MIT16_410F10_lec11b

# MIT16_410F10_lec11b - Encoding Planning Problems as...

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Unformatted text preview: 7/2/11 Encoding Planning Problems as Proposi6onal Logic Sa6sﬁability Sertac Karaman 16.410‐13 October 18th, 2010 Assignment •  Remember: •  Problem Set #6 Propositional Logic, due next Wednesday, October 27th. •  16:413 Project Part 1: Sat-based Activity Planner, due Wednesday, November 3rd. •  Reading –  Today: [AIMA] Chapter 10, re-read sections on SatPlan. –  Monday: Johan de Kleer and Brian C. Williams, "Diagnosing Multiple Faults," Artificial Intelligence, 32:100-117, 1987. 10/25/10 copyright Brian Williams, 2000-10 2 1 7/2/11 Planning problem •  Recall the planning problem: –  Objects •  robot1, robot2, load1, load2, room1 –  Predicates describing proper6es of objects •  (IN ?robot ?room), (HAS ?robot ?load) –  Ac6ons as means to change these proper6es •  Navigate (?robot, ?room_from, ?room_to) –  Ini6al condi6on –  Goal statement OX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXB BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX OXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX B BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX BOXBOX Image by MIT OpenCourseWare. Proposi6onal logic SAT problem •  Recall the SAT problem: –  Given a set of clauses, ﬁnd an assignment to all proposi6ons to sa6sfy all the clauses. p1 ∨ ¬ p2 ∨ p 3 ¬ p1 ∨ ¬ p2 ∨ p 4 ¬ p3 ∨ p4 ∨ p 5 •  SAT solvers are very powerful. •  Can process problems with tens of thousands of variables 2 7/2/11 Encoding planning as SAT •  Idea: –  Deﬁne proposi6ons for predicates and decisions –  Encode problem descrip6on in proposi6onal logic initial state ∧ all possible action descriptions ∧ goal Encoding planning as SAT •  Ini;al condi;on •  Encode the truth of predicates: 0 0 (IN robot1 bedroom) ∧ (IN robot2 kitchen) •  Remember to include those that are false: 0 0 ¬(IN robot1 kitchen) ∧ ¬(IN robot2 bedroom) 3 7/2/11 Encoding planning as SAT •  Ac;ons •  StraighOorward approach: •  One proposi6on for each ac6on: 0 Navigate(robot1 bedroom kitchen) •  True if robot navigates from bedroom to kitchen at 6me 0 1 (IN robot1 kitchen) ⇔ 0 0 0 ((IN robot1 kitchen) ∧ ¬(Navigate(robot1, kitchen, bedroom) ∧ (IN robot1 kitchen) )) 0 0 ∨(Navigate(robot1, bedroom, kitchen) ∧ (IN robot1 bedroom) )) Robot was in the kitchen at 6me 0 and did not leave the kitchen at 6me 0. Robot was in the bedroom at 6me 0 and leR the bedroom to go to kitchen at 6me 0. Encoding planning as SAT •  Ac;ons •  What may go wrong? 0 Navigate(robot1, kitchen, bedroom) –  However, robot1 is not in the kitchen at 6me 0 ! •  PrecondiAon axioms: 0 0 Navigate(robot1, kitchen, bedroom) ⇒ (IN robot1 kitchen) 4 7/2/11 Encoding planning as SAT •  Ac;ons •  What else may go wrong? 0 Navigate(robot1, kitchen, bedroom) 0 Navigate(robot1, bedroom, livingroom) •  Ensure that one ac6on can be taken at a 6me: 0 0 ¬(Navigate(robot1, kitchen, bedroom) ∧ Navigate(robot1, bedroom, livingroom) ) Encoding planning as SAT •  Outline of the algorithm: –  Check sa6sﬁability for increasing number of steps i = 1 If sa6sﬁable for i steps then construct the solu6on Else i = i + 1 5 MIT OpenCourseWare http://ocw.mit.edu 16.410 / 16.413 Principles of Autonomy and Decision Making Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. ...
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• Fall '10
• Prof.BrianWilliams
• MIT OpenCourseWare, Massachusetts Institute of Technology, AirTrain Newark, OpenCourseWare, Brian C. Williams, BOXBOX

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