Dynamics-aware numerical coarsening for fabrication design

The realistic simulation of highly-dynamic elastic objects is important for a broad range of applications in computer graphics, engineering and computational fabrication. However, whether simulating flipping toys, jumping robots, prosthetics or quickly moving creatures, performing such simulations in the presence of contact, impact and friction is both time consuming and inaccurate. In this paper we present Dynamics-Aware Coarsening (DAC) and the Boundary Balanced Impact (BBI) model which allow for the accurate simulation of dynamic, elastic objects undergoing both large scale deformation and frictional contact, at rates up to 79 times faster than state-of-the-art methods. DAC and BBI produce simulations that are accurate and fast enough to be used (for the first time) for the computational design of 3D-printable compliant dynamic mechanisms. Thus we demonstrate the efficacy of DAC and BBI by designing and fabricating mechanisms which flip, throw and jump over and onto obstacles as requested.

[1]  LoepfeMichael,et al.  An Untethered, Jumping Roly-Poly Soft Robot Driven by Combustion , 2015 .

[2]  Markus H. Gross,et al.  Computational design of actuated deformable characters , 2013, ACM Trans. Graph..

[3]  Bin Wang,et al.  Deformation capture and modeling of soft objects , 2015, ACM Trans. Graph..

[4]  Kathrin Abendroth,et al.  Nonlinear Finite Elements For Continua And Structures , 2016 .

[5]  Miguel A. Otaduy,et al.  High-resolution interaction with corotational coarsening models , 2016, ACM Trans. Graph..

[6]  Mathieu Desbrun,et al.  Numerical coarsening of inhomogeneous elastic materials , 2009, ACM Trans. Graph..

[7]  Jernej Barbic,et al.  Real-Time subspace integration for St. Venant-Kirchhoff deformable models , 2005, ACM Trans. Graph..

[8]  M. Gross,et al.  Unified simulation of elastic rods, shells, and solids , 2010, SIGGRAPH 2010.

[9]  Rolf Krause,et al.  Presentation and comparison of selected algorithms for dynamic contact based on the Newmark scheme , 2012 .

[10]  Steve Marschner,et al.  Physical Face Cloning , 2022 .

[11]  Wojciech Matusik,et al.  Data-driven finite elements for geometry and material design , 2015, ACM Trans. Graph..

[12]  Theodore Kim,et al.  Optimizing cubature for efficient integration of subspace deformations , 2008, SIGGRAPH Asia '08.

[13]  Doug L. James,et al.  Real-Time subspace integration for St. Venant-Kirchhoff deformable models , 2005, SIGGRAPH 2005.

[14]  Peter Deuflhard,et al.  A contact‐stabilized Newmark method for dynamical contact problems , 2008 .

[15]  Hujun Bao,et al.  Space-time editing of elastic motion through material optimization and reduction , 2014, ACM Trans. Graph..

[16]  D. Rus,et al.  Design, fabrication and control of soft robots , 2015, Nature.

[17]  Eitan Grinspun,et al.  TRACKS: toward directable thin shells , 2007, SIGGRAPH 2007.

[18]  C. Karen Liu,et al.  Orienting in mid-air through configuration changes to achieve a rolling landing for reducing impact after a fall , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[19]  Daniela Rus,et al.  A soft cube capable of controllable continuous jumping , 2015, 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[20]  Sung-Hoon Ahn,et al.  Review of manufacturing processes for soft biomimetic robots , 2009 .

[21]  Eitan Grinspun,et al.  Computational design of linkage-based characters , 2014, ACM Trans. Graph..

[22]  Sarah Bergbreiter,et al.  Effective and efficient locomotion for millimeter-sized microrobots , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[23]  J. Marsden,et al.  Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanical Systems , 2000 .

[24]  Dinesh K. Pai,et al.  DyRT: dynamic response textures for real time deformation simulation with graphics hardware , 2002, SIGGRAPH.

[25]  Pedro M. Reis,et al.  A Perspective on the Revival of Structural (In) Stability With Novel Opportunities for Function: From Buckliphobia to Buckliphilia , 2015 .

[26]  Kristofer S. J. Pister,et al.  Design of an Autonomous Jumping Microrobot , 2022 .

[27]  A. Ammar,et al.  PGD-Based Computational Vademecum for Efficient Design, Optimization and Control , 2013, Archives of Computational Methods in Engineering.

[28]  J. Marsden,et al.  Time‐discretized variational formulation of non‐smooth frictional contact , 2002 .

[29]  H. Lipson Challenges and Opportunities for Design, Simulation, and Fabrication of Soft Robots , 2014 .

[30]  G. Whitesides Soft Robotics. , 2018, Angewandte Chemie.

[31]  M. Gross,et al.  Unified simulation of elastic rods, shells, and solids , 2010, ACM Trans. Graph..

[32]  Kyu-Jin Cho,et al.  Flea-Inspired Catapult Mechanism for Miniature Jumping Robots , 2012, IEEE Transactions on Robotics.

[33]  James U. Korein,et al.  Robotics , 2018, IBM Syst. J..

[34]  J. P. Paul,et al.  Biomechanics , 1966 .

[35]  J. Marsden,et al.  Discrete mechanics and variational integrators , 2001, Acta Numerica.

[36]  Chen Shen,et al.  Interactive Deformation Using Modal Analysis with Constraints , 2003, Graphics Interface.

[37]  Robert J. Wood,et al.  A jumping robotic insect based on a torque reversal catapult mechanism , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[38]  Dominic Vella,et al.  Two leaps forward for robot locomotion , 2015, Science.

[39]  Olga Sorkine-Hornung,et al.  Spin-it , 2017, Commun. ACM.

[40]  Zoltan MAJOR,et al.  Combination of Novel Virtual and Real Prototyping Methods in a Rapid Product Development Methodology , 2012 .

[41]  Kyu-Jin Cho,et al.  Role of compliant leg in the flea-inspired jumping mechanism , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[42]  E. A. Repetto,et al.  Finite element analysis of nonsmooth contact , 1999 .

[43]  R. Wood,et al.  Jumping on water: Surface tension–dominated jumping of water striders and robotic insects , 2015, Science.

[44]  Kyu-Jin Cho,et al.  Fabrication of Composite and Sheet Metal Laminated Bistable Jumping Mechanism , 2015 .

[45]  Alexandre Ern,et al.  Time-Integration Schemes for the Finite Element Dynamic Signorini Problem , 2011, SIAM J. Sci. Comput..

[46]  Mathieu Desbrun,et al.  Numerical coarsening of inhomogeneous elastic materials , 2009, SIGGRAPH 2009.

[47]  Wojciech Matusik,et al.  Computational design of mechanical characters , 2013, ACM Trans. Graph..

[48]  Robert J. Wood,et al.  SOFT ROBOTICS A 3 D-printed , functionally graded soft robot powered by combustion , 2022 .

[49]  Robert J. Wood,et al.  A 3D-printed, functionally graded soft robot powered by combustion , 2015, Science.

[50]  Doug L. James,et al.  Optimizing cubature for efficient integration of subspace deformations , 2008, SIGGRAPH 2008.

[51]  Heinrich M. Jaeger,et al.  Designer Matter: A perspective , 2015 .

[52]  A. Shabana Theory of vibration , 1991 .

[53]  Sarah Bergbreiter,et al.  First leaps toward jumping microrobots , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[54]  J. Moser,et al.  Discrete versions of some classical integrable systems and factorization of matrix polynomials , 1991 .

[55]  Sylvain Lefebvre,et al.  Make it stand , 2013, ACM Trans. Graph..

[56]  V. Mandelshtam,et al.  Harmonic inversion of time signals and its applications , 1997 .