Consider the task get milk, bananas, and a cordless drill

Consider the task get milk, bananas, and a cordless drill

Search vs. planning Standard search algorithms seem to fail miserably: Problems with search approach too many irrelevant actions finding good heuristics is difficult cannot take advantage of problem decomposition

Planning as search with logic Planning systems do the following: 1. open up action and goal representation to allow selection 2. divide-and-conquer by subgoaling 3. relax requirement for sequential construction of solutions

Classic Planning Planning: devising a sequence of actions achieving a goal fully observable deterministic static discrete specific language to represent planning problems

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)

STRIPS actions actions are described by actions contain variables preconditions: when the action can be applied effects: state changes by the action delete-list: propositions that become false add-list: propositions that become true actions contain variables a single action schema represents different actions (instantiation of variables)

STRIPS operators Have(X) ^ GoesOn(X,Y) ^ Bare(Y) PutOn(X) HaveOn(X) In order to PutOn(LeftSock) we have to Have(LeftSock) ^ GoesOn(LeftSock,LeftFoot) ^ Bare(LeftFoot) This leaves us with HaveOn(LeftSock)

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

Semantics Given a state (conjunction of literals) precondition is satisfied if there is a variable assignment s.t. the literals are included in the state; e.g., state At(HW) ^ Sell(HW,Drill) satisfies precondition At(p) ^ Sells(p, x) with assignment p/HW and x/Drill actions with preconditions satisfied can be applied delete items from the delete-list add items from the add-list order does matter! new state: At(HW) ^ Sell(HW,Drill) ^ Have(Drill)

Example: Shopping Start State? Goal State?

Example: Shopping Start State? Goal State? At(Home) Have(Milk) ^ Have(Banana) ^ Have(Drill) At(Home) ??

Example: Shopping Start State? Goal State? Actions? At(Home) Have(Milk) ^ Have(Banana) ^ Have(Drill) ^ At(Home) Actions? Buy(x) Go(x, y)

Example: Shopping Start State? Goal State? Actions? At(Home) Have(Milk) ^ Have(Banana) ^ Have(Drill) ^ At(Home) Actions? Buy(x) PRE: At(store), Sells(store, x) EFF: Have(x) Go(x, y) PRE: At(x) EFF: At(y),¬At(x)