Mixing deformable and rigid-body mechanics simulation

Julien Lenoir

Sylvère Fonteneau

Alcove Project - INRIA Futurs - LIFL - University of Lille (France)

1/23

Outlines

• Introduction

• Proposition for articulated bodies

• A generic framework

• Results

2/23

Introduction - Objectives

• A physically based simulation of multiple objects (rigid-bodies and/or deformable bodies) with different physical formalism

• - Constrained these objects = articulated bodies- propose a generic simulation framework dedicated to articulated bodies.

5/23

Previous Works

• [TR 97 Baraff and Witkin]– Constrained different simulators– Iterative algorithm

• [Visual Computer 03 Jansson and Vergeest]– One object = set of mass-spring/rigid bodies

elements

4/23

Outlines

• Previous works, Objectives

• Proposition for articulated bodies

• A generic framework

• Results

6/23

Dynamics simulation

• One object:– Dynamics simulation => ODE of order 2

q degrees of freedom, f external contributionmatrices: M (mass), C (viscosity), K (rigidity)

– M.A=B

• Multiple bodies simulationIndependent simulation

without constraints

fKqqCqM

nnn B

B

A

A

M

M

111

0

0

7/23

Example of heterogeneous simulation

• Dynamics spline [Remion99]:Lagrange physical formalism,

continuous model

• Rigid-body :Newton-Euler formalism

• Mass spring net :Newton formalism, discrete model

z

y

x

z

y

x

spline

spline

spline

B

B

B

A

A

A

M

M

M

00

00

00

13/23

ii

ii

IM

FG

I

mId

)(0

03

nn

n F

F

F

P

P

P

m

m

m

2

1

2

1

2

1

000

000

000

A generic framework

• Example of dynamics bodies

16/23

Constrain a dynamic simulation

• The overall constraints method:– Constraint between objects– Lagrange multipliers =>– Baumgarte scheme

=> L.A=E

• 1 lagrange multiplier (λi) for 1 constraint= 1 condition on a degree of freedom(examples: fixed point, plan)

0

M TL

EL

BA

8/23

Constrain a dynamic simulation

• Resolution:Decomposition of the acceleration A [Remion00]:– tendency At (computed by each object)

– correction Ac

)(

)(1

1

Tc

tT

t

LMA

LAELLM

BMA

9/23

Constant

Variable

Constrain a dynamic simulation

• Resolution:

matrices update automaton

start

L & M-1.Lt

Local initializations

L.M-1.Lt

Global initialization

Initialization Running

Global(mechanics solver)

Local(objects)

resol

ready

updateL & M-1.Lt

UpdateL.M-1.Lt

no change

local changes global

change

ready

10/23

Outlines

• Previous works, Objectives

• Proposition for articulated bodies

• A generic framework

• Results

11/23

A generic framework

Model nModel n RotationRotation

ArticulatedBodiesArticulatedBodies

ArticulableBodyArticulableBody ConstraintConstraint

Model 1Model 1

Model 2Model 2

…

FixedPointFixedPoint

SlideSlide

…

12/23

A generic framework• Constraint example: fixed point between two

objects (o1,o2)P(o1)=P(o2)

– Spline:

P(spline)=P(s,t)=– Rigid Body:

P(rigid body)=(Px,Py,Pz)T

– Mass-spring:

P(mass-spring)=Pi

( ) ( )i ii

b s q t

17/23

A generic framework

• Constraint insertion example– fixed point between spline and rigid object :

Prigid body(M)=Pspline(0.5,t)

– Baumgarte : 2

2 10C C C

t t

1 1 1: (0.5) ( ) where is mass centeri ii

C OG G M b q t G

11 1 1 1 12

2 1(0.5) ( ) ( )i i

i

OG G M b q t C C G Mt t

ELA

18/23

Outlines

• Previous works, Objectives

• Proposition for articulated bodies

• A generic framework

• Results

19/23

• Soft rings articulation (3 ms on a Bi-Xeon 2,4 GHz)

Results

20/23

• Rigid-bodies articulation (2 ms)

Results

21/23

• Swing articulation (15 ms)

Results

22/23

Conclusion

• Proposition to constrain multiple bodies with different physical formalism

• Drawback : Baumgarte scheme => constraints not necessarily verified at each simulation step

23/23