L11. Planning Agents and STRIPS Search vs. planning Situation calculus STRIPS operators

Search in problem solving Problem solution: A path through the state space tree State space search: Search is a traversal of the tree until the goals is reached. State transitions is performed by operators 　　a b c

Search in problem solving Difficulty using standard search algorithms Standard search algorithms seems to fail since the goal test is inadequate. What is “finish”?

Search in problem solving Planning problem in situation calculus Consider the same task get milk, bananas, and a cordless drill A planning problem is represented in situation calculus by logical sentences that describe the three main parts of a problem. Initial state: At(home, S0)  Have(Milk, S0)  Have(Banana, S0)  Have(Drill, S0) Goal state:  s At(home, s)  Have(Milk, s)  Have(Bananas, s)  Have(Drill, s) Operators: a, s Have(Milk, Result (a,s)) [ (a=Buy(Milk)) At(Supermarket, s)  (Have(Milk, s) a Drop(Milk) )] Plan: p = [Go(Supermarket), Buy(Milk), Buy(Bananas), Go(HWS), …]

Search in problem solving Problem solving vs. planning Representation of states PS: Direct assignment of a symbol to each state PL: Logic sentences Representation of goals PS: A goal state symbol PL: Sentences that describe objective Representation of actions PS: Operators that transform one state symbol into another PL: Addition/deletion of logic sentences describing world state Representation of plans PS: Path through state space PL: Ordered or partially-ordered sequence of actions.

Search in problem solving Advantages of Planning Systems Uniform language for describing states, goals, actions, and their effects. Ability to add actions to a plan whenever they are needed, not just in an incremental sequence from some initial state. Ability to capture the fact that most parts of the world are independent of most other parts. It performs better for complex worlds over standard search algorithm since searching space becomes huge when there are many initial states and operators in standard search algorithms.

The Situation Calculus Wff - well formed formula A goal can be described by a wff:  x On(x, B) if we want to have a block on B Planning: finding a set of actions to achieve a goal wff. Situation Calculus (McCarthy, Hayes, 1969, Green 1969) A Predicate Calculus formalization of states, actions, and their effects. So state in figure can be described by: On(B, A)  On(A, C)  On(A, Fl)  Clear(B) we reify the state and include them as arguments The atoms denotes relations over states. On(B, A, S0)  On(A, C, S0)  On(C, Fl, S0)  Clear(B, S0) We can also have. x, y, s On(x, y, s)  (y = Fl)   Clear(y, s) s Clear(Fl, s)

Representing actions Reify the actions: denote an action by a symbol actions are functions move(B,A,Fl): move block B from block A to Fl move (x,y,z) - action schema do: A function constant, do denotes a function that maps actions and states into states Express the effects of actions. Example: (on, move) (expresses the effect of move on On) positive effect axiom: action state

Effect axioms for (clear, move) move(x, y, z) matching? precondition are satisfied with B/x, A/y, S0/s, F1/z what was true in S0 remains true figure 21

STRIPS: describing goals and state STRIPS: STanford Research Institute Planning System Basic approach in GPS (general Problem Solver): Find a “difference” (Something in G that is not provable in S0) Find a relevant operator f for reducing the difference Achieve precondition of f; apply f; from resultant state, achieve G.

STRIPS planning STRIPS uses logical formulas to represent the states S0, G, P, etc: Description of operator f:

A STRIPS planning example On(B,A) On(A,C) On(C,F1) Clear(B) Clear(Fl) The formula describes a set of world states Planning search for a formula satisfying a goal description On(A, C) On(C, Fl) On(B, Fl) Clear(A)

STRIPS Description of Operators A STRIPS operator has 3 parts: A set, PC - preconditions A set D - the delete list A set A - the add list Usually described by Schema: Move(x,y,z) PC: On(x,y) and On(Clear(x) and Clear(z) D: Clear(z) , On(x,y) A: On(x,z), Clear(y), Clear(F1) A state S1 is created applying operator O by adding A and deleting D from S1.

Example: The move operator

Example1: The move operator G S0  f(P)->G S0->P    x/B, y/A, z/Fl x/B, y/A, z/Fl   On(x,y) Clear(x) Clear(z) f: move(x,y, z) add: On(x,z), Clear(y) del: On(x,y), Clear(z) On(x,z) Clear(x) Clear(y) P: f(P):

Example1: The move operator ABC + Clear(F2) G S0  f(P)->G S0->P    x/B, y/A, z/Fl x/B, y/A, z/Fl   On(x,y) Clear(x) Clear(z) f: move(x,y, z) add: On(x,z), Clear(y) del: On(x,y), Clear(z) On(x,z) Clear(x) Clear(y) P: f(P):

Tree representation S0->G0 S0->G1 pre: On(B, A) Clear(B) S0: On(B,A) On(A,C) On(C,F1) Clear(B) Clear(Fl) G0: On(A, C) On(C, Fl) On(B, Fl) Clear(A) Clear(B) S0->G0 S0->G1 pre: On(B, A) Clear(B) Clear(Fl) G1->S1 Move(B, A Fl) S1->G0