Rapidly Exploring Random          Trees   CSCI 7000 ADVANCED ROBOTICS               ~VISHAL VERMA
Agenda Intro to Motion Planning Problem Formulation Intro to RRTs RRT Algorithm RRT Analysis Implementing RRT Planne...
Intro to Motion Planning Used in:   Robotics (:D)   Spacecraft   Computer Graphics/Animations   Computational Biology...
Problem Formulation
Intro to RRTs Search high dimensional spaces Consider algebraic constraints   Obstacles Consider local constraints   ...
Differential Constraints
Non Holonomic Constraints Controllable DOF < Total DOF Example – Car:   Total DOF – 3  [x,y,θ]   Controllable DOF – 2 ...
Concept of RRTs Intuitively:   Monte-Carlo Search   Biased to favor largest Voronoi regions Binary Tree:   Searched S...
RRT - Justification Other similar options:   Randomized Potential Field Method:       Depends on a good heuristic poten...
RRT Algorithm
RRT Analysis
Implementing RRT Planners
The RRT CONNECT() Routine Replaces EXTEND() Multiple calls to EXTEND() Better for holonomic planning EXTEND() still be...
Bidirectional RRT
Further Thoughts More than 2 RRTs?   Computation time divided     Construct RRTs/Explore state space     Interconnect ...
Example: Growing RRT
Example: Holonomic Planning
Example: Holonomic Planning
Example: Holonomic Planning
Example: Non - Holonomic Planning
Example: Non - Holonomic Planning
Example: Non - Holonomic Planning
Example: KinodynamicPlanning
Questions?
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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?

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