High speed multibody dynamics

1. SimTK Simbody™
High speed multibody dynamics for
biosimulation
Michael Sherman (Sherm)
OpenSim Science Advisor Workshop, 2 June 2006

2. 2
Topics
• Motivation: DBPs
• Multibody mechanics
• Several S’s of SimTK Simulation
• Where does Simbody fit in?
• Simbody features
• Simbody release schedule

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RNA structure prediction

4. 4
Myosin dynamics

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Neuromuscular dynamics
F.C. Anderson, M. Pandy

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What do these have in common?
• Biological structures
• Dynamics well described by classical
physics — that is, F=ma
• They’re “chunky”

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Multibody systems
• Rigid parts …
• … mobilized by Joints
• … influenced by Forces
• … and restricted by Constraints.
• Key feature: motion is localized.

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Multibody mechanics

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Abstractions for classical physics
• Matter
• Energy
• Um …

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Matter
• Mass
• Spatial distribution
• Motion

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Abstract matter
• The rigid body
• What is a rigid body?
Bi
• Mass distribution: 10 constants
• Decorate w/geom & other props
• Ground is a (heavy) rigid body

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Abstract motion (1)
• The joint. What is it?
• Defines relative mobility btw 2 rigid bodies
• Examples
Ball
Slider
Pin
• Defines topology & mechanical
coordinates q

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Multibody system (1)
• Tree of bodies interconnected by joints

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Abstract motion (2)
• Oops! That’s a little too floppy …
• Restrict with constraints.
• Algebraic invariant relating q’s: g(q)=0
• Restricts allowable motion

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Multibody system (2)
• Constraints permit loops
g(q)= 0

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That’s it for rigid matter
• Rigid bodies + mobility – restrictions
• Solve for (response)
• Integrate for trajectory
• Still need forces …
but that’s another matter.

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Summary
• Rigid body mechanics is a solved problem
– Everything else is much harder and more
interesting
• But … the implementation is a bit tricky
• Simbody addresses that problem.

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Simbody in context

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Terminology: modeling creates a
“System”
System
Physical world
Modeling
• We’re not talking about modeling today
• A “System” is a computational embodiment of a
mathematical model

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Properties of a System
System
• Defines its
parametrization
• But … it is stateless.
• Given a State, performs
useful computations
State

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Studying a system
• System+State+Study  Simulation
Study
State
System
Results
states

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Under the hood: subsystems
• Interlocking computations
• System provides the “edge pieces”
Study
State
System
subsystem

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What’s in a multibody system?
• Matter and energy
• Simbody deals with matter
Forces
(User supplied)
Simbody
Multibody System
State

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Software stack
Lapack/Blas
Simmatrix
Simbody Forces
CVODE
Root finding
Spatial
operators
State
Multibody system Time
stepper
Projection
Study Results

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Software stack
(where’s Waldo?)
OpenSim

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Simbody™
a SimTK toolset for internal coordinate
(torsion angle) mechanics

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SimTK Core
GUI Tools | Documentation Tools | Installation
Modeling
Linear
Algebra
Multi
Body
Dynamics
Simbody
TAO
•
Integrator
ODE
DAE
Contact
Rigid
Penalty
•
Optimize
Sim Anneal
Genetic
SQ Prog Control
PD
PDEs
Solids
Fluids
Meshing
Monte
Carlo
Force
Fields

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Ancestry
IVM (Charles
Schweiters, NIH)
TAO (Chang,
Ruspini, Arachi Corp.)
Simbody
Spatial operator algebra,
Jain & Rodriguez, JPL
Feathersone, Australian
Natl. U.
Khatib lab, Stanford
Rosenthal &
Sherman,
Symbolic Dynamics,
Protein Mechanics
Linda Petzold,
UCSB
SD/FAST,
Pro/Mechanica, Imagiro
Thomas Kane,
Stanford
William Gear,
UIUC

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Simbody vs. SD/FAST
• All numerical – no compiler needed
• No dealing with, um, (a company)
– Completely open source, not GPL (MIT/BSD license)
– But can I <whatever>? Yes.
• O(N) all the time; targeted at 1000 bodies + 100 constraints
– Goal: within 2X of sd/fast O(n) on small problems, faster on big ones
• Structured as a set of O(N) operators
– Including Operational Space Control
• No internal state
• Shareable subsystems, systems & studies
– Mechanical models
– Forces, constraints, custom joints
– Numerical methods
• Coordinate projection instead of Baumgarte stabilization
• Advanced numerical integration (implicit/explicit/multistep)

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Simbody basic features
• A linkable library with nice API
• Solid theory; not a “game engine”
• Technology is internal coordinate mechanics
• Open & closed-chain models
• Forward/inverse kinematics & dynamics
• Parametrization/design studies
• Easily extensible (e.g., new joint types)
• Multiplatform binaries (Windows,Mac,Linux) & easily
portable to more
• Agnostic about forces & numerical methods, but …
• … will come with some good ones.

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Schedule
• Simbody 0.5 available now
– Very rough; brave souls only
– Basic functions; C++ only; lightly tested
– Everything will change before 1.0
• Simbody 1.0 (March 2007)
– Complete functionality; SD/FAST replacement
– Extensive testing & good documentation
– Stable API: C++, C, Fortran, SD/FAST compatible
– Integrated into several GUIs (OpenSim, ToRNAdo)
• Simbody 2.0 (~ +1 year)
– Analytic Jacobian in O(n2)
– High level modeling support
– Matlab/Java/Python wrapping
– (Even) faster
– Extensive libraries of force, constraint, joint, studies, reporters, etc.
Simbody info & downloads:
https://simtk.org/home/simbody

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Acknowledgments (software)
• Charles Schwieters
• Arachi Corp. (K.C. Chang & D. Ruspini)
• Paul Mitiguy
• Bryan Keller
• Jack Middleton
Simbody info & downloads:
https://simtk.org/home/simbody