Adaptive Dynamics of Articulated Bodies

Articulated bodies in Computer Graphics – Humans, hair, animals – Trees, forests, grass – Deformable bodies – Molecular graphics – … Motivation

Adaptive Dynamics of Articulated Bodies Forward dynamics Optimal solutions are linear Production constraints “Dynamics computations should take less than seconds per frame to make animators’ lives easy” Sunil Hadap, PDI/DreamWorks Motivation  Optimal forward dynamics methods are too slow for numerous or complex articulated bodies

Adaptive Dynamics of Articulated Bodies Forward dynamics Adaptive forward dynamics – Specify the number of degrees of freedom – Only this number of degrees of freedom is simulated – The most relevant degrees of freedom are automatically found Contributions

Adaptive Dynamics of Articulated Bodies Hybrid bodies – Novel articulated-body representation – To reduce the number of degrees of freedom Adaptive joint selection – Novel customizable motion metrics – To determine the most relevant degrees of freedom Adaptive update mechanisms Contributions

Adaptive Dynamics of Articulated Bodies Related work Hybrid bodies Adaptive joint selection Adaptive update mechanisms Results Outline

Adaptive Dynamics of Articulated Bodies Related work Hybrid bodies Adaptive joint selection Adaptive update mechanisms Results Outline

Adaptive Dynamics of Articulated Bodies Optimal algorithms – [Hollerbach 1980] – [Featherstone 1987] – [McMillan and Orin 1995] – [Baraff 1996] Parallel algorithms – [Fijany et al. 1995] – [Featherstone 1999] Divide and Conquer Algorithm (DCA) – [Yamane and Nakamura 2002] Related work Forward dynamics of articulated bodies

Adaptive Dynamics of Articulated Bodies Human motion – [Carlson and Hodgins 1997] – [Popovic and Witkin 1999] Plant motion – [Perbet and Cani 2001] – [Beaudoin and Keyser 2004] Hair modeling – [Bertails et al. 2003] – [Ward et al. 2003] Related work Simulation levels of detail

Adaptive Dynamics of Articulated Bodies View-dependent dynamics – [Chenney and Forsyth 1997] – [Chenney et al. 1999] – [Chenney et al. 2001] Articulated-body motion simplification – [Faure 1999] – [Redon and Lin 2005] – Adaptive quasi-statics Related work Simulation levels of detail

Adaptive Dynamics of Articulated Bodies Related work Hybrid bodies Adaptive joint selection Adaptive update mechanisms Results Outline

Adaptive Dynamics of Articulated Bodies Recursive definition Hybrid bodies Featherstone’s DCA An articulated body is formed by assembling two articulated bodies

Adaptive Dynamics of Articulated Bodies Hybrid bodies Featherstone’s DCA An articulated body is formed by assembling two articulated bodies Recursive definition

Adaptive Dynamics of Articulated Bodies Recursive definition Hybrid bodies Featherstone’s DCA The assembly tree of an articulated body Rigid bodies The complete articulated body Pairs of rigid bodies

Adaptive Dynamics of Articulated Bodies Recursive definition Articulated-body equation Hybrid bodies Featherstone’s DCA Body Accelerations Inverse inertias and cross-inertias Applied Forces Bias accelerations

Adaptive Dynamics of Articulated Bodies Hybrid bodies Featherstone’s DCA The cross-coupling inverse inertia describes the effect of a force applied to body 2, on the acceleration of body 1 Recursive definition Articulated-body equation

Adaptive Dynamics of Articulated Bodies Hybrid bodies Featherstone’s DCA The bias acceleration is the acceleration of body 1 when no forces are applied Recursive definition Articulated-body equation

Adaptive Dynamics of Articulated Bodies Recursive definition Articulated-body equation Two main steps – Compute the articulated-body coefficients (  ) Hybrid bodies Featherstone’s DCA Inverse inertias Bias accelerations

Adaptive Dynamics of Articulated Bodies Recursive definition Articulated-body equation Two main steps – Compute the joint accelerations and forces (  ) Hybrid bodies Featherstone’s DCA Joint acceleration Kinematic constraint forces

Adaptive Dynamics of Articulated Bodies Active region Hybrid bodies Definitions The active region contains the mobile joints

Adaptive Dynamics of Articulated Bodies Active region Hybrid-body coefficients Hybrid bodies Definitions Rigidify joint Articulated-body coefficients Hybrid-body coefficients

Adaptive Dynamics of Articulated Bodies Active region Hybrid-body coefficients Hybrid-body simulation – Same steps as articulated-body simulation – Computations restricted to a sub-tree (cf. paper) Hybrid bodies Definitions

Adaptive Dynamics of Articulated Bodies Related work Hybrid bodies Adaptive joint selection Adaptive update mechanisms Results Outline

Adaptive Dynamics of Articulated Bodies Acceleration metric Velocity metric Adaptive joint selection Motion metrics

Adaptive Dynamics of Articulated Bodies Theorem The acceleration metric value of an articulated body can be computed before computing its joint accelerations Adaptive joint selection Motion metrics

Adaptive Dynamics of Articulated Bodies Example Adaptive joint selection Motion metrics =6 =-3=2 =-1=1 =-6=3 = 96

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification = 96 Compute the acceleration metric value of the root

Adaptive Dynamics of Articulated Bodies = Compute the joint acceleration of the root Adaptive joint selection Acceleration simplification

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification = 96 = 6 = 81 Compute the acceleration metric values of the two children -3

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification = 96 Select the node with the highest acceleration metric value -3 = 6 = 81

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification = 96 Compute its joint acceleration = 81 = 6

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification = 96 = 9= 36 Compute the acceleration metric values of its two children = 6 = 81

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification = 96 = 9= = 6 = 81 Select the node with the highest acceleration metric value = 36

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification = 96 = 9= = 6 = 81 Compute its joint acceleration 6

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification Stop because a user-defined sufficient precision has been reached = 96 = 9 = 6

Adaptive Dynamics of Articulated Bodies Adaptive joint selection Acceleration simplification Four subassemblies with joint accelerations implicitly set to zero = 96 = 9 = 6

Adaptive Dynamics of Articulated Bodies Related work Hybrid bodies Adaptive joint selection Adaptive update mechanisms Results Outline

Adaptive Dynamics of Articulated Bodies Position-dependent coefficients Hierarchical state representation [Redon and Lin 2005] Adaptive update mechanisms

Adaptive Dynamics of Articulated Bodies Velocity-dependent coefficients Linear coefficients tensors (Implementation sketch tomorrow 11:20am 515B) Adaptive update mechanisms

Adaptive Dynamics of Articulated Bodies Related work Hybrid bodies Adaptive joint selection Adaptive update mechanisms Results Outline

Adaptive Dynamics of Articulated Bodies Results Adaptive selection MOVIE Adaptive joint selection example (10x speed-up)

Adaptive Dynamics of Articulated Bodies Results Adaptive joint selection Adaptive joint selection example (10x speed-up)

Adaptive Dynamics of Articulated Bodies Results Time-dependent simplification One color per sub-assembly

Adaptive Dynamics of Articulated Bodies Results Time-dependent simplification One color per sub-assembly

Adaptive Dynamics of Articulated Bodies Results Adaptive selection MOVIE Time-dependent simplification

Adaptive Dynamics of Articulated Bodies Progressive dynamics of a 300-link pendulum Results Progressive dynamics

Adaptive Dynamics of Articulated Bodies Progressive dynamics of a 300-link pendulum Results Progressive dynamics N=300 N=20 N=100 N=50 N=1 Number of active joints

Adaptive Dynamics of Articulated Bodies Progressive dynamics of a 300-link pendulum Results Progressive dynamics 5ms 0.25ms 1.7ms 0.7ms 0.02ms Average cost per time step N=300 N=20 N=100 N=50 N=1

Adaptive Dynamics of Articulated Bodies Results Test application MOVIE

Adaptive Dynamics of Articulated Bodies Conclusion Summary A new adaptive dynamics algorithm – Hybrid bodies – Adaptive joint selection – Adaptive update mechanisms Precision / Performance trade-off

Adaptive Dynamics of Articulated Bodies Conclusion Applications and future research View-dependent articulated-body dynamics Perceptually-based simplification Adaptive collision detection and response Articulated-body control simplification

Adaptive Dynamics of Articulated Bodies Acknowledgements Roy Featherstone Miguel A. Otaduy James T. Pineda Anonymous reviewers

Adaptive Dynamics of Articulated Bodies Acknowledgements Army Research Office Intel Corporation National Science Foundation Office of Naval Research

Adaptive Dynamics of Articulated Bodies Thanks for your attention For more information Implementation Sketch Tomorrow 11:20am Room 515B