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## Blocks World Planning Examples

What is the Blocks World? -- The world consists of:

• A flat surface such as a tabletop
• An adequate set of identical blocks which are identified by letters.
• The blocks can be stacked one on one to form towers of apparently unlimited height.
• The stacking is achieved using a robot arm which has fundamental operations and states which can be assessed using logic and combined using logical operations.
• The robot can hold one block at a time and only one block can be moved at a time.

We shall use the four actions:

UNSTACK(A,B)
-- pick up clear block A from block B;
STACK(A,B)
-- place block A using the arm onto clear block B;
PICKUP(A)
-- lift clear block A with the empty arm;
PUTDOWN(A)
-- place the held block A onto a free space on the table.

and the five predicates:

ON(A,B)
-- block A is on block B.
ONTABLE(A)
-- block A is on the table.
CLEAR(A)
-- block A has nothing on it.
HOLDING(A)
-- the arm holds block A.
ARMEMPTY
-- the arm holds nothing.

Using logic but not logical notation we can say that If the arm is holding a block it is not empty If block A is on the table it is not on any other block If block A is on block B,block B is not clear.

Why Use the Blocks world as an example?

The blocks world is chosen because:

• it is sufficiently simple and well behaved.
• easily understood
• yet still provides a good sample environment to study planning:
• problems can be broken into nearly distinct subproblems
• we can show how partial solutions need to be combined to form a realistic complete solution.

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dave@cs.cf.ac.uk