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MIT16_410F10_lec08a - Activity Planning and Execution I...

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1 Activity Planning and Execution I: Operator-based Planning and Plan Graphs Brian C. Williams 16.410-13 October 4 th , 2010 Slides draw upon material from: Prof. Maria Fox, Univ Strathclyde Brian Williams, Fall 10 2 Assignments • Remember: Problem Set #5: Constraint Satisfaction and Activity Planning, out Wed. Sep. 29 th , due Wed, Oct. 6 th , 2010. • Reading: Today: Advanced Planning [AIMA] Ch. 11; " GraphPlan, # by Blum & Furst. Wednesday: Dechter, R., I. Meiri, J. Pearl, “Temporal Constraint Networks,” Artificial Intelligence, 49, pp. 61-95,1991 posted on Stellar. • Exam: Mid-Term - October 20 th .
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2 Simple Spacecraft Problem Observation-1 target instruments Observation-2 Observation-3 Observation-4 calibrated pointing Propositions: Target Pointed To, Camera Calibrated?, Has Image? Operators: Calibrate, Turn to Y, and Take Image. Outline Graph Plan – Problem Statement – Planning Graph Construction – Plan Extraction Image credit: NASA.
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3 Graph Plan Developed in 1995 by Avrim Blum and Merrick Furst, at CMU. The Plan Graph compactly encodes all possible plans. has been a key to scaling up to realistic problems. Plan Graph representation used for: An encoding method for formulating planning as a CSP. Relaxed planning as an admissible heuristic (state space search + A*). Approach has been extended to reason with temporally extended actions, metric and non-atomic preconditions and effects. Approach: Graph Plan 1. Construct compact constraint encoding of state space from operators and the initial state. - Planning Graph 2. Generate plan by searching for a consistent subgraph that achieves the goals. Proposition Init State Action Time 1 Proposition Time 1 Action Time 2
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4 Representing States 7 State A consistent conjunction of propositions (positive literals). E.g., (and (cleanhands) ( quiet) (dinner) (present) (noGarbage)) All unspecified propositions are false. Initial State Problem state at time i = 0. E.g., (and (cleanHands) (quiet)). Goal State A partial state. E.g., (and (noGarbage) (dinner) (present)). A Plan moves a system from its initial state to a final state that extends the goal state. Representing Operators 8 (:operator cook :precondition (cleanHands) :effect (dinner)) Preconditions : Propositions that must be true to apply the operator. A conjunction of propositions (no negated propositions). Effects : Propositions that the operator changes, given that the preconditions are satisfied. A conjunction of propositions (called adds ) and their negation (called deletes ). }
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5 (Parameterized) Operator Schemata Instead of defining many operator instances: pickup-A and pickup-B and … Define a schema: (:operator pick-up : parameters ((?ob1 - block)) : precondition (and (clear ?ob1) (on-table ?ob1) (arm-empty)) :effect (and (not (clear ?ob1)) (not (on-table ?ob1)) (not (arm-empty)) (holding ?ob1))) Example Problem: Dinner Date Initial Conditions : (:init (cleanHands) (quiet)) Goal : (:goal (noGarbage) (dinner) (present)) Actions : (:operator carry :precondition :effect (and (noGarbage) (not (cleanHands))) (:operator dolly :precondition :effect (and (noGarbage) (not (quiet))) (:operator cook
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