“A unified newton barrier method for multibody dynamics” by Chen, Li, Lan, Su, Yang, et al. …

We present a simulation framework for multibody dynamics via a universal variational integration. Our method naturally supports mixed rigid-deformables and mixed codimensional geometries, while providing guaranteed numerical convergence and accurate resolution of contact, friction, and a wide range of articulation constraints. We unify (1) the treatment of simulation degrees of freedom for rigid and soft bodies by formulating them both in terms of Lagrangian nodal displacements, (2) the handling of general linear equality joint constraints through an efficient change-of-variable strategy, (3) the enforcement of nonlinear articulation constraints based on novel distance potential energies, (4) the resolution of frictional contact between mixed dimensions and bodies with a variational Incremental Potential Contact formulation, and (5) the modeling of generalized restitution through semi-implicit Rayleigh damping. We conduct extensive unit tests and benchmark studies to demonstrate the efficacy of our method.

1. Masniezam Ahmad, Khairul A Ismail, and Fauziah Mat. 2016. Impact models and coefficient of restitution: a review. ARPN Journal of Engineering and Applied Sciences 11 (2016).Google Scholar
2. Sheldon Andrews, Marek Teichmann, and Paul G Kry. 2017. Geometric Stiffness for Real-time Constrained Multibody Dynamics. In Computer Graphics Forum, Vol. 36. Wiley Online Library, 235–246.Google Scholar
3. Yunfei Bai and Karen Liu. 2014. Coupling cloth and rigid bodies for dexterous manipulation. In Proceedings of the Seventh International Conference on Motion in Games.Google ScholarDigital Library
4. David Baraff. 1989. Analytical methods for dynamic simulation of non-penetrating rigid bodies. In Proceedings of the 16th annual conference on Computer graphics and interactive techniques. 223–232.Google ScholarDigital Library
5. Nathan Bell, Yizhou Yu, and Peter J Mucha. 2005. Particle-based simulation of granular materials. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation. 77–86.Google ScholarDigital Library
6. Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, and Mark Pauly. 2014. Projective dynamics: Fusing constraint projections for fast simulation. ACM transactions on graphics (TOG) 33, 4 (2014), 1–11.Google ScholarDigital Library
7. Jumyung Chang, Fang Da, Eitan Grinspun, and Christopher Batty. 2019. A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects. Proceedings of the ACM on Computer Graphics and Interactive Techniques 2, 2 (2019), 1–18.Google ScholarDigital Library
8. Byoungwon Choe, Min Gyu Choi, and Hyeong-Seok Ko. 2005. Simulating complex hair with robust collision handling. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation. 153–160.Google ScholarDigital Library
9. Eulalie Coevoet, Otman Benchekroun, and Paul G Kry. 2020. Adaptive merging for rigid body simulation. ACM Transactions on Graphics (TOG) 39, 4 (2020), 35–1.Google ScholarDigital Library
10. Erwin Coumans. 2015. Bullet Physics Simulation. In ACM SIGGRAPH 2015 Courses. Article 7.Google Scholar
11. Richard Courant, Kurt Friedrichs, and Hans Lewy. 1967. On the partial difference equations of mathematical physics. IBM journal of Research and Development 11, 2 (1967), 215–234.Google ScholarDigital Library
12. Crispin Deul, Patrick Charrier, and Jan Bender. 2016. Position-based rigid-body dynamics. Computer Animation and Virtual Worlds 27, 2 (2016), 103–112.Google ScholarDigital Library
13. Andreas Enzenhöfer, Nicolas Lefebvre, and Sheldon Andrews. 2019. Efficient block pivoting for multibody simulations with contact. In Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. 1–9.Google ScholarDigital Library
14. Kenny Erleben. 2007. Velocity-based shock propagation for multibody dynamics animation. ACM Transactions on Graphics (TOG) 26, 2 (2007), 12–es.Google ScholarDigital Library
15. Zachary Ferguson, Minchen Li, Teseo Schneider, Francisca Gil-Ureta, Timothy Langlois, Chenfanfu Jiang, Denis Zorin, Danny M Kaufman, and Daniele Panozzo. 2021. Intersection-free rigid body dynamics. ACM Transactions on Graphics 40, 4 (2021), 183.Google ScholarDigital Library
16. Mihai Frâncu and Florica Moldoveanu. 2017a. Position based simulation of solids with accurate contact handling. Computers & Graphics 69 (2017), 12–23.Google ScholarDigital Library
17. Mihai Frâncu and Florica Moldoveanu. 2017b. Unified Simulation of Rigid and Flexible Bodies Using Position Based Dynamics.. In VRIPHYS. 49–58.Google Scholar
18. Theodore F Gast, Craig Schroeder, Alexey Stomakhin, Chenfanfu Jiang, and Joseph M Teran. 2015. Optimization integrator for large time steps. IEEE transactions on visualization and computer graphics 21, 10 (2015), 1103–1115.Google ScholarDigital Library
19. Moritz Geilinger, David Hahn, Jonas Zehnder, Moritz Bächer, Bernhard Thomaszewski, and Stelian Coros. 2020. ADD: analytically differentiable dynamics for multi-body systems with frictional contact. ACM Transactions on Graphics (TOG) 39, 6 (2020).Google ScholarDigital Library
20. Eran Guendelman, Robert Bridson, and Ronald Fedkiw. 2003. Nonconvex rigid bodies with stacking. ACM transactions on graphics (TOG) 22, 3 (2003), 871–878.Google Scholar
21. David Harmon, Etienne Vouga, Breannan Smith, Rasmus Tamstorf, and Eitan Grinspun. 2009. Asynchronous contact mechanics. In ACM SIGGRAPH 2009 papers. 1–12.Google ScholarDigital Library
22. Sumit Jain and Karen Liu. 2011. Controlling physics-based characters using soft contacts. In Proceedings of the 2011 SIGGRAPH Asia Conference. 1–10.Google ScholarDigital Library
23. Danny M Kaufman, Timothy Edmunds, and Dinesh K Pai. 2005. Fast frictional dynamics for rigid bodies. In ACM SIGGRAPH 2005 Papers. 946–956.Google ScholarDigital Library
24. Danny M Kaufman, Shinjiro Sueda, Doug L James, and Dinesh K Pai. 2008. Staggered projections for frictional contact in multibody systems. In ACM SIGGRAPH Asia 2008 papers. 1–11.Google Scholar
25. Yuki Koyama, Shinjiro Sueda, Emma Steinhardt, Takeo Igarashi, Ariel Shamir, and Wojciech Matusik. 2015. AutoConnect: computational design of 3D-printable connectors. ACM Transactions on Graphics (TOG) 34, 6 (2015), 1–11.Google ScholarDigital Library
26. Lei Lan, Danny M Kaufman, Minchen Li, Chenfanfu Jiang, and Yin Yang. 2022. Affine Body Dynamics: Fast, Stable & Intersection-free Simulation of Stiff Materials. ACM Transactions on Graphics (TOG) 41, 4 (2022).Google ScholarDigital Library
27. Lei Lan, Yin Yang, Danny Kaufman, Junfeng Yao, Minchen Li, and Chenfanfu Jiang. 2021. Medial IPC: accelerated incremental potential contact with medial elastics. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1–16.Google ScholarDigital Library
28. Jing Li, Tiantian Liu, and Ladislav Kavan. 2020b. Soft Articulated Characters in Projective Dynamics. IEEE Transactions on Visualization and Computer Graphics (2020).Google ScholarDigital Library
29. Minchen Li. 2020. Robust and Accurate Simulation of Elastodynamics and Contact. Ph.D. Dissertation. University of Pennsylvania.Google Scholar
30. Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M Kaufman. 2020a. Incremental potential contact: Intersection- and inversion-free, large-deformation dynamics. ACM transactions on graphics 39, 4 (2020).Google ScholarDigital Library
31. Minchen Li, Ming Gao, Timothy Langlois, Chenfanfu Jiang, and Danny M Kaufman. 2019. Decomposed Optimization Time Integrator for Large-Step Elastodynamics. ACM Transactions on Graphics 38, 4 (2019).Google ScholarDigital Library
32. Minchen Li, Danny M Kaufman, and Chenfanfu Jiang. 2021. Codimensional Incremental Potential Contact. ACM Trans. Graph. (SIGGRAPH) 40, 4, Article 170 (2021).Google ScholarDigital Library
33. Tiantian Liu, Sofien Bouaziz, and Ladislav Kavan. 2017. Quasi-newton methods for real-time simulation of hyperelastic materials. Acm Transactions on Graphics (TOG) 36, 3 (2017), 1–16.Google ScholarDigital Library
34. Miles Macklin, Kenny Erleben, Matthias Müller, Nuttapong Chentanez, Stefan Jeschke, and Viktor Makoviychuk. 2019. Non-smooth newton methods for deformable multi-body dynamics. ACM Transactions on Graphics (TOG) 38, 5 (2019), 1–20.Google ScholarDigital Library
35. Hammad Mazhar, Toby Heyn, Dan Negrut, and Alessandro Tasora. 2015. Using Nesterov’s method to accelerate multibody dynamics with friction and contact. ACM Transactions on Graphics (TOG) 34, 3 (2015), 1–14.Google ScholarDigital Library
36. Brian Mirtich and John Canny. 1994. Impulse-based dynamic simulation. Citeseer.Google Scholar
37. Brian Vincent Mirtich. 1996. Impulse-based dynamic simulation of rigid body systems. University of California, Berkeley.Google ScholarDigital Library
38. Jean J Moreau. 1985. Standard inelastic shocks and the dynamics of unilateral constraints. In Unilateral problems in structural analysis. Springer, 173–221.Google Scholar
39. Matthias Müller, Bruno Heidelberger, Marcus Hennix, and John Ratcliff. 2007. Position based dynamics. Journal of Visual Communication and Image Representation 18, 2 (2007), 109–118.Google ScholarDigital Library
40. Matthias Müller, Miles Macklin, Nuttapong Chentanez, Stefan Jeschke, and Tae-Yong Kim. 2020. Detailed rigid body simulation with extended position based dynamics. In Computer Graphics Forum, Vol. 39. Wiley Online Library, 101–112.Google Scholar
41. Albert Peiret, Sheldon Andrews, József Kövecses, Paul G Kry, and Marek Teichmann. 2019. Schur complement-based substructuring of stiff multibody systems with contact. ACM Transactions on Graphics (TOG) 38, 5 (2019), 1–17.Google ScholarDigital Library
42. Jovan Popović, Steven M Seitz, Michael Erdmann, Zoran Popović, and Andrew Witkin. 2000. Interactive manipulation of rigid body simulations. In Proceedings of the 27th annual conference on Computer graphics and interactive techniques. 209–217.Google ScholarDigital Library
43. Stephane Redon, Nico Galoppo, and Ming C Lin. 2005. Adaptive dynamics of articulated bodies. In ACM SIGGRAPH 2005 Papers. 936–945.Google ScholarDigital Library
44. Edward John Routh. 1905. The advanced part of a treatise on the dynamics of a system of rigid bodies. MacMillan & Co.Google Scholar
45. Robert Seifried, Werner Schiehlen, and Peter Eberhard. 2010. The role of the coefficient of restitution on impact problems in multi-body dynamics. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 224, 3 (2010), 279–306.Google ScholarCross Ref
46. Tamar Shinar, Craig Schroeder, and Ronald Fedkiw. 2008. Two-way coupling of rigid and deformable bodies. In Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Citeseer, 95–103.Google ScholarDigital Library
47. Breannan Smith, Danny M Kaufman, Etienne Vouga, Rasmus Tamstorf, and Eitan Grinspun. 2012. Reflections on simultaneous impact. ACM Transactions on Graphics (TOG) 31, 4 (2012), 1–12.Google ScholarDigital Library
48. David E Stewart. 2000. Rigid-body dynamics with friction and impact. SIAM review 42, 1 (2000), 3–39.Google Scholar
49. William J Stronge. 1991. Unraveling paradoxical theories for rigid body collisions. Journal of Applied Mechanics 58 (1991).Google Scholar
50. Shinjiro Sueda, Garrett L Jones, David IW Levin, and Dinesh K Pai. 2011. Large-scale dynamic simulation of highly constrained strands. In ACM SIGGRAPH 2011 papers.Google ScholarDigital Library
51. Joseph Teran, Eftychios Sifakis, Geoffrey Irving, and Ronald Fedkiw. 2005. Robust quasistatic finite elements and flesh simulation. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation. 181–190.Google ScholarDigital Library
52. Bernhard Thomaszewski, Stelian Coros, Damien Gauge, Vittorio Megaro, Eitan Grinspun, and Markus Gross. 2014. Computational design of linkage-based characters. ACM Transactions on Graphics (TOG) 33, 4 (2014), 1–9.Google ScholarDigital Library
53. Maxime Tournier, Matthieu Nesme, Benjamin Gilles, and François Faure. 2015. Stable constrained dynamics. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1–10.Google ScholarDigital Library
54. Christopher D Twigg and Doug L James. 2008. Backward steps in rigid body simulation. In ACM SIGGRAPH 2008 papers. 1–10.Google ScholarDigital Library
55. Jui-Hsien Wang, Rajsekhar Setaluri, Doug L James, and Dinesh K Pai. 2017. Bounce maps: an improved restitution model for real-time rigid-body impact. ACM Trans. Graph. 36, 4 (2017), 150–1.Google ScholarDigital Library
56. Yu Wang and Matthew T Mason. 1992. Two-dimensional rigid-body collisions with friction. Journal of Applied Mechanics 59 (1992).Google Scholar
57. Ying Wang, Nicholas J Weidner, Margaret A Baxter, Yura Hwang, Danny M Kaufman, and Shinjiro Sueda. 2019. REDMAX: Efficient & flexible approach for articulated dynamics. ACM Transactions on Graphics (TOG) 38, 4 (2019), 1–10.Google ScholarDigital Library
58. Rachel Weinstein, Joseph Teran, and Ronald Fedkiw. 2006. Dynamic simulation of articulated rigid bodies with contact and collision. IEEE Transactions on Visualization and Computer Graphics 12, 3 (2006), 365–374.Google ScholarDigital Library
59. Keenon Werling, Dalton Omens, Jeongseok Lee, Ioannis Exarchos, and Karen Liu. 2021. Fast and Feature-Complete Differentiable Physics Engine for Articulated Rigid Bodies with Contact Constraints. In Robotics: Science and Systems.Google Scholar
60. Edmund Taylor Whittaker. 1937. A treatise on the analytical dynamics of particles and rigid bodies. CUP Archive.Google Scholar
61. Hongyi Xu, Yili Zhao, and Jernej Barbič. 2014. Implicit multibody penalty-baseddistributed contact. IEEE transactions on visualization and computer graphics 20, 9 (2014), 1266–1279.Google ScholarCross Ref
62. Yidong Zhao, Jinhyun Choo, Yupeng Jiang, Minchen Li, Chenfanfu Jiang, and Kenichi Soga. 2022. A barrier method for frictional contact on embedded interfaces. Computer Methods in Applied Mechanics and Engineering 393 (2022), 114820.Google ScholarCross Ref