Computation of Force Closure Grasps from Finite Contact Point Set

1. Computation of Force Closure Grasps from Finite Contact Point Set Nattee Niparnan Advisor: Dr. Attawith Sudsang

2. General Outline • The story so far: robotic grasping • What lies behind us: literature review • Where shall we go: the problem • Who walk along the same road: related work • Problem Detail • Grasping Basic • How do we reach the goal: attack point • Boring stuffs • work plan, objective, scopes, benefit

3. Robotic Grasping • To hold an object firmly • Prevent motion of an object

4. State of the Art

5. Ultimate Goal of Grasping • Sense the object • Calculate grasping position • Initiate a grasp

6. Grasping Components Task Model • Purpose of grasp • Power grasp • Dexterous grasp • Tool-specific grasp Objective Function Algorithm Grasp PlanningAlgorithm • Grasp Planning • Where to grasp • Physical of hands • Power • Degree of Freedom • Hand property Hand Model Grasping constraints

7. Example: Grasping a Hammer • Task: Moving a Hammer • Maximize stability • Task: Using a Hammer • Maximize head speed • Hand: Parallel Jaw Gripper • Hand: 4-fingered Hand

8. Grasp Planning Algorithm Input Output Object to be grasped Algorithm GraspingConfiguration

9. What comes before us 1800 1900 2000 Reuleaux Sumov 80’s 90’s 2006 • Grasping Definition • Hanafusa Asada ’77, ’79 • Ohwovoriore ‘80 • Salisbury ’82 • Asada By ’85 • Nguyen ’88, ’89 • Grasp Planning • Ponce et al. ’95 • Lui ’99 – ’05 • Li et al ’03 • Zhu Wang ’03 • Grasping Quality • Li Sastry ’88 • Kirkpatric et al. ’90 • Ferarri Canny ’92 • Trinkle ’92 • Existence of Grasps • Lakshminarayara ’78 • Mishra et al. ’87 • Markenscoff et al. ’89

10. Hand Model Robonaut Hand Utah/MIT Dextrous Hand Barrette Hand DLR Hand II

11. Task Model

12. Grasping Objective Function ObjectiveFunction Stability Accuracy Tolerance Minimizeeffect Tolerance Minimizeeffect • Kirkpatric et al • Ferrari Canny • Ponce et al • Lui et al • Ponce et al. • Nguyen • Ding et al

13. Conventional Grasping ObjectiveFunction Hand Model ObjectiveFunction Hand Model Task Model Hand Model Customized algorithm

14. Issues • No generally good grasp!!! • No general task model • No general hand model • Different measurement and constraints • Object modeling • Modeling accuracy

15. Object Modeling Curve ContactPoint • Modeling accuracy • Polygon • Linear • Low accuracy • Curve • High cost of curve fitting • Nonlinear • High Accuracy • Contact points • High number of contact points • Almost the same accuracy of curve • Practical Polygon

16. Where shall we go • New grasp planning framework Task Model Hand Model Use Contact Points (Model-less) Generalized Algorithm Take no a prioriknowledge

17. Where shall we go • Instead of finding one best grasp • Just find “firm” grasps • Find lots of grasps • Use no a priori knowledge of Task/Hand • Let task model and hand model choose appropriate grasp • Using contact points • Model-less input • a large number of input

18. Is It Hard? • Consider one single “firm grasp” problem in Polygonal model • Computational intensive • Linear Programming / Ray Shooting / Point Inclusion • Multiple grasping solution? • Almost unobtainable until recently • With contact point model? • Polygon  around 10-20 faces • Contact Point  around 1000 contact points • Much more computational extensive

19. Challenge • SPEED!!!

20. Usage of the Result • Given Task/Hand • enumerate solution to find the best one • O(n) • Result is associated to the object • Normal use usually involve multiple step • Regrasp

21. Problem Statement: First Draft • Given a set of contact points • Find • As many good grasps as possible • In a short time

22. one single “firm grasp” problem Still is an active topic Lui ’99 – ’05 Li et al ’03 Zhu Wang ’03 Borst et al ’03 Zhu et al ’04 Naïve Approach

23. Finding all solutions Combinatorial Problem 1000 points 4 fingers Must check O(N4)Search space Naïve Approach 1000 4

24. Contact point input Wallack Canny ‘94 Brost Goldberg ‘96 Wang ‘00 Multiple solutions van der Stappen ‘04 Who walk along the same road • Multiple solutions & Contact point Input • None...

25. Problem Detail

26. Grasping Basic • Force Closure • Formal definition of firm grasp • “Hand can influence the object such that any external disturbance can be nullified”

27. Influence of a hand • via contact points between a hand and an object • Described by • Contact positions ( r ) • Contact directions ( n )

28. Influence of a Contact Point • Force (contact direction) • Force vector ( f ) • Torque (contact position & direction) • Torque vector ( r x f )

29. Wrench • To combine force and torque into one component • Easier to describe • Wrench = force vector concatenates with torque vector • w = ( f, r x f ) • Model a contact point by a wrench

30. Wrench Example

31. Force Closure in terms of Wrenches • External disturbance can also be written as a wrench • Contact points can exert • Their respective wrenches • Also positive combinations of the wrenches • Force Closure = any wrench can be expressed by a positive combination of contact point wrenches GraspingHand Contact Points Forces &Torques Wrenches

32. Problem Transformation • Equivalence • Wrenches achieve force closure • Wrenches positively span R6 (or R3) • A Convex hull of wrenches contains the origin Force Closure? GraspingHand Contact Points Forces &Torques Wrenches Positively Spanning? The origin inside CH?

33. Positively Spanning • any vector can be expressed by a positive combination of given vectors

34. Point in Convex Hull • The origin is strictly inside the convex hull of contact point vectors • In the interior of the convex hull

35. Contact Model (Friction) • With friction • One contact point is associated with many wrenches

36. Check Point • Grasping problem is • A mathematical problem • A computational geometry problem • Emphasize on deriving of an efficient algorithm for reporting several solutions from contact point input

37. Problem Configuration Role Contact Model Object Model Frictional Finger Optimizer n fingers Frictionless Contact point Classifier 7 fingers (3D) Curved object 4 fingers (2D,3D) 3 fingers (2D) Polygon 2 fingers

38. The Problem: Revisited • Input: A set of contact points • Output: A set of grasping solutions • Combinatorial problem Sol Sol ContactPoints as wrenches 2D Frictional (3 fingers) Sol Sol Sol 2D Frictionless (4 fingers) Algorithm Sol Sol 3D Frictional (4 fingers) Sol Sol Sol 3D Frictionless (7 fingers)

39. How do we reach the goal • Exploit multiple solution nature of the problem • Try to use pre-computation • Sorting, searching, suitable data structure, etc. • Problem reformulation • Reduce dimension of wrench space

40. Work Plan • Study the works in the related fields • Preliminary works on a heuristic algorithm • Study a reformulation of the problem • In-depth study of grasp planning algorithms • Perform extensive comparison of various grasping condition • Develop algorithms • Comparison • Publish a journal article • Prepare and engage in a thesis defense

41. Recent Works • Fast Computation of 4-Fingered Force-Closure Grasps from Surface Points. Proc. of the IEEE/RSJ International Conf. on Intelligent Robots and Systems, pp 3692-3697, 2004. • Regrasp Planning of Four-Fingered Hand for Parallel Grasp of a Polygonal Object. Proc. of the IEEE International Conf. on Robotics and Automation, pp 791-796, 2005. • A Heuristic Approach for Computing Frictionless Force-Closure Grasps of 2D Objects from Contact Point Set. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 • Planning Optimal Force-Closure Grasps for Curved Objects by Genetic Algorithm. Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006 • 4-Fingered Force-Closure Grasps from Surface Points using Genetic Algorithm . Proc. of the IEEE International Conference on Robotics, Automation and Mechatronics, 2006

42. Objective • To develop efficient algorithms that report several force closure grasps from a set of finite contact points

43. Scope of the Research • Considers force closure grasping in both 2D and 3D in friction and frictionless case • Derived algorithms must work faster than an enumerative approach that uses the fastest computation • Performance measurement can be either an actual running time (in case of a heuristic algorithm) or a complexity analysis (in case of a complete algorithm)

44. Scope of the Research 2D Frictional (3 fingers) 2D Frictionless (4 fingers) 3D Frictional (4 fingers) 3D Frictionless (7 fingers) Compare with the best known “single solution” algorithm • Evidence of superiority • Proof of complexity analysis • Running Time Comparison • Evidence of superiority • Proof of complexity analysis • Running Time Comparison • Evidence of superiority • Proof of complexity analysis • Running Time Comparison • Evidence of superiority • Proof of complexity analysis • Running Time Comparison

45. Expected Contribution • Having algorithms that report several force closure grasps from a set of discrete contact points.

46. Thank You Comments are heartily welcomed

47. Coulomb Friction a = tan-1(u) fn ft = ufN

48. DLR Hand • Sensor per each finger • 3 joint position sensors: • 3 joint torque sensors: • 3 motor position/speed sensors: • 1 six-dimensional finger tip force torque sensor: • 3 motor temperature sensors: • 3 sensors for temperature compensation: integrated sensors