1. Human interface Section, P&I Lab, Titech Haptic interaction with rigid bodies by SPIDAR Shoichi Hasegawa Makoto Sato’s group Precision and Intelligence Lab. Tokyo Institute of Technology Shoichi Hasegawa Makoto Sato’s group Precision and Intelligence Lab. Tokyo Institute of Technology

2. Human interface Section, P&I Lab, Titech Contents qControl of SPIDAR qCharacteristics of SPIDAR qPosition measuring, Force displaying qUpdate rate of haptic rendering qRigid body simulation qContact force modeling qHaptic rendering for 6DOF qSimulation of articulated body qDemo qFor demonstration, please visit our booth.

3. Human interface Section, P&I Lab, Titech Hardware of SPIDAR SPIDAR Motor and encoder Present force to user. Measure length of string.

4. Human interface Section, P&I Lab, Titech Hardware performance qSPIDAR is the best device in performance qStiff and light SPIDARPHANTOM Shape Stiffness20N/mm1N/mm Weight50g75g

5. Human interface Section, P&I Lab, Titech qAny DOF and arrangements are designable. qSame control algorithm can be used 7DOF 8Strings 6DOF 8Strings 3DOF 4Strings Reconfigurable hardware

6. Human interface Section, P&I Lab, Titech Position measurement r p1p1 p2p2 p3p3 pmpm q1q1 q2q2 q3q3 qmqm l1l1 l2l2 l3l3 lmlm r : posture vector (x,y,z,  x,  y,  z ) p i :tied point of string on the grip q i :position of a motor l i :length of string

7. Human interface Section, P&I Lab, Titech Position measurement Jp#Jp# Jr#Jr# Solve r by iterative method

8. Human interface Section, P&I Lab, Titech Displaying force qSimple solution Directions of strings tensions 11 22 33 11 22 33 f

9. Human interface Section, P&I Lab, Titech Displaying force qDiscontinuous problem Tension Position Present the same force and move the pointer.

10. Human interface Section, P&I Lab, Titech Displaying force qSimple solution qUse smaller tension qLimitation qFinally Quadratic programming problem

11. Human interface Section, P&I Lab, Titech Displaying force 0 10 20 λ=0 λ=0.1 λ=0.2 λ=1.0 (0,0,0)(-0.2,-0.2,-0.2)(0.2,0.2,0.2) Position of end effecter [m] Full presentation areaPartial presentation area Calculated tension [N]

12. Human interface Section, P&I Lab, Titech Displaying force -0.100.10.20.3 0 2 4 6 Expanded figure λ= 0 λ= 0.1 λ= 0.2 λ= 0.3 x component of presentation force [N] x coordinate of end effecter [m]

13. Human interface Section, P&I Lab, Titech Haptic rendering and update rate Force display 1.Measure finger position 2.Collision detection and force calculation 3.Display the force 2 F=kx 3 Virtual World 1

14. Human interface Section, P&I Lab, Titech Haptic rendering and update rate qProblem on slow update rate time Finger position In the object Out of the object penetration Stiff objects (large k) make too much force F=kx

15. Human interface Section, P&I Lab, Titech Haptic rendering and update rate qSolution by fast update rate time Finger position In the object Out of the object Stable contact qStiff object requires fast update. qIt is commonly said that 1kHz or more is needed.

16. Human interface Section, P&I Lab, Titech Effect of fast update qAdvantage of stiffness qDisplay of friction disturbs display of shapes. But, enough stiffness realizes both. -0.2-0.100.1 0 0.2 -0.2-0.100.1 0 0.2 2N/mm, 1kHz20N/mm, 10kHz Trajectory of the haptic pointer on surfaces with friction (  =0.5) Virtual object (gear) Virtual object (gear)

17. Human interface Section, P&I Lab, Titech Real-time Rigid Body Simulation for Haptic Interactions

18. Human interface Section, P&I Lab, Titech qTouch the virtual world qUser feels contact force from haptic interface Haptic interaction VirtualReal

19. Human interface Section, P&I Lab, Titech qTouch the virtual world qUser feels contact force from haptic interface qThe touched object receives force from the user. qThe response : Dynamics Haptic interaction VirtualReal

20. Human interface Section, P&I Lab, Titech Video Darumaw

21. Human interface Section, P&I Lab, Titech Contact force Haptic pointer Contact force to feedback user Contact force for dynamics simulation F=mv N=I  v(t+  t)= v(t) + F/m  t  (t+  t)=  (t)  + I -1 N  t

22. Human interface Section, P&I Lab, Titech Contact model qNormal force qPrevent penetration qFriction force (coulomb’s model) qStatic friction lPrevent sliding motion qDynamic friction lProportional to normal force Normal force Friction force |f f | < |  0 f n | |f f | = |  f n |

23. Human interface Section, P&I Lab, Titech qAnalytical method qDavid Baraff SIGGRAPH `89 … Solving constraints(1) (eq. of motion) (normal) (friction) Advantages qObject motions are stable. Wide time steps are affordable. qSolves constraints accurately. Completely rigid. Drawbacks qMuch computation time for one step. O(n 3 ) qA virtual coupling is needed to connect a haptic interface. qCoulomb's friction model comes to NP complete problem.

24. Human interface Section, P&I Lab, Titech Solving constraints(2) qPenalty method penetration d ， penetrating velocity d. SpringDamper slide l ， sliding velocity l. SpringDamper Advantages qVery fast for one step. O(n) qDirect connection to haptic interfaces. qCoulomb’s friction model is easily realized. qIntegration of other models are easy. (e.g. Featherstone’s method) Drawbacks qStability and rigidity requires small time steps. (Haptic interfaces also need this.) qTreatment of large contact area makes instability or takes a lot of computation time.

25. Human interface Section, P&I Lab, Titech Problem on large contact area qWhere should we put spring-damper model? ? On the most penetrating point

26. Human interface Section, P&I Lab, Titech Problem on large contact area qWhere should we put spring-damper model? Top view ? On vertices

27. Human interface Section, P&I Lab, Titech Problem on large contact area qWhere should we put spring-damper model? Many points Will works well. But, it will takes much computation time and memory. ?

28. Human interface Section, P&I Lab, Titech Proposal for the problem qIntegrate forces from distributed model for each triangle. Distributed model !

29. Human interface Section, P&I Lab, Titech Steps qFinding Contact force: 1.Find contact point and normal. 2.Find the shape of the contact volume. 3.Integrate forces over the contact area.

30. Human interface Section, P&I Lab, Titech Contact detection qGilbert, Johnson, and Keerthi (GJK) algorithm. qFind closest points of two convex shapes. lA complex shape can be represented by a set of convex shapes. lAfter the contact, GJK can’t find closest points, So… t=t 0 t=t 1 New closest points

31. Human interface Section, P&I Lab, Titech Contact Analysis qContact part = Intersection of two convexes. qD. E. Muller and F.P.Preparata: “Finding the intersection of two convex” (1978) qFor given two convex and a point in the intersection. qFind the intersection.

32. Human interface Section, P&I Lab, Titech Contact Analysis(2) qFinding the intersection of two convex Half space representation

33. Human interface Section, P&I Lab, Titech Contact Analysis(3) qFinding the intersection of two convex(2) Dual transform Vertex of intersection Dual transform Half space representation Quick hull

34. Human interface Section, P&I Lab, Titech Integration of force qPenalty force qDynamic friction force qMaximum static friction force Integrate forces from distributed model for each triangle.

35. Human interface Section, P&I Lab, Titech Integration for a triangle p3p3 Force from spring model: Torque from from spring model: p1p1 p2p2 h3h3 h2h2 p3p3

36. Human interface Section, P&I Lab, Titech Static friction force qSpring-damper model for sliding constraint. Distributed model = = Two (translation and rotation) models

37. Human interface Section, P&I Lab, Titech Evaluation qCompare three simulators qProposed lPenalty method ldistributed model. qPoint based lPenalty method lA model on the most penetrating point. qAnalytic lAnalytical method lOpen Dynamics Engine (Smith R. 2000)

38. Human interface Section, P&I Lab, Titech Computation time 3 5 13 051015 0 10 20 30 40 50 60 Average computation time[ms] Number of blocks Proposed simulator Point based method Analytical method

39. Human interface Section, P&I Lab, Titech Stability on normal force qA cube on a floor. qMeasure angular momentum. angular momentum 2m32m3 g=9.8m/s 0.1rad 012 0 1 time[s] Angular momentum [Nms] Proposed method Point based penalty method Analytical method

40. Human interface Section, P&I Lab, Titech Motion of top

41. Human interface Section, P&I Lab, Titech Stick-slip motion qState transition between static and dynamic friction makes stick-slip motion. Spring 400N/m 2kg 0.0642m/s friction force 2.0kg weight wrapped by paper Tension force Friction force Cardboard floor   =0.265  =0.160 spring 400N/m Velocity 0.0642m/s   =0.265  =0.160

42. Human interface Section, P&I Lab, Titech Result 012 -5 0 5 0 0.1 Force[N] Time[s] Position[m] Real world position of object friction force 012 -5 0 5 0 0.1 Force[N] Time[s] Position[m] Proposed simulator 012 -5 0 5 0 0.1 Force[N] Time[s] Position[m] Point based simulator 012 -5 0 5 0 0.1 Force[N] Time[s] Position[m] Analytical simulator position of object friction force position of object friction force position of object friction force

43. Human interface Section, P&I Lab, Titech Both hand 6DOF haptic interaction

44. Human interface Section, P&I Lab, Titech Update rate of the simulation q Update rate > 300Hz Computation time [ms] Simulation iterations Contact detection Contact volume analysis Force integration D C B 1 2 3 A The computation time for the Simulation A B C D

45. Human interface Section, P&I Lab, Titech Articulated body qConstraints of joints should strictly be kept. qSmall errors can be magnified by mechanisms. qTo solve generic constraints, we need much computation time. But, qEfficient computation method is affordable under some restriction of structure. qRestriction: Tree structure without ring one ring many rings

46. Human interface Section, P&I Lab, Titech Generic method A’s eq of motion ： Constraint of 1 ： B’s ・・・・・・・・・・・・・・・・ So, we can write: Many 0 ， sparse matrix: There can be fast calculation method. 1 2 3 A B C D

47. Human interface Section, P&I Lab, Titech Featherstone’s method 1.Suppose whole rigid bodies are one rigid body. Then find the acceleration. Find the acceleration of A 2.Suppose two rigid bodies of A and others. 1.Find the force applied to the joint 1 2.Find the acceleration of B 3.Suppose three rigid bodies of A and B and others. … 1 2 3 A B C D 1 2 3 A B C D

48. Human interface Section, P&I Lab, Titech Featherstone’s method qLook the method from a viewpoint of the sparse matrix: 1 2 3 A B C D 1. From the leaves to the root we merge M 2.Find acceleration.

49. Human interface Section, P&I Lab, Titech Featherstone’s method 3.Find from the root to the leaves.

50. Human interface Section, P&I Lab, Titech Demo

51. Human interface Section, P&I Lab, Titech Our booth （１ F ） We are here 5 minutes walk