stack(A,B)
- Execution of a plan: achieved through a data structure called Triangular Table.

Triangular Table

on(C,A)

1

clear(C)

unstack(C,A)

hand empty

holding(C)

putdown(C)

2

on(B,table)

hand empty

pickup(B)

3

clear(C)

holding(B)

stack(B,C)

4

on(A,table)

clear(A)

hand empty

pickup(A)

5

6

clear(B)

holding(A)

stack(A,B)

on(C,table)

on(B,C)

on(A,B)

7

clear(A)

0

3

6

1

2

4

5

Triangular Table

- For n operations in the plan, there are :
- (n+1) rows : 1 n+1
- (n+1) columns : 0 n
- At the end of the ith row, place the ith component of the plan.
- The row entries for the ith step contain the pre-conditions for the ith operation.
- The column entries for the jth column contain the add list for the rule on the top.
- The <i,j> th cell (where 1 ≤ i ≤ n+1 and 0≤ j ≤ n) contain the pre-conditions for the ith operation that are added by the jth operation.
- The first column indicates the starting state and the last row indicates the goal state.

Search in case of planning

Start

Pickup(B)

Unstack(C,A)

- Ex: Blocks world
- Triangular table leads
- to some amount of fault-tolerance in the robot

S1

S2

NOT ALLOWED

A

C

C

C

B

A

B

A

B

START

WRONG MOVE

Resilience in Planning

- After a wrong operation, can the robot come back to the right path ?
- i.e. after performing a wrong operation, if the system again goes towards the goal, then it has resilience w.r.t. that operation
- Advanced planning strategies
- Hierarchical planning
- Probabilistic planning
- Constraint satisfaction

- The kernel in the lr table controls the execution of the plan
- At any step of the execution the current state as given by the sensors is matched with the largest kernel in the perceptual world of the robot, described by the lr table

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