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Unformatted text preview: 16.410/413 Principles of Autonomy and Decision Making Lecture 14: Informed Search Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology November 1, 2010 E. Frazzoli (MIT) L05: Informed Search November 1, 2010 1 / 46 Outline 1 Informed search methods: Introduction Shortest Path Problems on Graphs Uniformcost search Greedy (BestFirst) Search 2 Optimal search 3 Dynamic Programming E. Frazzoli (MIT) L05: Informed Search November 1, 2010 2 / 46 A step back We have seen how we can discretize collisionfree trajectories into a finite graph. Searching for a collisionfree path can be converted into a graph search. Hence, we can solve such problems using the graph search algorithms discussed in Lectures 2 and 3 (BreadthFirst Search, DepthFirst Search, etc.). E. Frazzoli (MIT) L05: Informed Search November 1, 2010 3 / 46 A step back We have seen how we can discretize collisionfree trajectories into a finite graph. Searching for a collisionfree path can be converted into a graph search. Hence, we can solve such problems using the graph search algorithms discussed in Lectures 2 and 3 (BreadthFirst Search, DepthFirst Search, etc.). However, roadmaps are not just “generic” graphs. Some paths are much more preferable with respect to others (e.g., shorter, faster, less costly in terms of fuel/tolls/fees, more stealthy, etc.). Distances have a physical meaning. Good guesses for distances can be made, even without knowing optimal paths. E. Frazzoli (MIT) L05: Informed Search November 1, 2010 3 / 46 A step back We have seen how we can discretize collisionfree trajectories into a finite graph. Searching for a collisionfree path can be converted into a graph search. Hence, we can solve such problems using the graph search algorithms discussed in Lectures 2 and 3 (BreadthFirst Search, DepthFirst Search, etc.). However, roadmaps are not just “generic” graphs. Some paths are much more preferable with respect to others (e.g., shorter, faster, less costly in terms of fuel/tolls/fees, more stealthy, etc.). Distances have a physical meaning. Good guesses for distances can be made, even without knowing optimal paths. Can we utilize this information to find efficient paths, efficiently? E. Frazzoli (MIT) L05: Informed Search November 1, 2010 3 / 46 Shortest Path Problems on Graphs Input: h V , E , w , start , goal i : V : (finite) set of vertices. E ⊆ V × V : (finite) set of edges. w : E → R > , e 7→ w ( e ): a function that associates to each edge a strictly positive weight (cost, length, time, fuel, prob. of detection) . start , goal ∈ V : respectively, start and end vertices. Output: h P i P is a path (starting in start and ending in goal , such that its weight w ( P ) is minimal among all such paths....
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 Fall '10
 Prof.BrianWilliams
 Mass, Search algorithm, A* search algorithm, Consistent heuristic

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