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Research Papers

Performance of a Method for Formulating Geometrically Exact Complementarity Constraints in Multibody Dynamic Simulation

[+] Author and Article Information
Daniel Montrallo Flickinger

Research Assistant
CS Robotics Laboratory,
Department of Computer Science,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: dmflickinger@gmail.com

Jedediyah Williams

Research Assistant
CS Robotics Laboratory,
Department of Computer Science,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: jedediyah@gmail.com

Jeffrey C. Trinkle

Professor
CS Robotics Laboratory,
Department of Computer Science,
Rensselaer Polytechnic Institute,
Troy, NY 12180
e-mail: trinkle@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 20, 2013; final manuscript received March 24, 2014; published online September 12, 2014. Assoc. Editor: Dan Negrut.

J. Comput. Nonlinear Dynam 10(1), 011010 (Sep 12, 2014) (12 pages) Paper No: CND-13-1151; doi: 10.1115/1.4027314 History: Received June 20, 2013; Revised March 24, 2014

Contemporary problem formulation methods used in the dynamic simulation of rigid bodies suffer from problems in accuracy, performance, and robustness. Significant allowances for parameter tuning, coupled with careful implementation of a broad-phase collision detection scheme are required to make dynamic simulation useful for practical applications. A constraint formulation method is presented herein that is more robust, and not dependent on broad-phase collision detection or system tuning for its behavior. Several uncomplicated benchmark examples are presented to give an analysis and make a comparison of the new polyhedral exact geometry (PEG) method with the well-known Stewart–Trinkle method. The behavior and performance for the two methods are discussed. This includes specific cases where contemporary methods fail to match theorized and observed system states in simulation, and how they are ameliorated by the new method presented here. The goal of this work is to complete the groundwork for further research into high performance simulation.

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References

Rahnejat, H., 1998, Multi-Body Dynamics: Vehicles, Machines, and Mechanisms, Professional Engineering, Wiley, New York.
Sinha, R., Paredis, C., Liang, V., and Khosla, P., 2001, “Modeling and Simulation Methods for Design of Engineering Systems,” ASME J. Comput. Inf. Sci. Eng., 123(1), pp. 84–91. [CrossRef]
Flores, P., Leine, R., and Glocker, C., 2012, “Application of the Nonsmooth Dynamics Approach to Model and Analysis of the Contact-Impact Events in Cam-Follower Systems,” Nonlinear Dyn., 69(4), pp. 2117–2133. [CrossRef]
Ma, Z., and Perkins, N., 2003, “An Efficient Multibody Dynamics Model for Internal Combustion Engine Systems,” Multibody Syst. Dyn., 10(4), pp. 363–391. [CrossRef]
Chakraborty, N., Berard, S., Akella, S., and Trinkle, J., 2008, “An Implicit Time-Stepping Method for Quasi-Rigid Multibody Systems With Intermittent Contact,” Proceedings of ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Las Vegas, NV, Sept. 4–7, ASME Vol. 5, Part A, pp. 455–464. [CrossRef]
Sauer, J., and Schömer, E., 1998, “A Constraint-Based Approach to Rigid Body Dynamics for Virtual Reality Applications,” Proceedings of the ACM Symposium on Virtual Reality Software and Technology, ACM, pp. 153–162.
Coumans, E., 2013, Bullet Physics Library. Available at: http://www.bulletphysics.com
Lotstedt, P., 1981, “Coulomb Friction in Two-Dimensional Rigid Body Systems,” Z. Angew. Math. Mech., 61(12), pp. 605–615. [CrossRef]
Schiehlen, W., 1997, “Multibody System Dynamics: Roots and Perspectives,” Multibody Syst. Dyn., 1(2), pp. 149–188. [CrossRef]
Mirtich, B., 1998, “V-clip: fast and robust polyhedral collision detection,” ACM Trans. Graph., 17(3), pp. 177–208. [CrossRef]
Jiménez, P., Thomas, F., and Torras, C., 2001, “3D Collision Detection: A Survey,” Comput. Graphics, 25(2), pp. 269–285. [CrossRef]
Redon, S., Kheddar, A., and Coquillart, S., 2003, “Fast Continuous Collision Detection Between Rigid Bodies,” Computer Graphics Forum, Vol. 21, H. Rushmeier and O. Deussen eds., Eurographics Association and John Wiley & Sons Ltd., Geneve, Switzerland, Hoboken, NJ, pp. 279–287.
Trinkle, J. C., Pang, J.-S., Sudarsky, J.-S., and Lo, G., 1997, “On Dynamic Multi-Rigid-Body Contact Problems With Coulomb Friction,” Z. Angew. Math. Mech., 77(4), pp. 267–279. [CrossRef]
Johansson, L., 1999, “Linear Complementarity Algorithm for Rigid Body Impact With Friction,” Eur. J. Mech., A, 18(4), pp. 703–717. [CrossRef]
Baraff, D., 1994, “Fast Contact Force Computation for Nonpenetrating Rigid Bodies,” Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, ACM, pp. 23–34.
Mirtich, B., and Canny, J., 1995, “Impulse-Based Simulation of Rigid Bodies,” Proceedings of the Symposium on Interactive 3D graphics, ACM, pp. 181–ff.
Anitescu, M., and Potra, F. A., 1997, “Formulating Dynamic Multi-Rigid-Body Contact Problems With Friction as Solvable Linear Complementarity Problems,” Nonlinear Dyn., 14, pp. 231–247. [CrossRef]
Stewart, D., and Trinkle, J., 1996, “An Implicit Time-Stepping Scheme for Rigid Body Dynamics With Inelastic Collisions and Coulomb Friction,” Int. J. Numer. Methods Eng., 39(15), pp. 2673–2691. [CrossRef]
Trinkle, J., 2003, “Formulations of Multibody Dynamics as Complementarity Problems,” Proceedings of ASME International Design Engineering Technical Conferences. [CrossRef]
Berard, S., Trinkle, J., Nguyen, B., Roghani, B., Fink, J., and Kumar, V., 2007, “Davinci Code: A Multi-Model Simulation and Analysis Tool for Multi-Body Systems,” IEEE International Conference on Robotics and Automation, IEEE, pp. 2588–2593.
Bajaj, C., and Dey, T., 1992, “Convex Decomposition of Polyhedra and Robustness,” SIAM J. Comput., 21(2), pp. 339–364. [CrossRef]
Lien, J., and Amato, N., 2007, “Approximate Convex Decomposition of Polyhedra,” Proceedings of the ACM symposium on Solid and Physical Modeling, ACM, pp. 121–131.
Smith, R., 2013, “Open dynamics engine.” Available at: [CrossRef]
Stewart, D., and Trinkle, J., 2000, “Implicit Time-Stepping Scheme for Rigid Body Dynamics With Coulomb Friction,” Proceedings of IEEE International Conference on Robotics and Automation, Vol. 1, pp. 162–169.
Anitescu, M., and Potra, F., 2002, “A Time-Stepping Method for Stiff Multibody Dynamics With Contact and Friction,” Int. J. Numer. Methods Eng., 55(7), pp. 753–784. [CrossRef]
Nguyen, B., 2011, “Locally Non-Convex Contact Models and Solution Methods for Accurate Physical Simulation in Robotics,” Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, New York.
Nguyen, B., and Trinkle, J., 2010, “Modeling Non-Convex Configuration Space Using Linear Complementarity Problems,” Proceedings of IEEE International Conference on Robotics and Automation, pp. 2316–2321.
Ferris, M., and Munson, T., 2000, “Complementarity Problems in GAMS and the Path Solver,” J. Econ. Dyn. Control, 24(2), pp. 165–188. [CrossRef]
Dirkse, S., Ferris, M. C., and Munson, T., 2013, “The Path Solver.” Available at: pages.cs.wisc.edu/~ferris/path.html
Williams, J., Lu, Y., Flickinger, D. M., and Trinkle, J., 2013, “RPI Matlab Simulator.” Available at: http://code.google.com/p/rpi-matlab-simulator/

Figures

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Fig. 1

Vertex at times t1…t4 moving within the constraint half-spaces near an object, Stewart–Trinkle formulation. A large impulse acts on the vertex at t2 and the diagonal constraint is active at t3 and t4.

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Fig. 2

Vertex at times t1…t3 moving in proximity to an object, polyhedral exact geometry formulation

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Fig. 3

A particle interacting with a single edge

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Fig. 4

Particle M interacting with two edges, p1p2 and p2p3, with half-spaces represented by shaded areas

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Fig. 5

Particle M interacting with a planar polygon, the constraints are represented as dashed lines along edges 1 and 2

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Fig. 6

Trajectories of the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 7

Detailed trajectory of polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 8

Problem size of the polyhedral exact geometry and Stewart–Trinkle methods, hills simulation

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Fig. 9

Solver time for the polyhedral exact geometry and Stewart–Trinkle methods, hills simulation

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Fig. 10

Trajectories of the polyhedral exact geometry and Stewart–Trinkle methods without friction

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Fig. 11

Details of the trajectories of the polyhedral exact geometry and Stewart–Trinkle methods without friction

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Fig. 12

Problem size for the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 13

Solver time for the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 14

Trajectories of the sawtooth simulation with friction, using the polyhedral exact geometry, Stewart–Trinkle, and Anitescu–Potra methods

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Fig. 15

Sawtooth simulation trajectories in proximity to the beginning of the second ballistic phase

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Fig. 16

Trajectories of the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 17

Detailed view of trajectories of the polyhedral exact geometry and Stewart–Trinkle methods

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Fig. 18

Median error in particle simulation of the polyhedral exact geometry, Stewart–Trinkle, and Anitescu–Potra methods with respect to step size

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Fig. 19

Profile view of initial configuration of slender rod simulation

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Fig. 20

Oblique view of initial configuration of slender rod simulation

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Fig. 21

Plan view of initial configuration of slender rod simulation

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Fig. 22

Median error in slender rod simulation of the polyhedral exact geometry, Stewart–Trinkle, and Anitescu–Potra methods with respect to step size

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