1. RRT-Blossom RRT with local flood-fill behavior Maciej Kalisiak DGP Laboratory University of Toronto mac@dgp.toronto.edu Michiel van de Panne Imager Laboratory University of British Columbia van@cs.ubc.ca

2. Highly-constrained terrain

3. Purpose ► highly-constrained environments  less room to move  → smaller search space  → motion planning should be easier ► Rapidly-Exploring Random Trees (RRT)  popular motion planning algorithm  does poorly in highly-constrained terrain ► RRT-Blossom  variation of RRT well adapted to such terrain

4. Flood-fill traits to emulate ► generally, a flood-fill:  has a constant rate of fill  does not visit a location more than once ► in RRT context this translates to:  make sure tree gains an edge on each iteration  do not re-explore the same space twice

5. Key modifications ► receding edges  allow edges that recede from the target point ► re-exploration prevention  do not revisit same space with multiple nodes ► node “blossoming”  avoid duplicate work by immediately and permanently keeping or discarding tested edges

6. Receding edges ► often provide useful information → worth keeping ► RRT does not allow receding edges ► RRT-CT † allows receding edges, but does not guard against resultant re-exploration † P.Cheng & S.M.LaValle, Reducing Metric Sensitivity in Randomized Trajectory Design, IROS 2001

7. Re-exploration (“regression”) ► RRT guarantees no edge/node overlap ► receding edges break this guarantee ► now possible: multiple tree nodes exploring same space ► re-exploration = wasted effort (often huge!)

8. Preventing re-exploration ► generally, re-exploration non-trivial to detect ► approximation that works well: ► prevention: do not instantiate edges which satisfy the above edge regresses if its leaf node is closer to a tree node other than its parent

9. Blossoming ► instantiate all valid edges out of chosen node ► avoids duplicate edge computation and testing ► RRT: “memoryless”  recomputes good & bad edges ► RRT-CT: remembers only bad edges  recomputes good edges ► RRT-Blossom: “remembers” all edges  by instantiating all valid edges out of node, no need to remember anything

10. Viability issue ► dead-end branches can “block” needed edges  can prevent discovery of solution! ► fix for re-exploration check:  ignore such nonviable branches ► viability discovered on-the-fly

11. Experiments: agents pointcarbike kinematickinodynamic

12. Experiments: terrains T complex rooms tunnel

13. Results: point (holonomic)

14. Results: car (nonholonomic)

15. Results: bike (kinodynamic)

16. Take-away ► RRT-Blossom: more robust RRT  highly-constrained terrain → big speedup  deep local minima → big speedup  regular terrain → comparable performance ► performs well in both settings  kinematic  kinodynamic ► more at http://www.dgp.toronto.edu/~mac/rrt-blossom/