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# Vishal Verma: Rapidly Exploring Random Trees

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S.M. LaValle and J.J Kuffner. Rapidly-exploring random trees: Progress and prospects. In Robotics: The Algorithmic Perspective. 4th Int. Workshop on the Algorithmic Foundations of Robotics., Hanover, NH, 2000. A. K. Peters.

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### Vishal Verma: Rapidly Exploring Random Trees

1. 1. Rapidly Exploring Random Trees CSCI 7000 ADVANCED ROBOTICS ~VISHAL VERMA
2. 2. Agenda Intro to Motion Planning Problem Formulation Intro to RRTs RRT Algorithm RRT Analysis Implementing RRT Planners Examples
3. 3. Intro to Motion Planning Used in:  Robotics (:D)  Spacecraft  Computer Graphics/Animations  Computational Biology  Virtual Prototyping  Vehicle safety
4. 4. Problem Formulation
5. 5. Intro to RRTs Search high dimensional spaces Consider algebraic constraints  Obstacles Consider local constraints  Differential constraints of Motion  Non Holonomic constraints
6. 6. Differential Constraints
7. 7. Non Holonomic Constraints Controllable DOF < Total DOF Example – Car:  Total DOF – 3 [x,y,θ]  Controllable DOF – 2 [x, θ] Constraints introduced:  Cannot make sharp turns
8. 8. Concept of RRTs Intuitively:  Monte-Carlo Search  Biased to favor largest Voronoi regions Binary Tree:  Searched Systematically  NP-Hard RRT:  Searched (pseudo)randomly  Pull tree toward unexplored portions
9. 9. RRT - Justification Other similar options:  Randomized Potential Field Method:  Depends on a good heuristic potential function  Difficult to find with obstacles/Differential Constraints  Probabilistic Roadmap approach  Generates many random configurations  Connects with local planner  Good for Holonomic  Local planner too complicated for non holonomic  Needs non-linear control system
10. 10. RRT Algorithm
11. 11. RRT Analysis
12. 12. Implementing RRT Planners
13. 13. The RRT CONNECT() Routine Replaces EXTEND() Multiple calls to EXTEND() Better for holonomic planning EXTEND() still better for non-holonomic  Lack of good metric
14. 14. Bidirectional RRT
15. 15. Further Thoughts More than 2 RRTs?  Computation time divided  Construct RRTs/Explore state space  Interconnect RRTs Probabilistic Roadmap:  Limiting/Extreme version of this  Max separate RRTs merged
16. 16. Example: Growing RRT
17. 17. Example: Holonomic Planning
18. 18. Example: Holonomic Planning
19. 19. Example: Holonomic Planning
20. 20. Example: Non - Holonomic Planning
21. 21. Example: Non - Holonomic Planning
22. 22. Example: Non - Holonomic Planning
23. 23. Example: KinodynamicPlanning
24. 24. Questions?