PRM, RRT, and RRT* - Georgia Institute of...
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PRM, RRT, and RRT* Frank Dellaert Based on materials by Steve Lavalle, Lydia Kavraki, Emilio Frazzoli and their students Monday, February 21, 2011
Transcript of PRM, RRT, and RRT* - Georgia Institute of...
PRM, RRT, and RRT*Frank Dellaert
Based on materials by Steve Lavalle, Lydia Kavraki, Emilio Frazzoli and their students
Monday, February 21, 2011
Holonomic Planning
http://www.youtube.com/watch?v=cXm3WW-geD8
Monday, February 21, 2011
Non-Holonomic
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Non-Holonomic
Spacecraft Thrusting
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PRMRRTRRT*
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PRMRRTRRT*
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Probabilistic Roadmap
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Probabilistic Roadmap
Demo!
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PRM Properties
• Good
• Multiple Queries
• Probabilistically Complete
• Bad:
• Determining connectivity can be hard
• Especially in non-holonomic planning
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PRMRRTRRT*
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Problem Formulation
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RRT
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Naive Random Tree
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Algorithm
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Convex Region
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Voronoi Interpretation
Vertices on frontier selected more often
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RRT Advantages
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RRT in Planning
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Hovercraft
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Free Satellite in 3D
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Planning for a Car-Like Robot
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PRMRRTRRT*
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Problems with RRT
• Solution far from optimal
• Karaman & Frazzoli 2010: Probability of RRT converging to an optimal solution is 0
• Rapidly-exploring Random Graph (RRG): 1
• Downside: back to finding connections!
Monday, February 21, 2011
RRG
• RRT algorithm extends the nearest vertex towards the sample.
• RRG also extends all vertices returned by the Near procedure (if first was success).
Monday, February 21, 2011
RRG
• RRT algorithm extends the nearest vertex towards the sample.
• RRG also extends all vertices returned by the Near procedure (if first was success).
Monday, February 21, 2011
RRG
• RRT algorithm extends the nearest vertex towards the sample.
• RRG also extends all vertices returned by the Near procedure (if first was success).
Monday, February 21, 2011
RRG
• RRT algorithm extends the nearest vertex towards the sample.
• RRG also extends all vertices returned by the Near procedure (if first was success).
Monday, February 21, 2011
RRT*
• Frazzoli:
• RRT is a variant of RRG that essentially “rewires" the tree as better paths are discovered.
• After rewiring the cost has to be propagated along the leaves.
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RRT*
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RRT*
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RRT*
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RRT*
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RRT*
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RRT*
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RRT*
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RRT*
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RRT*
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RRT vs RRT*
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RRT vs RRT*
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RRT* with Obstacles
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Anytime RRT*
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Aggressive Drivinghttp://www.youtube.com/watch?v=Tdmm3i52WBc
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Conclusion
• RPM: multiple-query, holonomic
• RRT: single-query, non-holonomic, suboptimal
• RRG, RRT*: single-query, holonomic, optimal
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![Intelligent bidirectional rapidly-exploring random trees ... · (PRM) [14] [15] and Rapidly exploring Random Trees (RRT) [23]. However, PRMs tend to be ine cient when obstacle geometry](https://static.fdocuments.us/doc/165x107/5fed728ed484d45f7e7546fc/intelligent-bidirectional-rapidly-exploring-random-trees-prm-14-15-and.jpg)
