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Contact Simulation

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Abstract

This chapter discusses numerous topics related to simulating multi-rigid bodies undergoing contact, including rigid and pseudo-rigid models of contact, complementarity problems, the Coulomb friction model, rigid body impacts, coordinate selection for rigid bodies and multibodies, integrating the equations of motion, constructing Jacobian matrices for unilateral and bilateral constraints and time-stepping and event-driven simulation methods, and determining contact data from geometric representations of rigid bodies. The material is approached starting from foundational models and moves toward practical implementation. The chapter concludes with further reading, which includes both current research directions and open problems.

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References

  1. V. Acary, Toward higher order event-capturing schemes and adaptive time-step strategie for nonsmooth multibody systems. Technical report RR-7151, INRIA (2009)

    Google Scholar 

  2. M. Anitescu, Optimization-based simulation of nonsmooth dynamics. Math. Program. Ser. A 105, 113–143 (2006)

    Google Scholar 

  3. M. Anitescu, G.D. Hart, A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contacts, and friction. Int. J. Numer. Methods Eng. 60(14), 2335–2371 (2004)

    Article  MathSciNet  Google Scholar 

  4. M. Anitescu, F.A. Potra, Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems. Nonlinear Dyn. 14, 231–247 (1997)

    Google Scholar 

  5. U.M. Ascher, L. Petzold, Computer Methods for Ordinary Differential Equations and Differential Algebraic Equations (SIAM, Philadelphia, 1998)

    Google Scholar 

  6. U.M. Ascher, H. Chin, L.R. Petzold, S. Reich, Stabilization of constrained mechanical systems with DAEs and invariant manifolds. J. Mech. Struct. Mach. 23, 135–158 (1995)

    Article  MathSciNet  Google Scholar 

  7. D. Baraff, Fast contact force computation for nonpenetrating rigid bodies, in Proceedings of SIGGRAPH, Orlando, Jul 1994

    Google Scholar 

  8. D. Baraff, Linear-time dynamics using lagrange multipliers, in Proceedings of Computer Graphics, New Orleans, Aug 1996

    Google Scholar 

  9. J. Baumgarte, Stabilization of constraints and integrals of motion in dynamical systems. Comput. Math. Appl. Mech. Engr. 1, 1–16 (1972)

    Article  MathSciNet  Google Scholar 

  10. S. Berard, Using Simulation for Planning and Design of Robotic Systems with Intermittent Contact. PhD thesis, Rennselaer Polytechnic Institute (2009)

    Google Scholar 

  11. B. Brogliato, A.A. Ten Dam, L. Paoli, F. Génot, S. Abadie, Numerical simulation of finite dimensional multibody nonsmooth mechanical systems. ASME Appl. Mech. Rev. 55(2), 107–150 (2002)

    Article  Google Scholar 

  12. S. Cameron, Enhancing GJK: computing minimum and penetration distances between convex polyhedra, in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Albuquerque, Apr 1997

    Google Scholar 

  13. C. Canudas de Wit, H. Olsson, K.J. Ȧström, A new model for control of systems with friction. IEEE Trans. Autom. Control 40(3), 419–425 (1995)

    Google Scholar 

  14. E. Catto, Soft constraints reinventing the spring, in Game Developer’s Conference (2011)

    Google Scholar 

  15. A. Chatterjee, On the realism of complementarity conditions in rigid-body collisions. Nonlinear Dyn. 20, 159–168 (1999)

    Google Scholar 

  16. A. Chatterjee, A. Ruina, A new algebraic rigid body collision law based on impulse space considerations. ASME J. Appl. Mech. 65(4), 939–951 (1998)

    Article  Google Scholar 

  17. B. Chazelle, Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm. SIAM J. Comput. 13, 488–507 (1984)

    Article  MathSciNet  Google Scholar 

  18. B. Cheng Yi, E.M. Drumwright, Determining contact data for time stepping rigid body simulations with convex polyhedral geometries, in Proceedings of International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR), San Francisco (2016)

    Google Scholar 

  19. M.B. Cline, D.K. Pai, Post-stabilization for rigid body simulation with contact and constraints, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA) (2003), pp. 3744–3751

    Google Scholar 

  20. M.J. Coleman, A. Ruina, An uncontrolled toy that can walk but cannot stand still. Phys. Rev. Lett. 80(16), 3658–3661 (1998)

    Article  Google Scholar 

  21. M.J. Coleman, M. Garcia, K. Mombaur, A. Ruina, Prediction of stable walking for a toy that cannot stand. Phys. Rev. E 64(2) (2001)

    Google Scholar 

  22. R.W. Cottle, J.-S. Pang, R. Stone, The Linear Complementarity Problem (Academic, Boston, 1992)

    Google Scholar 

  23. D. Dobkin, J. Hershberger, D. Kirkpatrick, S. Suri, Computing the intersection-depth of polyhedra. Algorithmica 9, 518–533 (1993)

    Article  MathSciNet  Google Scholar 

  24. E. Drumwright, D.A. Shell, Modeling contact friction and joint friction in dynamic robotic simulation using the principle of maximum dissipation, in Proceedings of Workshop on the Algorithmic Foundations of Robotics (WAFR) (2010)

    MATH  Google Scholar 

  25. E. Drumwright, D. Shell, Extensive analysis of linear complementarity problem (LCP) solver performance on randomly generated rigid body contact problems, in Proceedings of IEEE/RSJ International Conference of Intelligent Robots and Systems (IROS), Vilamoura, Oct 2012

    Google Scholar 

  26. C. Ericson, Real-Time Collision Detection (Morgan Kaufmann, San Francisco, 2005)

    Google Scholar 

  27. P.L. Fackler, M.J. Miranda, LEMKE. http://people.sc.fsu.edu/~burkardt/m_src/lemke/lemke.m

  28. R. Featherstone, Robot Dynamics Algorithms (Kluwer, Boston, 1987)

    Book  Google Scholar 

  29. R. Featherstone, Rigid Body Dynamics Algorithms (Springer, New York, 2008)

    Chapter  Google Scholar 

  30. S.F. Frisken, R.N. Perry, A.P. Rockwood, T.R. Jones, Adaptively sampled distance fields: a general representation of shape for computer graphics, in Computer Graphics (Proceedings of ACM SIGGRAPH) (2000)

    Google Scholar 

  31. E.G. Gilbert, D.W. Johnson, S.S. Keerthi, A fast procedure for computing the distance between complex objects in three-dimensional space. IEEE J. Robot. Autom. 4(2), 193–203 (1988)

    Article  Google Scholar 

  32. S. Gottschalk, M.C. Lin, D. Manocha, OBB-tree: a hierarchical structure for rapid interference detection, in Proceedings of ACM SIGGRAPH (1996)

    Google Scholar 

  33. S. Goyal, Planar sliding of a rigid body with dry friction: limit surfaces and dynamics of motion. PhD thesis, Cornell University (1988)

    Google Scholar 

  34. G.D. Hart, M. Anitescu, An O(m + n) measure of penetration depth between convex polyhedral bodies for rigid multibody dynamics. Technical report, ANL/MCS-P1753-0510 (2010)

    Google Scholar 

  35. J.M. Hsu, S.C. Peters, Extending open dynamics engine for the DARPA virtual robotics challenge, in Proceedings of Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR) (2014)

    Google Scholar 

  36. A.P. Ivanov, On multiple impact. J. Appl. Math. Mech. 59(6), 887–902 (1995)

    Article  MathSciNet  Google Scholar 

  37. K.L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1987)

    Google Scholar 

  38. T.R. Kane, D.A. Levinson, Dynamics: Theory and Applications (McGraw-Hill, New York, 1985)

    Google Scholar 

  39. Y.J. Kim, M.A. Otaduy, M.C. Lin, D. Manocha, Fast penetration depth computation for physically-based animation, in Proceedings of Symposium on Computer Animation (SCA) (2002)

    Google Scholar 

  40. C. Lacoursière, Splitting methods for dry frictional contact problems in rigid multibody systems: preliminary performance results, in Proceedings of SIGRAD, ed. by M. Ollila, Nov 2003, pp. 11–16

    Google Scholar 

  41. C. Lacoursière, Ghosts and machines: regularized variational methods for interactive simulations of multibodies with dry frictional contacts. PhD thesis, Umeå University (2007)

    Google Scholar 

  42. P. Löstedt, Mechanical systems of rigid bodies subject to unilateral constraints. SIAM J. Appl. Math. 42(2), 281–296 (1982)

    Article  MathSciNet  Google Scholar 

  43. P. Löstedt, Numerical simulation of time-dependent contact friction problems in rigid body mechanics. SIAM J. Sci. Stat. Comput. 5(2), 370–393 (1984)

    Google Scholar 

  44. Y. Lu, J.C. Trinkle, On the convergence of fixed-point iteration in solving complementarity problems arising in robot locomotion and manipulation, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots & Systems (IROS) (2014)

    Google Scholar 

  45. M. Machado, P. Moreira, P. Flores, H. Lankarani, Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theory 53, 99–121 (2012)

    Article  Google Scholar 

  46. D. Meltz, Y. Or, E. Rimon, Experimental verification and graphical characterization of dynamic jamming in frictional rigid-body mechanics, in Proceedings of IEEE International Conference on Robotics and Automation, Rome (2007)

    Google Scholar 

  47. B. Mirtich, Impulse-based dynamic simulation of rigid body systems. PhD thesis, University of California, Berkeley (1996)

    Google Scholar 

  48. B. Mirtich, V-Clip: fast and robust polyhedral collision detection. ACM Trans. Graph. 17(3), 177–208 (1998)

    Article  Google Scholar 

  49. M.D.P. Monteiro-Marques, Differential inclusions in nonsmooth mechanical problems: shocks and dry friction, in Progress in Nonlinear Differential Equations and Their Applications, vol. 9 (Birkhäuser Verlag, Basel, 1993)

    Google Scholar 

  50. J.J. Moreau, Standard inelastic shocks and the dynamics of unilateral constraints, in C.I.S.M. Courses and Lectures, ed. by G. del Piero, F. Maceri, vol. 288 (Springer, Vienna, 1985), pp. 173–221

    Chapter  Google Scholar 

  51. K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming (Heldermann, Berlin, 1988)

    Google Scholar 

  52. P.E. Nikravesh, Computer-Aided Analysis of Mechanical Systems (Prentice Hall, Englewood Cliffs, 1988)

    Google Scholar 

  53. G. Nützi, A. Schweizer, M. Möller, C. Glocker, Projective jacobi and gauss-seidel on the GPU for non-smooth multi-body systems, in Proceedings of International Conference Multibody Systems, Nonlinear Dynamics, and Control, Buffalo (2014)

    Google Scholar 

  54. P. Painlevé, Sur le lois du frottement de glissemment. C. R. Académie des Sciences Paris 121, 112–115 (1895)

    Google Scholar 

  55. M. Posa, R. Tedrake, Direct trajectory optimization of rigid body dynamical systems through contact, in Proceedings of Workshop on Algorithmic Foundations of Robotics (WAFR), Boston (2012)

    Google Scholar 

  56. F.A. Potra, M. Anitescu, B. Gavrea, J. Trinkle, A linearly implicit trapezoidal method for stiff multibody dynamics with contact, joints, and friction. Int. J. Numer. Methods Eng. 66(7), 1079–1124 (2006)

    Google Scholar 

  57. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in C, 2nd edn. (Cambridge University Press, Cambridge, 1992)

    Google Scholar 

  58. S. Roy, Recent advances in numerical methods for fluid dynamics and heat transfer. J. Fluid Eng. 127(4):629–630 (2005)

    Article  Google Scholar 

  59. L. Saab, O.E. Ramos, F. Keith, N. Mansard, P. Souères, J.-Y. Fourquest, Dynamic whole-body motion generation under rigid contacts and other unilateral constraints. IEEE Trans. Robot. 29(2), 346–362 (2013)

    Article  Google Scholar 

  60. P.J. Schneider, D.H. Eberly, Geometric Tools for Computer Graphics (Morgan Kaufman, San Francisco, 2003)

    Chapter  Google Scholar 

  61. L. Sciavicco, B. Siciliano, Modeling and Control of Robot Manipulators, 2nd edn. (Springer, London, 2000)

    Chapter  Google Scholar 

  62. J.A. Sethian, A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93, 1591–1595 (1996)

    Article  MathSciNet  Google Scholar 

  63. A.A. Shabana, Computational Dynamics, 2nd edn. (Wiley, New York, 2001)

    Google Scholar 

  64. J. Shepherd, S. Zapolsky, E.M. Drumwright, Fast multi-body simulations of robots controlled with error feedback, in Proceedings of International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR), 2016

    Google Scholar 

  65. C.E. Smith, P.-P. Liu, Coefficients of restitution. ASME J. Appl. Mech. 59, 963–969 (1992)

    Article  Google Scholar 

  66. B. Smith, D.M. Kaufman, E. Vouga, R. Tamstorf, E. Grinspun, Reflections on simultaneous impact. ACM Trans. Graph. (Proc. SIGGRAPH) 31(4), 106:1–106:12 (2012)

    Article  Google Scholar 

  67. P. Song, M. Yashima, V. Kumar, Dynamic simulation for grasping and whole arm manipulation, in Proceedings of IEEE International Conference on Robotics and Automation, San Francisco, Apr 2000

    Google Scholar 

  68. D.E. Stewart, Convergence of a time-stepping scheme for rigid-body dynamics and resolution of Painlevé’s problem. Arch. Ration. Mech. Anal. 145, 215–260 (1998)

    Article  MathSciNet  Google Scholar 

  69. D.E. Stewart, J.C. Trinkle, An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and Coulomb friction. Int. J. Numer. Methods Eng. 39(15), 2673–2691 (1996)

    Article  MathSciNet  Google Scholar 

  70. D. Stewart, J.C. Trinkle, An implicit time-stepping scheme for rigid body dynamics with Coulomb friction, in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Francisco, Apr 2000

    Google Scholar 

  71. D. Stoianovici, Y. Hurmuzlu, A critical study of the applicability of rigid-body collision theory. ASME J. Appl. Mech. 63, 307–316 (1996)

    Article  Google Scholar 

  72. W.J. Stronge, Rigid body collisions with friction. Proc. R. Soc. Lond. A 431(169–181) (1990)

    Article  MathSciNet  Google Scholar 

  73. C. Studer, C. Glocker, Simulation of non-smooth mechanical systems with many unilateral constraints, in Proceedings of EUROMECH Nonlinear Oscillation Conference (ENOC) (2005)

    Google Scholar 

  74. C. Studer, R.I. Leine, C. Glocker, Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics. Int. J. Numer. Methods Eng. 76, 1747–1781 (2008)

    Article  MathSciNet  Google Scholar 

  75. J.R. Taylor, E.M. Drumwright, State estimation of a wild robot toward validation of rigid body simulation, in Proceedings of International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR), San Francisco (2016)

    Google Scholar 

  76. J.R. Taylor, E.M. Drumwright, J. Hsu, Analysis of grasping failures in multi-rigid body simulations, in Proceedings of International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR), San Francisco (2016)

    Google Scholar 

  77. E. Todorov, A convex, smooth and invertible contact model for trajectory optimization, in Proceedings of IEEE International Conference on Robotics and Automation (ICRA), Shanghai (2011)

    Google Scholar 

  78. E. Todorov, Analytically-invertible dynamics with contacts and constraints: theory and implementation in MuJoCo, in Proceedings of IEEE International Conference on Robotics and Automation (2014)

    Google Scholar 

  79. J. Trinkle, J.-S. Pang, S. Sudarsky, G. Lo, On dynamic multi-rigid-body contact problems with Coulomb friction. Zeithscrift fur Angewandte Mathematik und Mechanik 77(4), 267–279 (1997)

    Article  MathSciNet  Google Scholar 

  80. G. van den Bergen, Proximity queries and penetration depth computation on 3D game objects, in Proceedings of Game Developer’s Conference (2001)

    Google Scholar 

  81. M.W. Walker, D.E. Orin, Efficient dynamic computer simulation of robotic mechanisms. ASME J. Dyn. Syst. Meas. Control. 104, 205–211 (1982)

    Article  Google Scholar 

  82. Y.-T. Wang, V. Kumar, Simulation of mechanical systems with multiple frictional contacts. ASME J. Mech. Des. 116, 571–580 (1994)

    Article  Google Scholar 

  83. J. Williams, Y. Lu, J. C. Trinkle, A complementarity based contact model for geometrically accurate treatment of polytopes in simulation, in Proceedings of ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (2014)

    Google Scholar 

  84. S. Zapolsky, E.M. Drumwright, Adaptive integration for controlling speed vs. accuracy in multi-rigid body simulation, in Proceedings of IEEE/RSJ International Conference on Intelligent Robots & Systems (IROS) (2015)

    Google Scholar 

  85. S. Zapolsky, E. Drumwright, I. Havoutis, J. Buchli, C. Semini, Inverse dynamics for a quadruped robot locomoting on slippery surfaces, in Proceedings of International Conference Climbing Walking Robots (CLAWAR), Sydney (2013)

    Google Scholar 

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Authors and Affiliations

  1. Toyota Research Institute, Los Altos, CA, USA

    Evan Drumwright

  2. National Robotics Initiative, The National Science Foundation, Arlington, VA, USA

    Jeffrey C. Trinkle

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  1. Evan Drumwright
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Correspondence to Evan Drumwright .

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Editors and Affiliations

  1. Intuitive Surgical, Sunnyvale, CA, USA

    Ambarish Goswami

  2. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Prahlad Vadakkepat

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Drumwright, E., Trinkle, J.C. (2019). Contact Simulation. In: Goswami, A., Vadakkepat, P. (eds) Humanoid Robotics: A Reference. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6046-2_25

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