Human interface Section PI Lab Titech Realtime Rigid

Human interface Section, P&I Lab, Titech Real-time Rigid Body Simulation for Haptic Interactions Based on Contact Volume of Polygonal Objects Shoichi Hasegawa, Makoto Sato Tokyo institute of technology P&I lab human interface section

Human interface Section, P&I Lab, Titech Haptic interaction q. Touch the virtual world q. User feels contact force from haptic interface Virtual Real

Human interface Section, P&I Lab, Titech Haptic interaction q. Touch the virtual world q. User feels contact force from haptic interface Virtual Real q. The touched object receives force from the user. q. The response : Dynamics

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

Human interface Section, P&I Lab, Titech Contact force F=mv N=Iw v(t+D t)= v(t) + F/m. Dt w(t+D t)=w(t) + I-1 NDt Contact force for dynamics simulation Haptic pointer Contact force to feedback user

Human interface Section, P&I Lab, Titech Contact model q. Normal force q. Prevent penetration q. Friction force (coulomb’s model) Normal force Friction force |ff | < |m 0 fn | q. Static friction l. Prevent sliding motion q. Dynamic friction l. Proportional to normal force |ff | = |mfn |

Human interface Section, P&I Lab, Titech Solving constraints(1) q Analytical method q. David Baraff SIGGRAPH `89 … (eq. of motion) (normal) (friction) Advantages Drawbacks q Object motions are stable. Wide time steps are affordable. q Solves constraints accurately. Completely rigid. q Much computation time for one step. O(n 3 ) q A virtual coupling is needed to connect a haptic interface. q Coulomb's friction model comes to NP complete problem.

Human interface Section, P&I Lab, Titech Solving constraints(2) q. Penalty method . penetration d，penetrating velocity d Spring Damper . slide l，sliding velocity l Spring Damper Advantages Drawbacks q Stability and rigidity requires small q Very fast for one step. O(n) time steps. q Direct connection to haptic interfaces. (Haptic interfaces also need this. ) q Coulomb’s friction model is easily q Treatment of large contact area realized. makes instability or takes a lot of q Integration of other models are easy. computation time. (e. g. Featherstone’s method)

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

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

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

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

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

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

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

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

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

Human interface Section, P&I Lab, Titech Integration of force q Penalty force q Dynamic friction force q Maximum static friction force Integrate forces from distributed model for each triangle.

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

Human interface Section, P&I Lab, Titech Evaluation q. Compare three simulators q. Proposed l. Penalty method ldistributed model. q. Point based l. Penalty method l. A model on the most penetrating point. q. Analytic l. Analytical method l. Open Dynamics Engine (Smith R. 2000)

Human interface Section, P&I Lab, Titech Computation time 60 Proposed simulator Point based method Analytical method Average computation time[ms] 50 3 40 5 30 20 13 10 0 0 5 10 Number of blocks 15

Human interface Section, P&I Lab, Titech Stability on normal force q. A cube on a floor. q. Measure angular momentum. 1 Angular momentum [Nms] Proposed method Point based penalty method Analytical method angular momentum 0 g=9. 8 m/s 2 m 3 0. 1 rad -1 0 1 time[s] 2

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

Human interface Section, P&I Lab, Titech Stick-slip motion q. State transition between static and dynamic friction makes stick-slip motion. m 0=0. 265 m =0. 160 Cardboard floor m 0=0. 265 m =0. 160 2. 0 kg weight wrapped by paper spring 400 N/m Friction force Tension force Velocity 0. 0642 m/s 2 kg 0. 0642 m/s friction force Spring 400 N/m

Human interface Section, P&I Lab, Titech Result Real world Analytical simulator -5 friction force position of object 1 Time[s] Proposed simulator 0 0 2 0. 1 Force[N] Position[m] 5 0 -5 1 Time[s] Point based simulator 2 0. 1 0 friction force position of object 0 2 0 5 -5 friction force position of object 0 friction force position of object Position[m] 0 0 Force[N] -5 Position[m] Force[N] 0 0. 1 5 Force[N] 0. 1 5 0 1 Time[s] 0 2

Human interface Section, P&I Lab, Titech Demo

Human interface Section, P&I Lab, Titech Conclusion q. Proposed a real-time rigid body simulator for haptic interaction q. Penalty method q. Fast update rate q. Pointed out a problem on a large contact area q. Solved the problem by integrating penalty over the intersection area q. Fast and accurate simulation was achieved.

Human interface Section, P&I Lab, Titech Thank you for listening q. Source codes, demos, movies. . . http: //springhead. info

Human interface Section, P&I Lab, Titech Dual Transform q. Finding the intersection of two convex(2) q. Dual Transformation l. Dual transformation transform a face into a vertex and a vertex into a face. l. Dual transformation’s dual transformation is original facet. Dual Transformation O O