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Rapidly Exploring Random Trees

Rapidly Exploring Random Trees. RRT-Connected: An Efficient Approach to Single-Query Path Planning. Rapidly Exploring Random Trees. Data structure/algorithm to facilitate path planning Developed by Steven M. La Valle (1998)

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Rapidly Exploring Random Trees

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  1. Rapidly Exploring Random Trees RRT-Connected: An Efficient Approach to Single-Query Path Planning

  2. Rapidly Exploring Random Trees • Data structure/algorithm to facilitate path planning • Developed by Steven M. La Valle (1998) • Originally designed to handle problems with nonholonomic constraints and high degrees of freedom

  3. Rapidly Exploring Random Trees Algorithm: BUILD_RRT(qinit) 1 T.init(qinit); 2 for k=1 to K do 3 qrand ← RANDOM_CONFIG(); 4 EXTEND(T, qrand); 5 Return T;

  4. Rapidly Exploring Random Trees EXTEND(T,q) 1 qnear ← Nearest_NEIGHBOUR(q,T); 2 if NEW_CONFIG(q, qnear, qnew) then 3 T.add_vertex(qnew); 4 T.add_edge(qnear, qnew); 5 ifqnew = q then 6 Return Reached; 7 else 8 Return Advanced; 9 Return Trapped;

  5. Rapidly Exploring Random Trees

  6. Rapidly Exploring Random Trees • Main advantage: biased towards unexplored regions Probability node selected for extension proportional to size voronoi region

  7. Rapidly Exploring Random Trees Nice properties: • Expansion heavily biased towards unexplored areas of state space • Distribution nodes approaches the sampling distribution (important for consistency), usually uniform but not necessarily! • Relatively simple algorithm • Always remains connected

  8. RRT-Connect Path Planner • How to use RRT in a path planner? • RRT-Connect: • Single shot method • Grow twoRRTs one from the start position and one from the goal position • After every extension try to connect the trees • If the trees connect a path has been found

  9. RRT-Connect Path Planner Algorithm: RRT_CONNECT_PLANNER(qinit, qgoal) 1 Ta.init(qinit);Tb.init(qgoal); 2 for k=1 to K do 3 qrand ← RND_CFG(); 4 if not(EXTEND(Ta, qrand)= Trapped) then 5 if(CONNECT(Tb, qnew) = Reached) then 6 Return PATH(Ta, Tb); 7 SWAP(Ta, Tb); 8 Return Failure;

  10. RRT-Connect Path Planner CONNECT(T, q) 1repeat 2 S ← EXTEND(T, q) 3 until not (S = Advanced) 4 Return S;

  11. RRT-Connect Path Planner

  12. RRT-Connect Path Planner • Variations: • RRT_EXTEND_EXTEND • RRT_CONNECT_CONNECT • In CONNECT step only add last vertex to graph • Grow more RRTs

  13. RRT-Connect Path Planner • Analysis: • RRT-Connect is probabilistic complete • Distribution vertices in RRT converges toward sampling distribution • No theoretical characterization of the rate of converge!

  14. RRT-Connect Path Planner • Experiments: Average 100 trials • Scene 1: 0.228s • Scene 2: 5,94s • Scene 3: 2.92s Using 3D non incremental collision checking algorithm

  15. RRT-Connect Path Planner • Experiments: • In uncluttered scenes connect heuristic 3 to 4 times faster than other RRT-based variants • Useful for complicated 3D scenes • 7-DOF kinematic chain, over 8000 triangle primitives average 2 s for each motion to reach, grasp and move

  16. RRT-Connect Path Planner • Experiments: • over 13.000 triangles • 80 s SGI Indigo2 • 15 s high-end SGI

  17. RRT-Connect Path Planner • Conclusion: Randomised approach that yields good experimental performances with • no parameter tuning • no pre-processing • simple and consistent behaviour • balance between greedy searching and uniform exploration • well suited for incremental distance computation and fast nearest neighbour algorithms

  18. RRT-Connect Path Planner • To do: • optimise distance travelled during each step by using the radius of a collision free ball • use approximate nearest neighbour methods • use incremental collision detection algorithm • compare performance to other path planning approaches • identify conditions that lead to poor performance

  19. RRT-Connect Path Planner • Issues: • Randomness can cause great variance in runtime due to ‘unlucky instance’

  20. RRT-Connect Path Planner • Issues: • Ugly paths

  21. References • RRT-connect: An efficient approach to single-query path planning. J. J. Kuffner and S. M. LaValle. In Proceedings IEEE International Conference on Robotics and Automation, pages 995--1001, 2000 • On Heavy-tailed Runtimes and Restarts in Rapidly-exploring Random Trees. Nathan A. Wedge and Michael S. Branicky. 2008 • Chapter 5: Sampling-Based Motion Planning, Planning Algorithms. S. M. LaValle. Cambridge UniversityPress, Cambridge, U.K., • Rapidly-exploring random trees: A new tool for path planning. S. M. LaValle. TR 98-11, Computer Science Dept., Iowa State University, October 1998 2006.  • http://msl.cs.uiuc.edu/rrt/gallery.html • Rapidly-Exploring Random Trees in Highly Constrained Environments.AmjadAlmahairi. 2010.

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