Discrete mechanics and optimal control for constrained multibody dynamics

2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007

Volumn 5 PART A, Issue , 2008, Pages 623-632

  Leyendecker, Sigrid ^c   Ober Blöbaum, Sina ^d   Marsden, Jerrold E ^a   Ortiz, Michael ^b  

^a Applied Mechanics and Control and Dynamical Systems   (United States)

^b Graduate Aeronautical Laboratories   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^d UNIVERSITY OF PADERBORN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

(I ,J) CONDITIONS; (PL) PROPERTIES; ACTUATING FORCES; CONJUGATE MOMENTUM; COST FUNCTIONAL; DISCRETE CONFIGURATIONS; DISCRETE MECHANICS; DISCRETE OPTIMAL CONTROL; DYNAMICAL EQUATIONS; EQUALITY CONSTRAINTS; EXTERNAL FORCING; HOLONOMIC CONSTRAINTS; INTERNATIONAL CONFERENCES; INTERNATIONAL DESIGNS; LAG RANGE; MECHANICAL STRUCTURES; MOMENTUM BUDGET; MOMENTUM WHEELS; MULTI BODY DYNAMICS; MULTI-BODY SYSTEM (MBS); NON-LINEAR DYNAMICS; NULL SPACE METHOD; NUMERICAL DISSIPATION; OPTIMAL CONTROL (OC); RIGID BODY (RB); STRUCTURE PRESERVING; TECHNICAL CONFERENCES; TIME-STEPPING; TIME-STEPPING SCHEMES;

ALGORITHMS; ARCHITECTURAL DESIGN; BOOLEAN FUNCTIONS; CANNING; COMPUTER CONTROL; COMPUTER NETWORKS; COMPUTERS; CONTROL SYSTEMS; DYNAMICAL SYSTEMS; DYNAMICS; ENGINEERING; EQUATIONS OF STATE; EVOLUTIONARY ALGORITHMS; INFORMATION SYSTEMS; INTERSECTIONS; LARGE SCALE SYSTEMS; MATHEMATICAL MORPHOLOGY; MECHANICS; MOBILE TELECOMMUNICATION SYSTEMS; MOMENTUM; NONLINEAR PROGRAMMING; NUMBER THEORY; NUMERICAL METHODS; SCHEDULING ALGORITHMS; TECHNOLOGY;

NONLINEAR EQUATIONS;

EID: 44949230283     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2007-34574     Document Type: Conference Paper

References (41)

1. Bertsekas, D., 1995. Nonlinear Programming. Athena Scientific.
2. Luenberger, D., 1984. Linear and Nonlinear Programming. Addison-Wesley.
3. Leyendecker, S., Betsch, P., and Steinmann, P., 2004. "Energy-conserving integration of constrained Hamiltonian systems - a comparison of approaches". Comput. Mech., 33, pp. 174-185.
4. Benzi, M., Golub, G., and Liesen, J., 2005. "Numerical solution of saddle point problems". Acta Numerica, pp. 1-137
5. Betsch, P., and Steinmann, P., 2002. "Conserving properties of a time FE method - Part III: Mechanical systems with holonomic constraints". Int. J. Numer. Meth. Engng., 53, pp. 2271-2304.
6. Gonzalez, O., 1999. "Mechanical Systems Subject to Holonomic Constraints: Differential-Algebraic Formulations and Conservative Integration". Physica D, 132, pp. 165-174
7. Wendlandt, J., and Marsden, J., 1997. "Mechanical integrators derived from a discrete variational principle". Physica D, 106, pp. 223-246.
8. Petzold, L., and Loetstedt, P., 1986. "Numerical solution of nonlinear differential equations with algebraic constraints II: Practical implications". SIAM J. Sci. Comput., 7 (3), pp. 720-733.
9. Hairer, E., Lubich, C., and Roche, M., 1989. The numerical solution of differential algebraic equations by Runge-Kutta methods. Springer.
10. Leimkuhler, B., and Reich, S., 2004. Simulating Hamiltonian Dynamics. Cambridge University Press.
11. Rheinboldt, W., 1997. "Solving algebraically explicit daes with the manpak-manifold-algorithms". Computers Math. Applic., 33 (3), pp. 31-43.
12. Betsch, P., 2005. "The discrete null space method for the energy consistent integration of constrained mechanical systems. Part I: Holonomic constraints". Comput. Methods Appl. Mech. Engrg., 194 (50-52), pp. 5159-5190.
13. Gill, P., Murray, W., and Saunders, M., 1997. "SNOPT: An SQP algorithm for large-scale constrained optimization". Numerical Analysis Report, Department of Mathematics, University of California, San Diego, La Jolla, CA, 97-2.
14. Gill, P., Jay, L., Leonard, M., Petzold, L., and Sharma, V., 2000. "An SQP method for the optimal control of large-scale dynamical systems". J. Comp. Appl. Math., 20, pp. 197-213.
15. Schittkowski, K., 1980. Nonlinear programming codes Lecture Notes in Economics and Mathematical Systems, Vol. 183, viii+242. Springer.
16. Stoer, J., and Bulirsch, R., 2002. Introduction to numerical analysis, Vol. 12, xvi+744. Springer.
17. Kraft, D., 1985. "On converting optimal control problems into nonlinear programming problems". Computational Mathematical Programming, F15, pp. 261-280.
18. Hicks, G., and Ray, W., 1971. "Approximation methods for optimal control systems". Can. J. Chem. Engng., 49, pp. 522-528.
19. Deuflhard, P., 1974. "A modified newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting". Numer. Math., 22, pp. 289-315.
20. Bock, H., and Plitt, K., 1984. "A multiple shooting algorithm for direct solution of optimal control problems". In Proc. 9th IFAC World Congress Budapest, pp. 243-247.
21. Leineweber, D., Bauer, I., Bock, H., and Schlöder, J., 2003. "An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization. part I: Theoretical aspects". Comp. Chem. Eng., 27, pp. 157-166.
22. von Stryk, O., 1991. "Numerical solution of optimal control problems by direct collocation". Optimal control (Freiburg, 1991), Internal. Ser. Numer. Math., pp. 129-143.
23. Biegler, L., 1984. "Solution of dynamic optimization problems by successive quadratic programming and orthogonal collocation". Comput. Chem. Engng., 8, pp. 243-248.
24. Betts, J., 1998. "Survey of numerical methods for trajectory optimization". Journal of Guidance, Control, and Dynamics, 21 (2).
25. Binder, T., Blank, L., Bock, H., Bulirsch, R., Dahmen, W., Diehl, M., Kronseder, T., Marquardt, W., Schlöder, J., and vonStryk, O., 2001. "Introduction to model based optimization of chemical processes on moving horizons". Online Optimization of Large Scale Systems: State of the Art, pp. 295-340. http://www.zib.de/dfg-echtzeit/Publikatio nen/Preprints/Preprint-01-15.html.
26. Junge, O., Marsden, J., and Ober-Blöbaum, S., 2005. "Discrete mechanics and optimal control". In Proceedings of the 16th IFAC World Congress.
27. Marsden, J., and West, M., 2001. "Discrete mechanics and variational integrators". Acta Numerica, pp. 357-514.
28. Junge, O., and Ober-Blöbaum, S., 2005. "Optimal reconfiguration of formation flying satellites". In IEEE Conference on Decision and Control and European Control Conference ECC.
29. Junge, O., and Ober-Blobaum, S., 2006. "Optimal reconfiguration of formation flying spacecraft - a decentralized approach". In Proceedings of the IEEE Conference on Decision and Control and European Control Conference ECC.
30. Kanso, E., and Marsden, J., 2005. "Optimal motion of an articulated body in a perfect fluid". In IEEE Conference on Decision and Control and European Control Conference ECC 2005.
31. Betsch, P., and Steinmann, P., 2001. "Constrained integration of rigid body dynamics". Comput. Methods Appl. Mech. Engrg., 191, pp. 467-488.
32. Reich, S., 1996. "Symplectic integrators for systems of rigid bodies". Fields Institute Commun., 10, pp. 181-191.
33. Betsch, P., Menzel, A., and Stein, E., 1998. "On the parametrization of finite rotations in computational mechanics; A classification of concepts with application to smooth shells". Comput. Methods Appl. Mech. Engrg., 155, pp. 273-305.
34. Bauchau, O., and Trainelli, L., 2003. "The Vectorial Parameterization of Rotation". Nonlin. Dynamics, 1, pp. 71-92.
35. Leyendecker, S., Betsch, P., and Steinmann, P., 2006. "Objective energy-momentum conserving integration for the constrained dynamics of geometrically exact beams". Comput. Methods Appl. Mech. Engrg., 195, pp. 2313-2333.
36. Betsch, P., and Leyendecker, S., 2006. "The discrete null space method for the energy consistent integration of constrained mechanical systems. Part II: Multibody dynamics". Int. J. Numer. Meth. Engng., 67 (4), pp. 499-552.
37. Leyendecker, S., Betsch, P., and Steinmann, P., 2007. "The discrete null space method for the energy consistent integration of constrained mechanical systems. Part III: Structural dynamics". Multibody System Dynamics. accepted for publication.
38. Marsden, J., and Ratiu, T, 1994. Introduction to Mechanics and Symmetry. A Basic Exposition of Classical Mechanical Systems. Texts in Applied Mathematics 17. Springer.
39. Goldstein, H., Poole, C., and Safko, J., 2002. Classical Mechanics. Addison Wesley.
40. Gonzalez, O., 1996. "Time Integration and Discrete Hamiltonian Systems". J. Nonlinear Sci., 6, pp. 449-467.
41. Antmann, S., 1995. Nonlinear Problems in Elasticity. Springer.