Real-time control of physically based simulations using gentle forces

ABSTRACT

Recent advances have brought real-time physically based simulation within reach, but simulations are still difficult to control in real time. We present interactive simulations of passive systems such as deformable solids or fluids that are not only fast, but also directable: they follow given input trajectories while simultaneously reacting to user input and other unexpected disturbances. We achieve such directability using a real-time controller that runs in tandem with a real-time physically based simulation. To avoid stiff and over-controlled systems where the natural dynamics are overpowered, the injection of control forces has to be minimized. This search for gentle forces can be made tractable in real-time by linearizing the system dynamics around the input trajectory, and then using a time-varying linear quadratic regulator to build the controller. We show examples of controlled complex deformable solids and fluids, demonstrating that our approach generates a requested fixed outcome for reasonable user inputs, while simultaneously providing runtime motion variety.

REFERENCES

• 1: Jernej Barbič , Doug L. James, Real-Time subspace integration for St. Venant-Kirchhoff deformable models, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 2: Ronen Barzel , Alan H. Barr, A modeling system based on dynamic constraints, Proceedings of the 15th annual conference on Computer graphics and interactive techniques, p.179-188, June 1988
• 3: Miklós Bergou , Saurabh Mathur , Max Wardetzky , Eitan Grinspun, TRACKS: toward directable thin shells, ACM Transactions on Graphics (TOG), v.26 n.3, July 2007
• 4: Lynne Shapiro Brotman , Arun N. Netravali, Motion interpolation by optimal control, Proceedings of the 15th annual conference on Computer graphics and interactive techniques, p.309-315, June 1988
• 5: Steve Capell , Seth Green , Brian Curless , Tom Duchamp , Zoran Popović, A multiresolution framework for dynamic deformations, Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 21-22, 2002, San Antonio, Texas [doi>10.1145/545261.545268]
• 6: Steve Capell , Matthew Burkhart , Brian Curless , Tom Duchamp , Zoran Popović, Physically based rigging for deformable characters, Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 29-31, 2005, Los Angeles, California [doi>10.1145/1073368.1073412]
• 7: Marco da Silva , Yeuhi Abe , Jovan Popović, Interactive simulation of stylized human locomotion, ACM Transactions on Graphics (TOG), v.27 n.3, August 2008
• 8: Gilles Debunne , Mathieu Desbrun , Marie-Paule Cani , Alan H. Barr, Dynamic real-time deformations using space & time adaptive sampling, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.31-36, August 2001 [doi>10.1145/383259.383262]
• 9: Sharif Elcott , Yiying Tong , Eva Kanso , Peter Schröder , Mathieu Desbrun, Stable, circulation-preserving, simplicial fluids, ACM Transactions on Graphics (TOG), v.26 n.1, p.4-es, January 2007 [doi>10.1145/1189762.1189766]
• 10: Petros Faloutsos , Michiel van de Panne , Demetri Terzopoulos, Dynamic Free-Form Deformations for Animation Synthesis, IEEE Transactions on Visualization and Computer Graphics, v.3 n.3, p.201-214, July 1997 [doi>10.1109/2945.620488]
• 11: Petros Faloutsos , Michiel van de Panne , Demetri Terzopoulos, Composable controllers for physics-based character animation, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.251-260, August 2001 [doi>10.1145/383259.383287]
• 12: Anthony C. Fang , Nancy S. Pollard, Efficient synthesis of physically valid human motion, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 13: Raanan Fattal , Dani Lischinski, Target-driven smoke animation, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 14: Ronald Fedkiw , Jos Stam , Henrik Wann Jensen, Visual simulation of smoke, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.15-22, August 2001 [doi>10.1145/383259.383260]
• 15: Eitan Grinspun , Petr Krysl , Peter Schröder, CHARMS: a simple framework for adaptive simulation, ACM Transactions on Graphics (TOG), v.21 n.3, July 2002
• 16: Jessica K. Hodgins , Nancy S. Pollard, Adapting simulated behaviors for new characters, Proceedings of the 24th annual conference on Computer graphics and interactive techniques, p.153-162, August 1997 [doi>10.1145/258734.258822]
• 17: Jessica K. Hodgins , Wayne L. Wooten , David C. Brogan , James F. O'Brien, Animating human athletics, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, p.71-78, September 1995 [doi>10.1145/218380.218414]
• 18: Paul M. Isaacs , Michael F. Cohen, Controlling dynamic simulation with kinematic constraints, Proceedings of the 14th annual conference on Computer graphics and interactive techniques, p.215-224, August 1987
• 19: Doug L. James , Kayvon Fatahalian, Precomputing interactive dynamic deformable scenes, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 20: Zoran Kačić-Alesić , Marcus Nordenstam , David Bullock, A practical dynamics system, Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 26-27, 2003, San Diego, California
• 21: Lucas Kovar , Michael Gleicher , Frédéric Pighin, Motion graphs, ACM Transactions on Graphics (TOG), v.21 n.3, July 2002
• 22: Li, R.-C., and Bai, Z. 2005. Structure preserving model reduction using a Krylov subspace projection formulation. Comm. Math. Sci. 3, 2, 179--199.
• 23: C. Karen Liu , Aaron Hertzmann , Zoran Popović, Learning physics-based motion style with nonlinear inverse optimization, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 24: Antoine McNamara , Adrien Treuille , Zoran Popović , Jos Stam, Fluid control using the adjoint method, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 25: Dimitri Metaxas , Demetri Terzopoulos, Dynamic deformation of solid primitives with constraints, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, p.309-312, July 1992
• 26: Matthias Müller , Markus Gross, Interactive virtual materials, Proceedings of Graphics Interface 2004, p.239-246, May 17-19, 2004, London, Ontario, Canada
• 27: Zoran Popović , Andrew Witkin, Physically based motion transformation, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.11-20, July 1999 [doi>10.1145/311535.311536]
• 28: Jovan Popović , Steven M. Seitz , Michael Erdmann, Motion sketching for control of rigid-body simulations, ACM Transactions on Graphics (TOG), v.22 n.4, p.1034-1054, October 2003 [doi>10.1145/944020.944025]
• 29: N. Rasmussen , D. Enright , D. Nguyen , S. Marino , N. Sumner , W. Geiger , S. Hoon , R. Fedkiw, Directable photorealistic liquids, Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, August 27-29, 2004, Grenoble, France [doi>10.1145/1028523.1028549]
• 30: Alla Safonova , Jessica K. Hodgins , Nancy S. Pollard, Synthesizing physically realistic human motion in low-dimensional, behavior-specific spaces, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 31: Andrew Selle , Ronald Fedkiw , Byungmoon Kim , Yingjie Liu , Jarek Rossignac, An Unconditionally Stable MacCormack Method, Journal of Scientific Computing, v.35 n.2-3, p.350-371, June 2008 [doi>10.1007/s10915-007-9166-4]
• 32: Sharon, D., and van de Panne, M. 2005. Synthesis of controllers for sylized planar bipedal walking. In International Conference on Robotics and Automation (ICRA), 2387--2392.
• 33: Lin Shi , Yizhou Yu, Controllable smoke animation with guiding objects, ACM Transactions on Graphics (TOG), v.24 n.1, p.140-164, January 2005 [doi>10.1145/1037957.1037965]
• 34: Roger B. Sidje, Expokit: a software package for computing matrix exponentials, ACM Transactions on Mathematical Software (TOMS), v.24 n.1, p.130-156, March 1998 [doi>10.1145/285861.285868]
• 35: Eftychios Sifakis , Igor Neverov , Ronald Fedkiw, Automatic determination of facial muscle activations from sparse motion capture marker data, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 36: Kwang Won Sok , Manmyung Kim , Jehee Lee, Simulating biped behaviors from human motion data, ACM Transactions on Graphics (TOG), v.26 n.3, July 2007
• 37: Jos Stam, Stable fluids, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.121-128, July 1999 [doi>10.1145/311535.311548]
• 38: Stengel, R. F. 1994. Optimal Control and Estimation. Dover Publications, New York.
• 39: Adnan Sulejmanpašić , Jovan Popović, Adaptation of performed ballistic motion, ACM Transactions on Graphics (TOG), v.24 n.1, p.165-179, January 2005 [doi>10.1145/1037957.1037966]
• 40: Russell L. Tedrake , H. Sebastian Seung, Applied optimal control for dynamically stable legged locomotion, Massachusetts Institute of Technology, Cambridge, MA, 2004
• 41: N. Thürey , R. Keiser , M. Pauly , U. Rüde, Detail-preserving fluid control, Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, September 02-04, 2006, Vienna, Austria
• 42: Adrien Treuille , Andrew Lewis , Zoran Popović, Model reduction for real-time fluids, ACM Transactions on Graphics (TOG), v.25 n.3, July 2006
• 43: Andrew Witkin , William Welch, Fast animation and control of nonrigid structures, Proceedings of the 17th annual conference on Computer graphics and interactive techniques, p.243-252, September 1990, Dallas, TX, USA [doi>10.1145/97879.565650]
• 44: Wooten, W. L., and Hodgins, J. K. 2000. Simulating leaping, tumbling, landing and balancing humans. International Conference on Robotics and Automation (ICRA), 656--662.
• 45: KangKang Yin , Michael B. Cline , Dinesh K. Pai, Motion Perturbation Based on Simple Neuromotor Control Models, Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, p.445, October 08-10, 2003
• 46: KangKang Yin , Kevin Loken , Michiel van de Panne, SIMBICON: simple biped locomotion control, ACM Transactions on Graphics (TOG), v.26 n.3, July 2007
• 47: Yongning Zhu , Robert Bridson, Animating sand as a fluid, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 48: Victor Brian Zordan , Jessica K. Hodgins, Motion capture-driven simulations that hit and react, Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation, July 21-22, 2002, San Antonio, Texas [doi>10.1145/545261.545276]
• 49: Victor Brian Zordan , Anna Majkowska , Bill Chiu , Matthew Fast, Dynamic response for motion capture animation, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.8 Types of Simulation
          Subjects: Animation

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Physically based modeling
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Virtual reality

Keywords:
control, deformations, fluids, model reduction, real-time simulation