1. On Improving the Clearance for Robots in High-Dimensional Configuration Spaces Roland Geraerts and Mark Overmars IROS 2005

2. Outline Related work Retraction algorithm Algorithmic details Experiments Conclusions

3. Related Work Preprocessing techniques –Extract path from graph with cycles –Create path along the medial axis Post processing technique –Retract path to the medial axis (MA) d d

4. Related Work Preprocessing techniques –Extract path from graph with cycles –Create path along the medial axis Post processing technique –Retract path to the medial axis (MA)

5. Related Work Preprocessing techniques –Extract path from graph with cycles –Create path along the medial axis Post processing technique –Retract path to the medial axis (MA) Initial path Retraction to MA Retraction to ridges

6. Retraction Algorithm

7. Algorithmic Details – Metric

8. Algorithmic Details – Vector

9. Algorithmic Details – Validate maximum step size

10. Experimental Setup Pentium 4 (2.66GHz) Comparison of retraction techniques –Workspace (1 run) –Configuration space (100 runs) Environments / paths planar (2 dofs) hole (6 dofs) manipulator (6 dofs)

11. Experimental Results minavgtime initial workspace C-space 0.35 1.80 1.79 2.84 4.49 4.47 0.0 1.5 15.0 initial paths workspace C-space n.a. Clearance minavgtime initial workspace C-space 0.21 0.44 1.27 1.55 3.37 4.69 0.0 1.5 50.0 minavgtime initial workspace C-space 0.01 n.a. 0.16 0.13 n.a. 0.33 0.0 n.a. 60.0

12. Conclusions Clearance along paths is improved –No complicated data structures are needed –The algorithm can handle robots with an arbitrary amount of DOFs Running times are too high for online usage –Does not matter for high-cost environments –Smarter implementation decreased the running times by an order of magnitude

13. Current Work Retraction of a roadmap yields online performance Reachability roadmapRetracted roadmap

14. Current Work Retraction of a roadmap yields online performance Reachability roadmapRetracted roadmap