Adaptive Dynamics of Articulated Bodies Motivation Adaptive Dynamics

Adaptive Dynamics of Articulated Bodies

Motivation 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 10 -20 seconds per frame to make animators’ lives easy” Sunil Hadap, PDI/Dream. Works ðOptimal forward dynamics methods are too slow for numerous or complex articulated bodies

Contributions 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

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

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

Related work Simulation levels of detail • 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] Adaptive Dynamics of Articulated Bodies

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

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

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

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

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

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

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

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

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

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

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

Hybrid bodies Definitions 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)

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

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

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 =3 =-6 =6 =-3 = 96 =2 =-1 =1

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

Adaptive joint selection Acceleration simplification = 96 Adaptive Dynamics of Articulated Bodies -3 Compute the joint acceleration of the root

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

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

Adaptive joint selection Acceleration simplification = 96 = 81 Adaptive Dynamics of Articulated Bodies -3 -6 Compute its joint acceleration =6

Adaptive joint selection Acceleration simplification = 96 = 81 =9 Adaptive Dynamics of Articulated Bodies -3 =6 -6 = 36 Compute the acceleration metric values of its two children

Adaptive joint selection Acceleration simplification = 96 = 81 =9 Adaptive Dynamics of Articulated Bodies -3 =6 -6 = 36 Select the node with the highest acceleration metric value

Adaptive joint selection Acceleration simplification = 96 = 81 Adaptive Dynamics of Articulated Bodies -3 =6 -6 =9 = 36 6 Compute its joint acceleration

Adaptive joint selection Acceleration simplification = 96 Adaptive Dynamics of Articulated Bodies -3 =6 -6 =9 6 Stop because a user-defined sufficient precision has been reached

Adaptive joint selection Acceleration simplification = 96 Adaptive Dynamics of Articulated Bodies -3 =6 -6 =9 6 Four subassemblies with joint accelerations implicitly set to zero

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

Adaptive update mechanisms 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: 20 am 515 B)

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

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

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

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

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

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

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

Results Progressive dynamics Adaptive Dynamics of Articulated Bodies Average cost per time step N=300 5 ms N=100 1. 7 ms N=50 0. 7 ms N=20 0. 25 ms N=1 0. 02 ms Progressive dynamics of a 300 -link pendulum

Results Test application Adaptive Dynamics of Articulated Bodies MOVIE

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 Adaptive Dynamics of Articulated Bodies • View-dependent articulated-body dynamics • Perceptually-based simplification • Adaptive collision detection and response • Articulated-body control simplification

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

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

Thanks for your attention Adaptive Dynamics of Articulated Bodies For more information http: //gamma. cs. unc. edu/AD http: //www. inrialpes. fr/i 3 d/people/redon Implementation Sketch Tomorrow 11: 20 am Room 515 B