Real-time Rigid Body Simulation for Haptic Interactions Based on Contact Volume of Polygonal Objects

1
Real-time Rigid Body Simulationfor Haptic
Interactions Based onContact Volume of Polygonal
Objects

• Shoichi Hasegawa, Makoto Sato
• Tokyo institute of technology
• PI lab human interface section

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Haptic interaction

• Touch the virtual world
• User feels contact force from haptic interface

Virtual
Real
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Haptic interaction

• Touch the virtual world
• User feels contact force from haptic interface
• The touched object receives force from the user.
• The response Dynamics

Virtual
Real
4
Video Darumaw
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Contact force
Fmv NIw v(tD t) v(t) F/mDt w(tD t)w(t)
I-1NDt
Haptic pointer
Contact force fordynamics simulation
Contact forceto feedback user
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Contact model
Normal force

• Normal force
• Prevent penetration
• Friction force (coulombs model)
• Static friction
• Prevent sliding motion
• Dynamic friction
• Proportional to normal force

Friction force
ff lt m0fn
ff mfn
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Solving constraints(1)

• Analytical method
• David Baraff SIGGRAPH 89

• Advantages
• Object motions are stable.Wide time steps are
  affordable.
• Solves constraints accurately.Completely rigid.

• Drawbacks
• Much computation time for one step. O(n3 )
• A virtual coupling is needed to connect a haptic
  interface.
• Coulomb's friction model comes to NP complete
  problem.

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Solving constraints(2)

• Penalty method

.
penetration d,penetrating velocity d
Spring
Damper
.
slide l,sliding velocity l
Spring
Damper

• Advantages
• Very fast for one step. O(n)
• Direct connection to haptic interfaces.
• Coulombs friction model is easily realized.
• Integration of other models are easy. (e.g.
  Featherstones method)

• Drawbacks
• Stability and rigidity requires small time
  steps.(Haptic interfaces also need this.)
• Treatment of large contact area makes instability
  or takes a lot of computation time.

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Problem on large contact area

• Where should we put spring-damper model?

On the most penetrating point
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Problem on large contact area

• Where should we put spring-damper model?

?
On vertices
Top view
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Problem on large contact area

• Where should we put spring-damper model?

Will works well. But, it will takes
muchcomputation time and memory.
?
Many points
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Proposal for the problem

• Integrate forces from distributed model for each
  triangle.

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Steps

• Finding Contact force
• Find contact point and normal.
• Find the shape of the contact volume.
• Integrate forces over the contact area.

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Contact detection

• Gilbert, Johnson, and Keerthi (GJK) algorithm.
• Find closest points of two convex shapes.
• A complex shape can be represented by a set of
  convex shapes.
• After the contact, GJK cant find closest points,
  So

tt0
tt1
New closest points
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Contact Analysis

• Contact part Intersection of two convexes.
• D. E. Muller and F.P.PreparataFinding the
  intersection of two convex (1978)
• For given two convex and a point in the
  intersection.
• Find the intersection.

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Contact Analysis(2)

• Finding the intersection of two convex

Half space representation
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Contact Analysis(3)

• Finding the intersection of two convex(2)

Half space representation
Dual transform
Vertex of intersection
Dual transform
Quick hull
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Integration of force

• Penalty force
• Dynamic friction force
• Maximum static friction force

Integrate forces from distributed model for each
triangle.
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Static friction force

• Spring-damper model for sliding constraint.

Two (translation and rotation) models
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Evaluation

• Compare three simulators
• Proposed
• Penalty method
• distributed model.
• Point based
• Penalty method
• A model on the most penetrating point.
• Analytic
• Analytical method
• Open Dynamics Engine (Smith R. 2000)

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Computation time
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Stability on normal force

• A cube on a floor.
• Measure angular momentum.

1
Proposed method
Point based penalty method
Analytical method
Angular momentum Nms
0
-1
0
1
2
times
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Motion of top
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Stick-slip motion

• State transition between static and dynamic
  friction makes stick-slip motion.

m00.265 m 0.160
2kg
0.0642m/s
Spring 400N/m
friction force
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Result
Real world
Analytical simulator
0.1
0.1
5
5
ForceN
Positionm
Positionm
ForceN
0
0
-5
-5
0
0
0
1
2
0
1
2
Times
Times
Proposed simulator
Point based simulator
0.1
0.1
5
5
ForceN
Positionm
ForceN
Positionm
0
0
-5
-5
0
0
0
1
2
0
1
2
Times
Times
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Demo
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Conclusion

• Proposed a real-time rigid body simulator for
  haptic interaction
• Penalty method
• Fast update rate
• Pointed out a problem on a large contact area
• Solved the problem by integrating penalty over
  the intersection area
• Fast and accurate simulation was achieved.

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Thank you for listening

• Source codes, demos, movies...
• http//springhead.info

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Dual Transform

• Finding the intersection of two convex(2)
• Dual Transformation
• Dual transformation transform a face into a
  vertex and a vertex into a face.
• Dual transformations dual transformation is
  original facet.