1 / 33

Adaptive dynamics for Articulated Bodies

Adaptive dynamics for Articulated Bodies. Articulated Body dynamics. Optimal forward dynamics algorithm Linear time complexity e.g. Featherstone’s DCA algorithm Not efficient enough for many DoF systems. Articulated body. Handle. B. A.

vin
Download Presentation

Adaptive dynamics for Articulated Bodies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Adaptive dynamics for Articulated Bodies

  2. Articulated Body dynamics • Optimal forward dynamics algorithm • Linear time complexity • e.g. Featherstone’s DCA algorithm • Not efficient enough for many DoF systems

  3. Articulated body Handle B A Handles: positions where external forces can be applied

  4. Articulated body Principal joint Created recursively by joining two articulated bodies C

  5. The complete articulated body Rigid bodies Articulated body C A B Tree representation of an articulated body

  6. Featherstone’s DCA • Articulated-body equation • Change of in causes a change of in Body Accelerations Inverse inertias and cross-inertias Applied Forces Bias accelerations

  7. Articulated body equations Kinematic constraint force at the principal joint of C

  8. Featherstone’s DCA Algorithm • Update body velocity and position • Main pass: Compute • Bottom-up pass • Solve articulated body equation by back substitution • Top down pass

  9. Main Pass • For internal nodes • For leaf nodes dependent on motion subspace dependent on active forces

  10. Back substitution • Receive from parent • Compute joint acceleration and using • Send to A and to B

  11. Adaptive Dynamics • Simulate n most “important” joints • Sacrifice amount of accuracy • Other joints are rigidified • “Important” and “accuracy” measures based on some motion metric

  12. Hybrid body

  13. Hybrid body

  14. Multilevel forward dynamics algorithm • Compute body velocity and position only in active region • Compute • Same as DCA for active nodes • Do not recompute for rigid nodes • (*) Compute in force update region using • Back substitute only in active region • Recompute hybrid body (at a different rate than the simulation timestep) * For the metric we discuss later, this step is not performed

  15. Motion metrics • Acceleration metric • Velocity metric are SPD matrix i.e. metrics correspond to weighted sum of squares

  16. Computing motion metric • TheoremThe acceleration metric value of an articulated body can be computed before computing its joint accelerations

  17. Computing • In active region compute using:

  18. Computing • Do not recompute at passive nodes • At passive nodes compute (velocity dependent coefficients) using linear coefficient tensors (not dependent on velocity) • Constant time

  19. Computing the hybrid body • Compute in fully articulated state • Determine transient hybrid body based on acceleration metric • Recompute acceleration for transient hybrid body • Compute velocity metric to determine hybrid body • Rigidification

  20. Adaptive joint selection Acceleration simplification = 96 Compute the acceleration metric value of the root

  21. Adaptive joint selection Acceleration simplification = 96 -3 Compute the joint acceleration of the root

  22. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 Compute the acceleration metric values of the two children

  23. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 Select the node with the highest acceleration metric value

  24. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 -6 Compute its joint acceleration

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

  26. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 -6 = 9 = 36 = 36 Select the node with the highest acceleration metric value

  27. Adaptive joint selection Acceleration simplification = 96 -3 = 6 = 81 -6 = 9 = 36 6 Compute its joint acceleration

  28. Adaptive joint selection Acceleration simplification = 96 -3 = 6 -6 = 9 6 Stop because a user-defined sufficient precision has been reached

  29. Adaptive joint selection Acceleration simplification = 96 -3 = 6 -6 = 9 6 Four subassemblies with joint accelerations implicitly set to zero

  30. Velocity simplification • Compute joint velocities in the transient active region (computed using acceleration metric) • Compute metric in a bottom up manner from the transient rigid front using • Compute rigid front like for acceleration metric

  31. Rigidification • Aim: Rigidify the joint velocities to 0 • Constraint: • Solve for • Compute by computing • Compute • Apply to the hybrid body basis vector for

  32. video

  33. References • FEATHERSTONE, R. 1999. A divide-and-conquer articulated body algorithm for parallel o(log(n)) calculation of rigid body dynamics. part 1: Basic algorithm. International Journal of Robotics Research 18(9):867-875. • S. Redon, N. Galoppo, and M. Lin. Adaptive dynamics of articulated bodies: ACM Trans. on Graphics (Proc. of ACM SIGGRAPH), 24(3), 2005.

More Related