1. Creating Small Roadmaps for Solving Motion Planning Problems Roland Geraerts and Mark Overmars MMAR 2005

2. Introduction Related work Reachability roadmap Experiments Conclusions & current work

3. Related Work – Probabilistic Roadmap Method Construction phase Forbidden space Free space Sample c Colliding path c c’ c Local path c’ c c

4. Related Work – Probabilistic Roadmap Method Query phase Forbidden space Free space Sample Start / goal Local path Shortest path

5. Related Work – Visibility Based Roadmap Forbidden space Free space Connector sample Guard sample Local path Start / goal Shortest path

6. Related Work – Shortcomings PRM –Path not always found –Large roadmap Visibility PRM –Path not always found –Slower 239 nodes, 0.3 seconds51 nodes, 17 seconds39 nodes, 0.15 seconds

7. Reachability 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

8. Reachability Roadmap Coverage Maximal connectivity Roadmap pruning

9. RR – Coverage Art gallery problem is NP-hard Calculate set of candidate guards Computation of reachability regions discretize spacemedial axis transf.distance transformoverlaycandidate guards

10. RR – Maximal Connectivity Calculate connector for each pair of nodes whose reachability areas overlap

11. RR – Pruning Steiner problem is NP-complete –Input:set of guards, set of connectors, all feasible connections between them –Output: shortest roadmap that spans the guards Graph operations initial roadmapSteiner treeall connectionsMST

12. Experimental Setup Test environments GridRotated gridManipulator Village

13. Experimental Results Grid resolutiontechniquetime (s)|N||E||G| 80 x 80 RR PRM vis-PRM 0.33 0.74 20.49 13 158 31 12 157 30 88 638 381

14. Experimental Results Rotated grid resolutiontechniquetime (s)|N||E||G| 200 x 200 RR PRM vis-PRM 7 16 >3600 249 5889 n.a. 248 5887 n.a. 388 2328 n.a.

15. Experimental Results Manipulator resolutiontechniquetime (s)|N||E||G| 60 x 60 x 60 RR PRM vis-PRM 11 86 >3600 313 11095 n.a. 306 11091 n.a. 388 2306 n.a.

16. Experimental Results Village resolutiontechniquetime (s)|N||E||G| 180x22x60 RR PRM vis-PRM 556 >3600 176 n.a. 142 n.a. 1268 n.a.

17. Conclusions New algorithm for creating roadmaps –Roadmap is small –Roadmap is resolution complete –Efficient for 2D and 3D problems Roadmap of RR is much smaller than the roadmap created by the PRM Vis-PRM creates small roadmaps, but takes much time to terminate

18. Current Work Roadmap with high clearance Reachability roadmapRetracted roadmap

19. Current Work Roadmap with high clearance Reachability roadmapRetracted roadmap

20. Current Work Roadmap with high clearance –Technique for adding clearance also works for articulated robots Start and goalInitial pathHigh-clearance path