l7_bw_ppag

l7_bw_ppag - Path Planning as Search Paul Robertson 16.410...

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Path Planning as Search Paul Robertson 16.410 16.413 Session 7 Slides adapted from: Brian C. Williams 6.034 Tomas Lozano Perez, Winston, and Russell and Norvig AIMA 1
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Assignment Remember: Online problem set #3 due Session 8 Hand in written part in class. Reading: – Adversarial Search: AIMA Ch. 6 From before: Path planning: AIMA Ch. 25.4 2
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Roadmaps are an effective state space abstraction 3
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4 start goal A* biases uniform cost towards the goal by using h f = g + h g = distance from start h = estimated distance to goal. B x x Uniform cost search spreads evenly from the start A A* finds an optimal solution if h never over estimates . Then h is called “admissible”
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Path Planning through Obstacles Start position Goal position 5
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1. Create Configuration Space Start position Vehicle translates, but no rotation Idea: Transform to equivalent Problem of navigating a point. Goal position 6
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2. Map From Continuous Problem to Graph Search: Create Visibility Graph Start position Goal position 7
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Start position 2. Map From Continuous Problem to Graph Search: Create Visibility Graph Goal position 8
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3. Find Shortest Path Start position Goal position 9
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Start position Resulting Solution Goal position 10
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A Visibility Graph is a Kind of Roadmap Start position What are some other types of roadmaps? Goal position 11
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Voronoi Diagrams Lines equidistant from CSpace obstacles 12
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Path Planning With an Adversary Start positions Goal position 13
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Types of Competitive Games Two Player and Multi-Player Zero and non-zero sum games f(player1) = - f(player2) Perfect and imperfect information Stochastic games Î Two player, zero sum games with perfect info 14
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Two Player Games With Perfect Information Initial State – Empty board Successor Function – Place X or 0 in empty square Terminal Test – Three X’s or O’s in a line is a win – Else no empty squares is a tie Utility Function – 1 for win – 0 for tie – -1 for lose Tic Tac Toe X X O 15
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Two Player Games With Perfect Information Initial State – Empty board Successor Function – Place X or 0 in empty square Terminal Test – Three X’s or O’s in a line is a win – Else no empty squares is a tie Utility Function – 1 for win – 0 for tie – -1 for lose Tic Tac Toe X X O 16
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Game Tree X turn 17 X X X X X X X X X O turn XO X
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This note was uploaded on 11/07/2011 for the course AERO 16.410 taught by Professor Brianwilliams during the Fall '05 term at MIT.