Modeling Contact Friction and Joint Friction in Dynamic Robotic Simulation Using the Principle of Maximum Dissipation

We present a unified treatment for modeling Coulomb and viscous friction within multi-rigid body simulation using the principle of maximum dissipation. This principle is used to build two different methods—an event-driven impulse-based method and a time stepping method—for modeling contact. The same principle is used to effect joint friction in articulated mechanisms. Experiments show that the contact models are able to be solved faster and more robustly than alternative models. Experiments on the joint friction model show that it is as accurate as a standard model while permitting much larger simulation step sizes to be employed.

[1]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[2]  Per Lötstedt.  Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints , 1982 .

[3]  Per Lötstedt.  Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics , 1984 .

[4]  J. Moreau.  Standard Inelastic Shocks and the Dynamics of Unilateral Constraints , 1985 .

[5]  G. Piero,et al.  Unilateral Problems in Structural Analysis , 1985 .

[6]  Roy Featherstone,et al.  Robot Dynamics Algorithms , 1987 .

[7]  J. Moreau,et al.  Unilateral Contact and Dry Friction in Finite Freedom Dynamics , 1988 .

[8]  J. Moreau,et al.  Nonsmooth Mechanics and Applications , 1989 .

[9]  David Baraff,et al.  Coping with friction for non-penetrating rigid body simulation , 1991, SIGGRAPH.

[10]  BaraffDavid.  Coping with friction for non-penetrating rigid body simulation , 1991 .

[11]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[12]  M. Marques,et al.  Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction , 1993 .

[13]  David Baraff,et al.  Fast contact force computation for nonpenetrating rigid bodies , 1994, SIGGRAPH.

[14]  Bruno Siciliano,et al.  Modeling and Control of Robot Manipulators , 1995 .

[15]  J. Trinkle,et al.  On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction , 1995 .

[16]  Brian Mirtich,et al.  Fast and Accurate Computation of Polyhedral Mass Properties , 1996, J. Graphics, GPU, & Game Tools.

[17]  Brian Mirtich,et al.  Impulse-based dynamic simulation of rigid body systems , 1996 .

[18]  B. Brogliato.  Nonsmooth Impact Mechanics: Models, Dynamics and Control , 1996 .

[19]  D. Stoianovici,et al.  A Critical Study of the Applicability of Rigid-Body Collision Theory , 1996 .

[20]  D. Baraff.  An Introduction to Physically Based Modeling: Rigid Body Simulation I—Unconstrained Rigid Body Dynamics , 1997 .

[21]  Michael C. Ferris,et al.  Complementarity and variational problems : state of the art , 1997 .

[22]  M. Anitescu,et al.  Formulating Dynamic Multi-Rigid-Body Contact Problems with Friction as Solvable Linear Complementarity Problems , 1997 .

[23]  D. Baraff.  An Introduction to Physically Based Modeling : Rigid Body Simulation II — Nonpenetration Constraints , 1997 .

[24]  Daimler Ag,et al.  Real-Time Rigid Body Simulations Of Some `classical Mechanics Toys' , 1998 .

[25]  D. Stewart,et al.  Time-stepping for three-dimensional rigid body dynamics , 1999 .

[26]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[27]  A. Chatterjee.  On the Realism of Complementarity Conditions in Rigid Body Collisions , 1999 .

[28]  Jeffrey C. Trinkle,et al.  An implicit time-stepping scheme for rigid body dynamics with Coulomb friction , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[29]  M. Ferris,et al.  Complementarity problems in GAMS and the PATH solver 1 This material is based on research supported , 2000 .

[30]  David E. Stewart,et al.  Rigid-Body Dynamics with Friction and Impact , 2000, SIAM Rev..

[31]  B. Brogliato,et al.  Numerical simulation of finite dimensional multibody nonsmooth mechanical systems , 2001 .

[32]  Yildirim Hurmuzlu,et al.  A New Look at an Old Problem: Newton’s Cradle , 2001 .

[33]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[34]  M. Anitescu,et al.  A Time-stepping Method for Stii Multibody Dynamics with Contact and Friction ‡ , 2022 .

[35]  BridsonRobert,et al.  Nonconvex rigid bodies with stacking , 2003 .

[36]  Henrik I. Christensen,et al.  Implementation of multi-rigid-body dynamics within a robotic grasping simulator , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[37]  Claude Lacoursière,et al.  Splitting Methods for Dry Frictional Contact Problems in Rigid Multibody Systems: Preliminary Performance Results , 2003 .

[38]  Ronald Fedkiw,et al.  Nonconvex rigid bodies with stacking , 2003, ACM Trans. Graph..

[39]  Evangelos Kokkevis,et al.  Practical Physics for Articulated Characters , 2004 .

[40]  Mihai Anitescu,et al.  A constraint‐stabilized time‐stepping approach for rigid multibody dynamics with joints, contact and friction , 2004 .

[41]  J.C. Trinkle,et al.  A time-stepping scheme for quasistatic multibody systems , 2005, (ISATP 2005). The 6th IEEE International Symposium on Assembly and Task Planning: From Nano to Macro Assembly and Manufacturing, 2005..

[42]  Mihai Anitescu,et al.  Optimization-based simulation of nonsmooth rigid multibody dynamics , 2006, Math. Program..

[43]  Mihai Anitescu,et al.  A linearly implicit trapezoidal method for integrating stiff multibody dynamics with contact, joints, and friction , 2006 .

[44]  Kenny Erleben,et al.  Velocity-based shock propagation for multibody dynamics animation , 2007, TOGS.

[45]  F. Pfeiffer,et al.  Dynamics of Rigid Body Systems , 2008 .

[46]  Dylan A. Shell,et al.  A robust and tractable contact model for dynamic robotic simulation , 2009, SAC '09.

[47]  Mihai Anitescu,et al.  A computational study of the use of an optimization-based method for simulating large multibody systems , 2009, Optim. Methods Softw..

[48]  Leon G. Higley,et al.  Forensic Entomology: An Introduction , 2009 .

[49]  Evan Drumwright,et al.  Avoiding Zeno's paradox in impulse-based rigid body simulation , 2010, 2010 IEEE International Conference on Robotics and Automation.

[50]  Yuval Tassa,et al.  Stochastic Complementarity for Local Control of Discontinuous Dynamics , 2010, Robotics: Science and Systems.

[51]  Mihai Anitescu,et al.  An iterative approach for cone complementarity problems for nonsmooth dynamics , 2010, Comput. Optim. Appl..

[52]  Emanuel Todorov,et al.  Implicit nonlinear complementarity: A new approach to contact dynamics , 2010, 2010 IEEE International Conference on Robotics and Automation.

[53]  M. Anitescu,et al.  A Convex Complementarity Approach for Simulating Large Granular Flows , 2010 .

[54]  Wolfgang Desch,et al.  Progress in nonlinear differential equations and their applications, Vol. 80 , 2011 .