MIT16_410F10_lec14

MIT16_410F10_lec14 - 16.410/413 Principles of Autonomy and...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 Uniform-cost search Greedy (Best-First) 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 collision-free trajectories into a finite graph. Searching for a collision-free 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 (Breadth-First Search, Depth-First Search, etc.). E. Frazzoli (MIT) L05: Informed Search November 1, 2010 3 / 46 A step back We have seen how we can discretize collision-free trajectories into a finite graph. Searching for a collision-free 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 (Breadth-First Search, Depth-First 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 collision-free trajectories into a finite graph. Searching for a collision-free 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 (Breadth-First Search, Depth-First 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....
View Full Document

This note was uploaded on 12/26/2011 for the course SCIENCE 16.410 taught by Professor Prof.brianwilliams during the Fall '10 term at MIT.

Page1 / 56

MIT16_410F10_lec14 - 16.410/413 Principles of Autonomy and...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online