A computational study of the use of an optimization-based method for simulating large multibody systems

Optimization Methods and Software

Volumn 24, Issue 6, 2009, Pages 871-894

  Petra, Cosmin ^a   Gavrea, Bogdan ^b   Anitescu, Mihai ^c   Potra, Florian ^a  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^b TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

^c ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

Contact and friction; Large scale optimization; Quadratic programming; Rigid multibody

Indexed keywords

CHOLESKY; COMPUTATIONAL PERFORMANCE; COMPUTATIONAL STUDIES; CONTACT AND FRICTION; CONVEX RELAXATION; COPOSITIVE; LARGE MULTIBODY SYSTEMS; LARGE SYSTEM; LARGE-SCALE OPTIMIZATION; LINEAR COMPLEMENTARITY PROBLEMS; MEMORY USE; MULTI BODY SYSTEMS; QP SOLVERS; RIGID BODY; RIGID MULTIBODY; TIME-STEPPING SCHEMES;

FRICTION; QUADRATIC PROGRAMMING; RELAXATION PROCESSES;

OPTIMIZATION;

EID: 70349617969     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780902806094     Document Type: Article

References (59)

1. E. Andersen and Y. Ye, On a homogeneous algorithm for the monotone complementarity problem, Math. Program. 84 (1999), pp. 375-399.
2. M. Anitescu, A fixed time-step approach for multibody dynamics with contact and friction, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (IROS 2003), Vol.4, Las Vegas, NV, (2003).
3. M. Anitescu, Optimization-based simulation of nonsmooth dynamics, Math. Program. 105 (2006), pp. 113-143.
4. M. Anitescu and G.D. Hart, Solving nonconvex problems of multibody dynamics with joints, contact and small friction by sequential convex relaxation, Mech. Based Des. Mach. Struct. 31(3) (2003), pp. 335-356.
5. M. Anitescu and G.D. Hart, A fixed-point iteration approach for multibody dynamics with contact and small friction, Math. Program. 101 (2004), pp. 3-32.
6. M. Anitescu and G. Hart, A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction., Int. J. Numer. Methods Eng. 60 (2004), pp. 2335-2371. (Pubitemid 39039874)
7. M. Anitescu and F.A. Potra, Formulating dynamic multi-rigid-body contact problems with friction as solvable linear complementarity problems, Nonlinear Dynam. 14 (1997), pp. 231-247.
8. M. Anitescu and A. Tasora, An iterative approach for cone complementarity problems for nonsmooth dynamics, preprint ANL/MCS-P1413-0507. Argonne National Laboratory, Argonne, IL, 2007.
9. M. Anitescu, J.F. Cremer, and F.A. Potra, Formulating 3D contact dynamics problems, Mech. Struct. Mach. 24(4) (1996), pp. 405-437.
10. M. Anitescu, J. Cremer, and F. Potra, On the existence of solutions to complementarity formulations of contact problems with friction, in Complementarity and Variational Problems: State of the Art, SIAM, Philadelphia, 1997, pp. 12-21.
11. M.Anitescu, F.A. Potra, and D. Stewart, Time-stepping for three-dimensional rigid-body dynamics, Comput. Methods Appl. Mech. Eng. 177 (1999), pp. 183-197.
12. D. Baraff, Issues in computing contact forces for non-penetrating rigid bodies,Algorithmica 10 (1993), pp. 292-352.
13. G. Bartels, T. Unger, D. Kadau, D.E. Wolf, and J. Kertsz, The effect of contact torques on porosity of cohesive powders, Granular Mat. 7 (2005), pp. 139-143.
14. S.J. Benson and J. Morée, A limited-memory variable-metric algorithm for bound-constrained minimization, Tech. Rep. ANL/MCS-P909-0901. Mathematics and Computer Science Division, Argonne National Laboratory, 2001.
15. A. Boeing and T. Bräunl, Evaluation of real-time physics simulation systems, Proceedings of the 5th International Conference on Computer Graphics and Interactive Techniques in Australia and Southeast Asia, Perth, Australia, 2007, pp. 281-288.
16. F. Camborde, C. Mariotti, and F.V. Donze, Numerical study of rock and concrete behaviour by discrete element modelling, Comput. Geotech. 27 (2000), pp. 225-247.
17. A. Chatterjee and A. Ruina, A new algebraic rigid-body collision law based on impulse space considerations, Trans. ASME, J. Appl. Mech. 65 (1998), pp. 939-951.
18. W.W.H.Y. Chen, T.A. Davis, and S. Rajamanicka, Algorithm 8xx: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate, Tech. Rep. CISE Department, University of Florida, September, 2006.
19. J. Czyzyk, S. Mehrotra, and S.J. Wright, PCx user guide, Tech. Rep. OTC 96/01. Optimization Technology Center, Argonne National Laboratory and Northwestern University, October, 1996.
20. T.A. Davis and W.W. Hager, Modifying a sparse Cholesky factorization, SIAM J. Matrix Anal. Appl. 20 (1999), pp. 606-627.
21. T.A. Davis and W.W. Hager, Row modifications of a sparse Cholesky factorization, SIAM J. Matrix Anal. Appl. 26 (2005), pp. 621-639.
22. T.A. Davis and W. Hager, Dynamic supernodes in sparse cholesky update/downdate and triangular solves, Tech. Rep. CISE Department University of Florida, September, 2006.
23. S. Dirkse and M. Ferris, The PATH solver: a non-monotone stabilization scheme for mixed complementarity problems, Optim. Methods Softw. 5 (1995), pp. 123-156.
24. B.R. Donald and D.K. Pai, On the motion of compliantly connected rigid bodies in contact: a system for analyzing designs for assembly, Proceedings of the Conference on Robotics and Automation, IEEE, Cincinnati, OH, 1990, pp. 1756-1762.
25. I.S. Duff, MA57 - a code for the solution of sparse symmetric definite and indefinite systems, ACM Trans. Math. Software 30 (2004), pp. 118-144.
26. J. Duff and J. Reid, The multifrontal solution of indefinite sparse symmetric linear equations, ACM Trans. Math. Softw. 9 (1983), pp. 302-325.
27. K. Erleben, Stable, robust, and versatile multibody dynamics animation, Ph.D. thesis. University of Copenhagen, Copenhagen, 2004.
28. R. Featherstone, Robot Dynamics Algorithms, Kluwer Academic Publishers., Boston, 1987.
29. M. Ferris and T. Munson, Interfaces to PATH 3.0: design, implementation and usage, Comput. Optim. Appl. 12 (1999), pp. 207-227.
30. J. Gauvin, A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming, Math. Program. 12 (1977), pp. 136-138.
31. E.M. Gertz and S.J. Wright, Object-oriented software for quadratic programming, ACM Trans. Math. Softw. 29 (2003), pp. 58-81.
32. J. Gondzio, HOPDM (version 2.12) - a fast lp solver based on a primal-dual interior point method, Eur. J. Oper. Res. 85 (1995), pp. 221-225.
33. H.D. Gougar, Advanced core design and fuel management for pebble-bed reactors, Ph.D. in Nuclear Engineering. Department of Nuclear Engineering, Penn State University, 2004.
34. N.I.M. Gould, J.A. Scott, and Y. Hu, A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations, ACM Trans. Math. Software 33 (2007), p. 10.
35. D. Goulding, J.-P. Hansen, and S. Melchionna, Size selectivity of narrow pores, Phys. Rev. Lett. 85 (2000), pp. 1132-1135.
36. S. Hasegawa and M. Sato, Real-time rigid body simulation for haptic interactions based on contact volume of polygonal objects, Comput. Graph. Forum 23 (2004), pp. 529-538.
37. E.J. Haug, Computer-Aided Kinematics and Dynamics of Mechanical Systems, Prentice-Hall., Englewood Cliffs, NJ, 1989.
38. D. Helbing, I. Farkas, and T.Vicsek, Simulating dynamical features of escape panic, Nature 407 (2000), pp. 487-490.
39. W. Jorgensen, J. Chandrasekhar, J. Madura, R. Impey, and M. Klein, Comparison of simple potential functions for simulating liquid water, J. Chem. Phys. 79 (1983), pp. 926-935.
40. D. Kadau, G. Bartels, L. Brendel, and D. Wolf, Pore stabilization in cohesive granular systems, Phase Transit. 76 (2003), pp. 315-331.
41. C. Lin and J. Moré, Incomplete Cholesky factorizations with limited memory, SIAM J. Sci. Comput. 21 (1999), pp. 24-45.
42. C.-J. Lin and J.J. Moré, Newton's method for large bound-constrained optimization problems, SIAM J. Optim. 9 (1999), pp. 1100-1127.
43. V. Milenkovic and H. Schmidl, Optimization-based animation, Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, Los Angels, CA, 2001, pp. 37-46.
44. R. Moeckel, Chaotic dynamics near triple collision, Arch. Ration. Mech. Anal. 107 (1989), pp. 37-69.
45. J.-S. Pang and J.C. Trinkle, Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction, Math. Program. 73 (1996), pp. 199-226.
46. J.-S. Pang, V. Kumar, and P. Song, Convergence of time-stepping method for initial and boundary-value frictional compliant contact problems, SIAM J. Numer. Anal. 43 (2005), pp. 2200-2226.
47. F.A. Potra, M. Anitescu, B. Gavrea, and J. Trinkle, A linearly implicit trapezoidal method for integrating stiff multibody dynamics with contact and friction, Int. J. Numer. Methods Eng. 66(7) (2006), pp. 1079-1124.
48. F. Radjai, M.J.J.-J. Moreau, and S. Roux, Force distributions in dense two-dimensional granular systems, Phys. Rev. Lett. 77(2) (1996), pp. 274-277.
49. C. Rycroft, M. Bazant, G. Grest, and J. Landry, Dynamics of random packings in granular flow, Phys. Rev. E 73 (2006), p. 51306.
50. M. Saraniti, S. Aboud, and R. Eisenberg, The simulation of ionic charge transport in biological ion channels: an introduction to numerical methods, Rev. Comput. Chem. 22 (2006), pp. 229-293.
51. P. Song, P. Kraus, V. Kumar, and P. Dupont, Analysis of rigid-body dynamic models for simulation of systems with frictional contacts, J. Appl. Mech. 68(1) (2001), pp. 118-128.
52. P. Song, J.-S. Pang, and V. Kumar, A semi-implicit time-stepping model for frictional compliant contact problems, Int. J. Numer. Methods Eng. 60 (2004), pp. 267-279.
53. D.E. Stewart, Rigid-body dynamics with friction and impact, SIAM Rev. 42(1) (2000), pp. 3-39.
54. D.E. Stewart and J. Trinkle, An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and coulomb friction, Int. J. Numer. Methods Eng. 39 (1996), pp. 281-287.
55. A. Tasora and M. Anitescu, A fast NCP solver for large rigid-body problems with contacts, friction, and joints, in ECCOMAS Thematic Conference in Multibody Dynamics, Carlo Botasso, ed., Springer, Berlin, 2008, pp. 45-56.
56. A. Tasora, E. Manconi, and M. Silvestri, Un nuovo metodo del simplesso per il problema di complementarità lineare mista in sistemi multibody con vincoli unilateri, Proceedings of AIMETA 05, Firenze, Italy, 2005.
57. J. Trinkle, J.-S. Pang, S. Sudarsky, and G. Lo, On dynamic multi-rigid-body contact problems with coulomb friction, Z. Angew. Math. Mech. 77 (1997), pp. 267-279. (Pubitemid 127780388)
58. A. Wallqvist and R. Mountain, Molecular models of water: Derivation and description, Rev. Comput. Chem. 13 (1999), pp. 183-247.
59. Y. Zhang, Solving large-scale linear programs by interior-point methods under the matlab environment, Tech. Rep. TR 96-101, University of Maryland, Baltimore County, February, 1996.