Realtime Rigid Body Simulation Based on Volumetric Penalty Method Shoichi Hasegawa, Nobuaki Fujii, Y

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Real-time Rigid Body Simulation Based on
Volumetric Penalty MethodShoichi Hasegawa,
Nobuaki Fujii, Yasuharu Koike, Makoto
SatoPrecision and Intelligence Laboratory, Tokyo
Institute of Technologyhttp//sklab-www.pi.titech
.ac.jp hase_at_hi.pi.titech.ac.jp

• Goal
• Real-time rigid body simulator 200Hz or faster
  update rate for Haptic.
• For natural virtual object manipulations.
• Haptic interfaces have been developed. It
  requires fast update.
• Objects should move under the law of motion.
• For simple virtual world for educational /
  training / entertainment applications.
• Choice of algorithm for contact solver
• D. Baraff Analytical methods for dynamic
  simulation of non-penetrating rigid bodies
  (1989)
• B. Mirtich Impulse-based Simulation of Rigid
  Bodies (1995)
• Penalty methods, which convert constraints into
  penalty force by spring and damper model. H.
  Keller Virtual Mechanics (1993)
• Invention
• Previous penalty method regards contacts occurs
  at a point. We regards contact area and integrate
  forces

Normal forces
Friction forces

• Where should we put spring damper models?
• Put on the most penetrating point?
• Integrate penetration over the contact area

• Where should we put Coulomb s friction model?
• Put on the application point of the normal force?
• Integrate forces from Coulomb model over the
  contact area

Unstable
Contact area (current)
Stable

• Proposed simulator
• The simulation step is consists from following
  procedure

1 Contact detection
3 Integrate normal forces and torques

• The intersection is convex polyhedron
• We integrate penalty by each face.

• Find collision normal and common
  point Gilbert, Johnson, and Keerthi (GJK)
  algorithm

?
Upper bound
Lower bound
Intersecting part
2 Contact Analysis

• Find penetrating part Intersection of two
  convexes

Half space representation
Dual transform
Vertex of intersection
Convex hull
Dual transform
(Fs force from spring models, Ms torque from
spring models)
D. E. Muller and F.P.Preparata 1978
2

• Proposed simulator (continue)

4 Friction forces and torques

• Dynamic friction
• Integrate dynamic friction force (fdy) over the
  contact area
• Static friction
• Object does not slip Constraint ? Convert into
  penalty force.
• State Transition

fdy
vp
Spring-damper model for translation
Spring-damper model
Object at previous step
Spring-damper model for rotation
Object at current step
Distributed models can be replaced by two models
Static friction force gt maximum friction force (
m0/m Dynamic friction force)
Static friction
Dynamic friction
Static friction force lt dynamic friction force

• Evaluation
• Compare stability on two simulators
• Proposed Integrate forces over the intersection.
• Simple Spring model is put on the most
  penetrating point.
• Simulate same virtual world

• Result

• Haptic interaction
• Choose a virtual object as a proxy object of
  haptic interface

Display force and torque
Set position and orientation
Haptic interface(SPIDAR)

• Conclusion
• We proposed a rigid body motion simulator which
  can
• Run at haptic rate (200Hz or faster) with simple
  virtual world.
• Treat dynamic and friction forces.