1/16 Planning Chapter 11- Part1 Author: Vali Derhami

2/16 Outline Search vs. planning STRIPS operators Forward and backward search algorithms in planning

3/16 Search vs. Planning Consider the task get milk, bananas. Standard search algorithms seem to fail miserably:

4/16 Search vs. Planning (cont.) Assume a problem-solving agent using search... ♦ Which actions are relevant? – Our previous state-space definition does not clarify this ♦ What is a good heuristic function? – Must be provided by a human in each individual case ♦ How to decompose the problem? – Most real-world problems are nearly decomposable – But the state-space definition does not reveal any structure of the problem

5/16 What is planning? Planning in AI is the problem of finding a sequence of actions to achieve some goals. The sequence of actions is the system’s plan which then can be executed. Planning requires the following: – representation of goal to achieve; – knowledge about what actions can be performed; – knowledge about state of the world; to generate a plan to achieve the goal.

6/16 Architecture of a Planner

7/16 Planning Language What is a good language? – Expressive enough to describe a wide variety of problems – Restrictive enough to allow efficient algorithms to operate on it Planning algorithm should be able to take advantage of the logical structure of the problem

8/16 STRIPS Language STanford Research Institute Problems Solver The language of predicate logic to represent  goal to be achieved;  state of environment;  actions available to agent;

9/16 Example: Blocks world To represent this environment, need the following predicate names: On(x, y) obj x on top of obj y OnTable(x) obj x is on the table Clear(x) nothing is on top of obj x Holding(x) arm is holding x ArmEmpty robot arm is empty Here is a FOL representation of the blocks world described above: Clear(A)  Clear(C)  On(A,B)  OnTable(B)  OnTable(C)  ArmEmpty

10/16 Representation of states and goal Representation of States = conjunction of ground and function free literals ترکیت عطفی از لیترالهای مثبت (در اینجا بیشتر لیترالهای گزاره ای) – e.g. At(A,B)  Clear(C),... But not At(A, x) or At(neighbour(A),B)! closed-world assumption is used, meaning that any conditions that are not mentioned in a state are assumed false. Representation of goals: A goal is a particular state – e.g. OnTable(A)  OnTable(B)  OnTable(C) A state s satisfies a goal g if s contains all the atoms in g (and possibly others) Rich  Famous  Miserable satisfies Rich  Famous

11/16 Representation of actions Action(Fly(p, from, to), PRECOND:At(p, from)  Plane(p)  Airport(from)  Airport(to) Effect:  At(p, from)  At(p, to))  Each action schema has: – a name and parameter list – a pre-condition list: conjunction of function-free positive literals, list of facts which must be true for action to be executed; Any variables in the precondition must also appear in the action's parameter list. – an effect list: a conjunction of function-free literals describing how the state changes when the action is executed. may be contains: a delete list: list of facts that are no longer true after action is performed (negative literals); an add list: list of facts made true by executing the action. (positive literals) Each of these may contain variables.

12/16 Applicable actions  An action is applicable in any state satisfying its preconditions  Example: Action(Fly(p, from, to), PRECOND:At(p, from)  Plane(p)  Airport(from)  Airport(to) Effect:  At(p, from)  At(p, to)) Current State: At(Pi, JFK)  At(P2, SFO)  Plane(Pi)  Plane(P2)  Airport(JFK)  Airport(SFO).  ={p/Pi, from/JFK, to/SFO} تعریف جایگزین Thus, the concrete action Fly (Pi, JFK, SFO) is applicable.

13/16 Effect of actions Starting in state s, the result of executing an applicable action a is a state s' that is the same as s except that  Any positive literal P in the effect of a is added to s'  any negative literal P is removed from s‘  all other atoms do not change their value ! After Fly (Pi, JFK, SFO), current state: At(Pi, SFO)  At(P2, SFO)  Plane(Pi)  Plane(P2)  Airport(JFK)  Airport(SFO).

14/16 Expressiveness and extensions

15/16 Air cargo transport In(c, p) means that cargo c is inside plane p, and At(x, a) means that object x (either plane or cargo) is at airport a.

16/16 Air cargo transport (Cont.) Following plan is a solution to the problem: [Load(C1, P1, SFO), Fly(P1, SFO, JFK), Unload(C1,P1, JFK),Load(C2, P2, JFK), Fly(P2, JFK, SFO), Unload(C2, P2, SFO)].