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

3. 3 RNA structure prediction

4. 4 Myosin dynamics

5. 5 Neuromuscular dynamics F.C. Anderson, M. Pandy

6. 6 What do these have in common? Biological structures Dynamics well described by classical physics — that is, F=ma They’re “chunky”

7. 7 Multibody systems Rigid parts … … mobilized byJoints … influenced byForces … and restricted byConstraints. Key feature: motion is localized.

8. 8 Multibody mechanics

9. 9 Abstractions for classical physics Matter Energy Um …

10. 10 Matter Mass Spatial distribution Motion

11. 11 Abstract matter The rigid body What is a rigid body? BiBi Mass distribution: 10 constants Decorate w/geom & other props Ground is a (heavy) rigid body

12. 12 Abstract motion (1) The joint. What is it? Defines relative mobility btw 2 rigid bodies Examples Ball SliderPin Defines topology & mechanical coordinates q

13. 13 Multibody system (1) Tree of bodies interconnected by joints

14. 14 Abstract motion (2) Oops! That’s a little too floppy … Restrict with constraints. Algebraic invariant relating q’s: g(q)=0 Restricts allowable motion

15. 15 Multibody system (2) Constraints permit loops g(q)= 0

16. 16 That’s it for rigid matter Rigid bodies + mobility – restrictions Solve for (response) Integrate for trajectory Still need forces … but that’s another matter.

17. 17 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.

18. 18 Simbody in context

19. 19 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

20. 20 Properties of a System System Defines its parametrization But … it is stateless. Given a State, performs useful computations State

21. 21 Studying a system System+State+Study  Simulation Study State System Results states

22. 22 Under the hood: subsystems Interlocking computations System provides the “edge pieces” Study State System subsystem

23. 23 What’s in a multibody system? Matter and energy Simbody deals with matter Forces (User supplied) Simbody Multibody System State

24. 24 Software stack Lapack/Blas Simmatrix SimbodyForces CVODE Root finding Spatial operators State Multibody system Time stepper Projection Study Results

25. 25 Software stack (where’s Waldo?) OpenSim

26. 26 Simbody™ a SimTK toolset for internal coordinate (torsion angle) mechanics

27. 27 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

28. 28 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

29. 29 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 ? 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)

30. 30 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.

31. 31 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(n 2 ) –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

32. 32 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