1. Language for planning problems
STRIPS: STanford Research Institute Problem Solver
world described by logical conditions
state as conjunction of positive literals
propositional; e.g., Happy ^ Hungry to represent the state of the agent
first-order ground and function-free terms;
e.g., At(Plane1, Verona) ^ At(Plane2,Malpensa)
closed-world assumption; i.e., any not mentioned condition is false
goal is a partially specified state
a state satisfies a goal if contains all the literals of the goal
e.g. state At(Plane1, Verona) ^ At(Plane2,Malpensa) satisfies goal At(Plane2,Malpensa)

2. STRIPS actions (contd.)
Tidily arranged actions descriptions, restricted language
Action schema:
ACTION: specifies name and parameter list
Buy(x)
PRECONDITION: conjunction of positive literals
At(p) ^ Sells(p, x)
EFFECT: conjunction of literals (positive or negative)
Have(x)
[Note: no information on how to execute the action!]
A complete set of STRIPS operators can be translated into a set of successor-state axioms

3. Example: Air cargo transport
predicates In(·, ·),At(·, ·)
type predicates: Cargo(·), Plane(·),Airport(·)
Start
At(C1, SFO) ^ At(C2, JFK) ^ At(P1, SFO) ^ At(P2, JFK) ^ Cargo(C1) ^ Cargo(C2) ^ Plane(P1) ^ Plane(P2) ^ Airport(JFK) ^ Airport(SFO)
Goal
At(C1, JFK) ^ At(C2, SFO)
Actions
Load(c, p, a)
Unload(c, p, a)
Fly(p, from, to)

4. Example: Air cargo transport
predicates In(·, ·),At(·, ·)
type predicates: Cargo(·), Plane(·),Airport(·)
Start
At(C1, SFO) ^ At(C2, JFK) ^ At(P1, SFO) ^ At(P2, JFK) ^ Cargo(C1) ^ Cargo(C2) ^ Plane(P1) ^ Plane(P2) ^ Airport(JFK) ^ Airport(SFO)
Goal
At(C1, JFK) ^ At(C2, SFO)
Actions
Load(c, p, a)
Unload(c, p, a)
Fly(p, from, to)

5. Example: Air cargo transport
Actions
Load(c, p, a)
PRE: At(c, a) ^ At(p, a) ^ Cargo(c) ^ Plane(p) ^ Airport(a)
EFF: ¬At(c, a) ^ In(c, p)
Unload(c, p, a)
PRE: In(c, p) ^ At(p, a) ^ Cargo(c) ^ Plane(p) ^ Airport(a)
EFF: At(c, a) ^ ¬In(c, p)
Fly(p, from, to)
PRE: At(p, from) ^ Plane(p) ^ Airport(from) ^ Airport(to)
EFF: ¬At(p, from) ^ At(p, to)

6. Example: Air cargo transport (contd.)
a solution is
Load(C1, P1, SFO),
Fly(P1, SFO, JFK),
Unload(C1, P1, JFK),
Load(C2, P2, JFK),
Fly(P2, JFK, SFO),
Unload(C2, P2, SFO)

7. STRIPS Planning STRIPS planning problem: State-space search
find a sequence of actions that lead to a goal
states and goals are defined by a conjunctions of literals
State-space search
Forward search (goal progression) from the initial state try to reach the goal
Backward search (goal regression) from the goal and try to project it to the initial state
Plan-space search
partial-order planning (POP) search the space of partially build plans

8. State-space search planning problem defines the search problem
initial state is the start state
goal test checks whether state satisfies the goal
actions define the operators
step cost is usually 1
(a) forward or
(b) backward search

9. Forward search main search loop
select an action and unify precondition with the state
if precondition is satisfied, apply the action generating a new state
check whether the new state satisfies the goal

10. Forward search with the Shopping Example
Start
At(Home) ^ Sells(SM,Milk) ^ Sells(SM,Banana) ^ Sells(HWS,Drill)^Loc(Home)^Loc(SM)^Loc(HWS)
Buy(x)
PRE: At(store), Sells(store, x)
EFF: Have(x)
Go(x, y)
PRE: At(x),Loc(y)
EFF: At(y),¬At(x)
Goal
Have(Milk) ^ Have(Banana) ^ Have(Drill)

11. Forward search main search loop
select an action and unify precondition with the state
if precondition is satisfied, apply the action generating a new state
check whether the new state satisfies the goal
state space is finite -> complete for complete search algorithms
inefficient because of irrelevant actions -- needs good heuristics

12. Backward search
idea: select relevant actions only starting from the goal
action is
relevant when it achieves one of the conjuncts (add-list)
consistent when doesn’t undo any desired literal (delete-list)
select a relevant and consistent action and generate new state
1. delete add-list
2. add preconditions
terminates with a state satisfied by the initial state
branching on relevant and consistent states

13. Backward search with the Shopping Example
Start
At(Home) ^ Sells(SM,Milk) ^ Sells(SM,Banana) ^ Sells(HWS,Drill)^Loc(Home)^Loc(SM)^Loc(HWS)
Buy(x)
PRE: At(store), Sells(store, x)
EFF: Have(x)
Go(x, y)
PRE: At(x),Loc(y)
EFF: At(y),¬At(x)
Goal
Have(Milk) ^ Have(Banana) ^ Have(Drill)

14. State-space vs. plan-space
forward and backward search explore linear sequences of actions
this is not necessary
consider the solution for the air cargo transport
Load(C1, P1, SFO), Fly(P1, SFO, JFK),Unload(C1, P1, JFK),
Load(C2, P2, JFK), Fly(P2, JFK, SFO),Unload(C2, P2, SFO)
the only required ordering is among Load, Fly and Unload
connected by causal effects; e.g., Load(C1, P1, SFO) achieve In(C1,P1), used by the precondition of Unload
there’s no need to put Load(C2, P2, JFK) after Unload(C1, P1, JFK)
partial-order plan: graph of actions including Start and Finish

15. Example

16. Partially ordered plans
Partially ordered collection of steps with
Start step has the initial state description as its effect
Finish step has the goal description as its precondition
causal links from outcome of one step to precondition of another
temporal ordering between pairs of steps
Open condition = precondition of a step not yet causally linked
plan is complete iff every precondition is achieved
precondition is achieved iff it is the effect of an earlier step and no possibly intervening step undoes it (conflict)
plans cannot contain cycles

18. Define the Start State and the Goal State

19. Define the Start State and the Goal State
On(A,Table), On(B,Table), On(C,B), Clear(A), Clear(C)
End
On(A,B), On(B,C), On(C,Table)

20. Define the Actions

23. Use either forward or backward search to build the plan for this problem.