Classical Planning in Artificial Intelligence

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JaydenGibbs,United States,Teacher
Published Date:19-07-2017
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Classical Planning Problems: Representation Languages – 20173 3 History: 1959  The language of Artificial Intelligence was/is logic  First-order, second-order, modal, …  1959: General Problem Solver (Newell, Shaw, Simon) jonkvi jonkvida da4 4 History: 1969  1969: Planner explicitly built on Theorem Proving (Green) jonkvi jonkvida da5 5 Basis in Logic  Full theorem proving generally proved impractical for planning  Different techniques were found  Foundations in logical languages remained ▪ Languages use predicates, atoms, literals, formulas ▪ We define states, actions, … relative to these ▪ Allows us to specify an STS at a higher level Formal representation using a first-order language: "Classical Representation" (from the book) "The simplest representation that is (more or less) reasonable to use for modeling" jonkvi jonkvida da6 6 Running Example  Running example (from the book): Dock Worker Robots Containers shipped Cranes move containers in and out of a harbor between ”piles” and robotic trucks jonkvi jonkvida da8 8 Objects 1: Intro  We are interested in objects in the world  Buildings, cards, aircraft, people, trucks, pieces of sheet metal, …  Must be a finite set Modeling: Which objects exist and are relevant for the problem? jonkvi jonkvida da9 9 Objects 2: Dock Worker Robots  Dock Worker Robots A crane moves containers between piles and robots A robot is an automated A container can be truck moving containers stacked, picked up, between locations loaded onto robots loc2 c2 p2 c3 c1 r1 p1 loc1 We can skip: A pile is a stack of containers – Hooks A location is an area that can at the bottom, there is a pallet be reached by a single crane Wheels Rotation angles Can contain several piles, at most one robot. Drivers – not relevant for this problem jonkvi jonkvida da10 10 Objects 3: Classical Representation  Classical representation:  We are constructing a first-order language𝐿  Every object is modeled as a constant  Add a constant symbol ("object name") for each object: 𝐿 contains loc2 c2 p2 c3 c1 r1 p1 loc1 jonkvi jonkvida da11 11 Objects 4: For all non-boolean values  All non-boolean constant values are modeled in the same way  Colors: red, green, blue  … jonkvi jonkvida da13 13 Internal Structure?  An STS only assumes there are states  What is a state? The STS doesn’t care  Its definitions don’t depend on what 𝑠 “represents” or “means” ′ ▪ Can execute𝑎 in 𝑠 if 𝛾𝑠,𝑎=𝑠  We (and planners) need more structure  "state 𝑠 "  23862497124985 " " jonkvi jonkvida da14 14 Predicates  First-order language: Start with a set of predicates  Properties of the world ▪  Properties of single objects ▪  Relations between objects ▪  Relations between 2 objects ▪  Non-boolean properties are "relations between constants" ▪ Essential: Determine what is relevant for the problem and objective jonkvi jonkvida da15 15 Predicates for DWR  All predicates for DWR, and their intended meaning: "Fixed/Rigid" ▪ (can't change) "Dynamic" (modified by actions) jonkvi jonkvida da16 16 Predicates, Terms, Atoms, Ground Atoms  Terminology:  Term: Constant symbol or variable ▪ ▪  Atom: Predicate symbol applied to the intended number of terms ▪ ▪ ▪ ▪  Ground atom: Atom without variables (only constants)  Plain first-order logic has no object types  Allows “strange” atoms: ▪ ▪ ▪ jonkvi jonkvida da17 17 States 1: Factored, Internally Structured  A state defines which ground atoms are true/false in the world We can compute differences between states Structure is essential We will see later how planners make use of structured states… jonkvi jonkvida da18 18 States 2: First-order Representation  Efficient specification / storage of a single state:  Specify which facts are true ▪ All other facts have to be false – what else would they be?  A classical state is a set of all ground atoms that are true ▪ 1 2 3 ∈ Why not store all ground atoms ∉ that are false instead? jonkvi jonkvida da19 19 States 3: State Set  "A state is a set of all ground atoms that are true"…  Set of states in the STS: 𝑑𝑛𝑔𝑟𝑜𝑢𝑠𝑎𝑡𝑜𝑚 ▪𝑆=2 (powerset: all sets of ground atoms)  Number of states: 𝑑𝑛𝑟𝑜𝑢𝑔𝑠𝑎𝑡𝑜𝑚 ▪𝑆=2= jonkvi jonkvida da20 20 States 4: Initial State  The STS assumes a single initial state𝑠 0 Complete relative to the model:  Complete information about We must know everything the current state of the world about those predicates and objects we have specified...  State = set of true facts… 𝑠=attachedp1,loc1,inc1,p1,onc1,pallet,onc3,c1,… 0 loc2 c2 c3 p2 c1 r1 loc1 p1 jonkvi jonkvida da

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