1. Regrasp planning of a polygon in the plane for a 4-fingered handการวางแผนการเปลี่ยนการจับวัตถุหลายเหลี่ยมบนระนาบด้วยมือที่มีสี่นิ้ว โดย นายธนะธร พ่อค้า 457 03433 21 อาจารย์ที่ปรึกษา ดร.อรรถวิทย์ สุดแสง

2. Outline • Introduction • Condition for grasping • Switching graph • Implementation and results • Conclusion

3. Introduction • Regrasp • Force-closure • Equilibrium • Concurrent grasp • Parallel grasp • 2-fingered grasp • Switching graph

4. Introduction • Switching diagram concurrent grasps 2-fingered grasps parallel grasps

5. Condition for grasping • Sufficient condition a1 C1   a3  a1 a2 C3 a2 C2 a3 “concurrent grasp” three-finger equilibrium grasp

6. Eb Ec Ea Switching graph • Point in the plane can represent a set of grasps. • Independent contact region Ec Eb Ec Eb Fa,b,c x0 Ea Ea

7. b c a d Switching graph Fa,b,c Fa,b,d a,b,c a,b,d

8. Switching graph • Finger aligning Fb,d,e Fa,b,c q1 Fa,b,d q2 . q1 . q2 Fa,b,d

9. i 2 2 2 2 j Switching graph i C B A 2 2 j O(n3), n is the number of polygon’s edges.

10. Condition for grasping two-finger equilibrium grasp

11. Eb Fa,b Ea Switching graph • Focus cell Eb Eb x0 Ea Ea ( - 2 ,  + 2 )

12. Ea Ed Eb Fa,c Fb,c,d . . . Fa,c Fb,c,d q q q Ec Ec 2 1 4 3 Switching graph • Finger switching

13. Fa,b Fb,c,d . . q1 q2 Switching graph • Finger aligning Eb q1 q2 Fa,b Ea

14. i 2 2 Switching graph j O(n2), n is the number of polygon’s edges.

15. Condition for grasping • three-finger equilibrium grasp with parallel contact forces middle

16. Condition for grasping  

17. Condition for grasping . . x1 x2 . x0

18. Eb Ec Switching graph • Set of parallel grasps Ec Eb Ea

19. Eb Eb Ec Ec Switching graph • Finger switching Ed Ea

20. Eb Ed Eb Ed Ea Ec Ec Switching graph • Finger switching

21. Ea Ed Ed Ea Eb Ec Eb Ec Switching graph • Finger switching

22. Eb Eb Fa,b Ea Ea Switching graph • Finger switching

23. Eb Ec Eb Fb,d Ea Ed Switching graph • Finger switching

24. Eb Eb Ec Fa,b Ea Switching graph • Finger switching Eb Ec Ea

25. Switching graph • Finger aligning

26. j i 2 Switching graph β+  - 2θ β β+  - θ α+θ β+θ α α+  + θ α+  + 2θ O(n3), n is the number of polygon’s edges.

27. Switching graph b,d,f a,b,d g,i,j a,b,c b,e g,h i,j,k k,l j,k,l

28. Implementation • Polygon objects • 1.8 GHz CPU • C++ & LEDA

29. Results • Concurrent grasp

30. Results • Parallel grasp

31. Results • Concurrent & 2-fingered grasp

32. Results • Parallel & 2-fingered grasp

33. Results • All grasps

34. Results • Connected components

40. Conclusion • Regrasp planning • Concurrent grasp • 2-fingered grasp • Parallel grasp • Dexterous manipulation • Other conditions for parallel grasp • Random approach

41. Future works • Optimal grasp • Independent contact region • Minimum force required for resist external force • Closest distance between centroid of contact points and center of mass • Other objects • Polyhedral object • Curved object

42. Thank you