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Automated Planning

Automated Planning. Dr. H é ctor Mu ñ oz-Avila. Source: Ch. 1 Appendix B.3 Dana Nau’s slides My own. What is Planning? Classical Definition. Planning: finding a sequence of actions to achieve a goal.

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Automated Planning

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  1. Automated Planning Dr. Héctor Muñoz-Avila • Source: • Ch. 1 • Appendix B.3 • Dana Nau’s slides • My own

  2. What is Planning? Classical Definition • Planning: finding a sequence of actions to achieve a goal • Domain Independent: symbolic descriptions of the problems and the domain. The plan generation algorithm remains the same • Domain Specific: The plan generation algorithm depends on the particular domain Advantage: - opportunity to have clear semantics Disadvantage: - symbolic description requirement Advantage: - can be very efficient Disadvantage: - lack of clear semantics - knowledge-engineering for adaptation

  3. Example of Planning Tasks: Military Planning

  4. Example of Planning Tasks: Playing a Game

  5. Example of Planning Tasks: Route Planning

  6. Classical Planning • Classical planning makes a number of assumptions: • Symbolic information (i.e., non numerical) • Actions always succeed • The “Strips” assumption: only changes that takes place are those indicated by the operators • Next slide enumerates all assumptions • Despite these (admittedly unrealistic) assumptions some work-around can be made (and have been made!) to apply the principles of classical planning to games • “Hot” research topic: to removes some of these assumptions

  7. State & Goals • Initial state: (on A Table) (on C A) (on B Table) (clear B) (clear C) • Goals: (on C Table) (on B C) (on A B) (clear A) A Initial state Goals C B A B C (Ke Xu)

  8. No block on top of ?x No block on top of ?y nor ?x transformation On table General-Purpose Planning: Operators Operator: (Unstack ?x) • Preconditions: (on ?x ?y) (clear ?x) • Effects: • Add: (on ?x table) (clear ?y) • Delete: (on ?x ?y) ?x ?y ?y ?x … …

  9. Classical Planning can be Hard C A B C A B C B A B A C B A C B A B C C B A B A C A C A A B C B C C B A A B C (Michael Moll)

  10. Conceptual Model1. Environment System  State transition system  = (S,A,E,) Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  11. s1 s0 put take location 2 location 1 location 2 location 1 move1 move2 move1 move2 s3 s2 put take location 2 location 2 location 1 location 1 load unload s4 s5 move2 move1 location 2 location 2 location 1 location 1 State Transition System  = (S,A,E,) • S = {states} • A = {actions} • E = {exogenous events} • State-transition function: S x (AE)  2S • S = {s0, …, s5} • A = {move1, move2, put, take, load, unload} • E = {} • : see the arrows The Dock Worker Robots (DWR) domain Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  12. s3 location 2 location 1 Conceptual Model2. Controller Given observation o in O, produces action a in A Controller Observation function h: SO State transition system  = (S,A,E,) Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  13. s3 location 2 location 1 Conceptual Model2. Controller Complete observability: h(s) = s Given observation o in O, produces action a in A Controller Observation function h: SO Given state s, produces action a State transition system  = (S,A,E,) Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  14. Planning problem Planning problem Planning problem Conceptual Model3. Planner’s Input Planner Depends on whether planning is online or offline Given observation o in O, produces action a in A Observation function h: SO State transition system  = (S,A,E,) Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  15. s1 s0 put take location 2 location 1 location 2 location 1 move1 move2 move1 move2 s3 s2 put take location 2 location 2 location 1 location 1 load unload s4 s5 move2 move1 location 2 location 2 location 1 location 1 PlanningProblem • Description of  • Initial state or set of states • Initial state = s0 • Objective • Goal state, set of goal states, set of tasks, “trajectory” of states, objective function, … • Goal state = s5 The Dock Worker Robots (DWR) domain Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  16. Planning problem Planning problem Planning problem Conceptual Model4. Planner’s Output Planner Instructions tothe controller Depends on whether planning is online or offline Given observation o in O, produces action a in A Observation function h(s) = s State transition system  = (S,A,E,) Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  17. Classical Assumptions (I) • A0: Finite system • finitely many states,actions, and events • A1: Fully observable • the controller alwaysknows what state  is in • A2: Deterministic • each action or event hasonly one possible outcome • A3: Static • No exogenous events: no changes except those performed by the controller Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  18. Classical Assumptions (II) A4: Attainment goals • a set of goal states Sg A5: Sequential plans • a plan is a linearlyordered sequence of actions (a1, a2, … an) A6 :Implicit time • no time durations • linear sequence of instantaneous states A7: Off-line planning • planner doesn’t know the execution status Dana Nau: Lecture slides for Automated PlanningLicensed under the Creative Commons Attribution-NonCommercial-ShareAlike License: http://creativecommons.org/licenses/by-nc-sa/2.0/

  19. This is Nice but How About Actual Deployed Applications? • We briefly discuss three deployed applications: • Fear: application of a “classical” planner • Bridge: application of a “new-classical” planner • MRB: planning + execution • We will discuss these again in detail later in the semester

  20. Detailed Discussion of Topics • See web page

  21. Math Background: Logic Source: Appendix B.3

  22. Introduction to Logic • A logic is a formal system of representing knowledge • A logic has: • Syntax – indicates the valid expressions • Semantics – provides meaning to the expressions • Inference mechanism – draw conclusions from a set of statements

  23. Example: propositional Logic • Definition. A propositonal formula is defined recursively as follows: • A symbol form a predefined list P is a proposition • If 1 and 2, are propositions then: • (1  2) • (1  2) • (1  2) are also propositions • If  is a proposition then ¬() is a proposition Example. (a)  (¬a  ¬b  c  d)  (¬c  ¬d)  (¬d) Semantics. Truth tables Inference mechanism. Modus ponens

  24. Predicate Logic • Definition. A term is defined as follows: • A constant is a term • A variable is a term • If t1, …, tn are terms and f is a function symbols then f(t1,…,tn) is a term • Definition. If t1, …, tn are terms and p is a symbol for an n-ary predicate then p(t1, …, tn ) are predicates

  25. Predicate Logic: Formulas • Definition. An atomic formula is defined recursively as follows: • An atom is an atomic formula • If 1 and 2, are atomic formulas then: • (1  2) • (1  2) • (1  2) are also atomic formulas • If  is a atomic formula then ¬() is an atomic formula • If  is a atomic formula and x is a variable then: • x() is an atomic formula • x() is an atomic formula Example: x (likes(Mephistus,x)  evilThing(x)) How do we say that Mephistus likes only evil things?

  26. Predicate Logic: Semantics • (1  2) • (1  2) • (1  2) • ¬() • x() • x()

  27. Predicate Logic: Literals and Clauses • Definition. A literal is an atomic formula consisting of a single atom and no quantifiers • likes(Mephistus,x) • ¬ evilThing(x) • Definition. A clause is a disjunction of literals • likes(Mephistus,x)  ¬ evilThing(x)

  28. Resolution: Inference Mechanism for Predicate Logic • Substitution,  • Unification • Most general unifier • Resolution: Given two clauses: • L = l1 l2  …  ln • M = m1 m2  …  mn If there is and li and mk such that: • li = a and mk = ¬a’ and • There is a most general unifier  for a and a’ Then: (L – li)  (M – mk) is a resolvent of L and M • Idea behind the resolution procedure

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