STRIPS HW 1: Blocks World

Transcription

1 STRIPS HW 1: Blocks World Operator Precondition Delete List Add List Stack(x, y) CLEAR(y) CLEAR(y) HOLDING(x) HOLDING(x) ON(x, y) Unstack(x, y) ON(x, y) ON(x, y) HOLDING(x) CLEAR(x) CLEAR(y) PickUp(x) CLEAR(x) ONTABLE(x) HOLDING(x) ONTABLE(x) PutDown(x) HOLDING(x) HOLDING(x) ONTABLE(x) Difference Table Difference Operator Stack(x, y) PutDown(x) HOLDING(x) Unstack(x, y) PickUp(x) ONTABLE(x) PutDown(x) CLEAR(y) Unstack(x, y) ON(x, y) Stack (x, y) Initial state: ON(B, C) ON(C, D) CLEAR(B) ONT ABLE(D) HOLDING(A) Goal state: 1

2 STRIPS HW1: Planning Note that there are many possible plans. A computational planner will try operators in a fixed order; this will most likely lead to many dead ends and/or plans that are inefficient (e.g., blocks get unnecessarily stacked or unstacked, etc. This depends on how smart the planner is. We ve only considered the simplest approach with no plan remediation.). Also, goals will be placed on the stack in some fixed order, presumably in the order they are listed in a rule s preconditions. This will also lead to many variations. In the following, the smartest choice is always made, producing the most efficient plan. Start off with the goal on the goal stack and the operator stack empty: ARMEMP T Y ONT ABLE(A) Comments: The three goals on top are the predicates that are not true in the current world state that need to be true in the goal state. Considering the topmost goal, the planner looks at the difference table to see which operators can achieve ARMEMP T Y. There are two: P utdown and Stack. 3. Try HOLDIN G(A) () ONT ABLE(A) Comments: ARMEMP T Y is replaced with the precondition for. This goal is true in the world model, which means that can be successfully carried out. is placed on the operator stack, the goal is popped from the goal stack, the predcates in its delete list are removed from the world model, and the predicates in its add list are added. successful 2

3 4. ON T ABLE(A) Comments: ONT ABLE(A) becomes true as a result of the, so it is simply popped from the goal stack. 5. Try Stack(B, A) CLEAR(B) HOLDIN G(B) CLEAR(B) HOLDIN G(B) (Stack(B, A)) Comments: is replaced with the precondition for Stack(B, A). The topmost is already true, so it is popped. 6. Try HOLDIN G(B) CLEAR(A) HOLDIN G(B) (Stack(B, A)) Comments: Two operators from the difference table apply: P ickup and Unstack. If P ickup were tried first, its preconditions would not be met and a more tortuous plan would result, so we ll assume Unstack is chosen first. 3

4 7. ARMEMP T Y ON(B, C) ARMEMP T Y ON(B, C) (Unstack(B, C)) CLEAR(A) HOLDIN G(B) (Stack(B, A)) Comments: The goal is replaced with the preconditions of U nstack. Both are true in the world model, so Unstack succeeds. It will pushed onto the operator stack, and the world model will be updated using the add and delete list of Unstack. successful 8. CLEAR(A) HOLDIN G(B) (Stack(B, A)) World: ON(C, D) CLEAR(A) CLEAR(C) ONT ABLE(A) ONT ABLE(D) HOLDING(B) Comments: The preconditions for Stack are now met, so the Stack operation can be carried out. It is placed on the operator stack and the world model is updated using the add and delete lists of Stack. Stack(B, A) successful 9. Stack(B, A) World: ON(C, D) ON T ABLE(D) ON T ABLE(A) CLEAR(C) CLEAR(B) ARM EM P T Y Comments: The world and goal states are identical, so the goal stack is popped and our plan is the sequence of operations on the operator stack, in reverse order.. 4

5 10. Stack(B, A) World: ON(C, D) ON T ABLE(D) ON T ABLE(A) CLEAR(C) CLEAR(B) ARM EM P T Y 5