1. Creating High-quality Roadmaps for Motion Planning in Virtual Environments Roland Geraerts and Mark Overmars IROS 2006

2. Requirements The roadmap –is resolution complete –is small –contains useful cycles –provides high-clearance paths res. complete, smalluseful cycleshigh-clearance paths

3. Outline Reachability Roadmap Method (RRM) –Resolution complete roadmap –Small roadmap Adding useful cycles Adding clearance to the roadmap Experiments Conclusions & current work

4. RRM – Criteria Coverage –Each free sample can be connected to a vertex in the graph Maximal connectivity –For each two vertices v’,v’’: If there exists a path between v’ and v’’ in the free space, then there exists a path between v’ and v’’ in the graph

5. Reachability Roadmap Method Paper –R. Geraerts and M.H. Overmars. Creating small roadmaps for solving motion planning problems. MMAR 2005, pp. 531-536 Outline of algorithm –Discretizes the free space –Computes small set of guards –Guards are connected via connector –Resulting roadmap is pruned

6. Adding Useful Cycles Paper –D. Nieuwenhuisen and M.H. Overmars. Useful cycles in probabilistic roadmap graphs. ICRA 2004, pp. 446-452 Useful edge –Edge (v,v’) is K-useful if K * d(v,v’) < G(v,v’) v’v

7. Adding Useful Cycles Useful node –Node v is useful if there is an obstacle inside the cycle being formed v’ v’’ v

8. Adding Useful Cycles Algorithm –Create RRM roadmap –Add useful nodes –Create a queue with all collision-free edges Queue is sorted on increasing edge length –Add edge from the queue to the graph if edge is K-useful RRMuseful nodesfinal roadmap

9. Providing High-clearance Paths Paper –R. Geraerts and M.H. Overmars. Clearance based path optimization for motion planning. ICRA 2004, pp. 531-536 Retract edges to the medial axis –Retraction of a sample d d

10. Providing High-clearance Paths Paper –R. Geraerts and M.H. Overmars. Clearance based path optimization for motion planning. ICRA 2004, pp. 531-536 Retract edges to the medial axis –Retraction of an edge

11. Experimental Setup Field House Office Quake

12. Experimental Results Field Graph statisticsPath statistics resolutiontechniquetime (s)|V||E|SPFavg query (ms) 94 x 94RRM RRM* 0.75 0.91 29 43 18 47 1.570 1.137 4.3 2.3 RRMRRM*RRRM

13. Experimental Results Field Clearancetime minavgmaxs RRM* RRRM 0.03 0.34 2.71 3.08 6.44 6.4624 RRMRRM*RRRM

14. Experimental Results Office Graph statisticsPath statistics resolutiontechniquetime (s)|V||E|SPFavg query (ms) 130x80RRM RRM* 1.10 2.70 154 167 147 180 1.812 1.181 3.8 3.6 RRMRRM*RRRM

15. Experimental Results Office Clearancetime minavgmaxs RRM* RRRM 0.00 0.01 1.60 1.77 6.82 7.53320 RRMRRM*RRRM

16. Experimental Results House Graph statisticsPath statistics resolutiontechniquetime (s)|V||E|SPFavg query (ms) 57 x 20 x40RRM RRM* 11.67 18.6834 33 34 1.225 1.2248.2 RRMRRM*RRRM

17. Experimental Results House Clearancetime minavgmaxs RRM* RRRM 0.00 0.13 2.17 3.33 5.64 10.4149 RRMRRM*RRRM

18. Experimental Results Quake Graph statisticsPath statistics resolutiontechniquetime (s)|V||E|SPFavg query (ms) 57 x 20 x40RRM RRM* 306.44 384.90 71 132 65 216 2.068 1.194 27.1 41.5 RRMRRM*RRRM

19. Experimental Results Quake Clearancetime minavgmaxs RRM* RRRM 0.00 0.05 2.90 3.28 9.45 9.75343 RRMRRM*RRRM

20. Conclusions High-quality roadmap –resolution complete –small –short and alternative paths –high-clearance paths –fast query times

21. Future Work Corridor Map Method –Creating high-quality paths within 1 ms Paths are smooth, short or have large clearance –Method is flexible Paths avoid dynamic obstacles

22. Future Work Corridor Map Method –Creating high-quality paths within 1 ms Paths are smooth, short or have large clearance –Method is flexible Paths avoid dynamic obstacles Smooth pathShort pathPath avoiding obstacles