Improved 'order-n' performance algorithm for the simulation of constrained multi-rigid-body dynamic systems

Multibody System Dynamics

Volumn 9, Issue 2, 2003, Pages 185-212

  Anderson, K S ^a   Critchley, J H ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Constrained system; Coordinate reduction; Recursive algorithm

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; NUMERICAL ANALYSIS; STATE SPACE METHODS;

COORDINATE REDUCTION;

SYSTEMS ANALYSIS;

EID: 0037344694     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022566107679     Document Type: Article

References (33)

1. Anderson, K.S., 'Recursive derivation of explicit equations of motion for efficient dynamic/control simulation of large multibody systems', Ph.D. Dissertation, Stanford University, 1990.
2. Anderson, K.S., 'An order-N formulation for motion simulation of general constrained multi-rigid-body systems', Computers & Structures 43(3), 1992, 565-572.
3. Anderson, K.S., 'An efficient formulation for the modeling of general multi-flexible-body constrained systems', International Journal of Solids and Structures 30(7), 1993, 921-945.
4. Armstrong, W.W., 'Recursive solution of the equations of motion of an N-link manipulator', in Proceedings of the Fifth World Congress on the Theory of Machines and Mechanisms, Montreal, Canada, 1979, Vol. 2, 1342-1346.
5. Bae, D.S. and Haug, E.J., 'A recursive formation for constrained mechanical systems dynamics: Part I, Open loop systems', Mechanisms, Structures, and Machines 15(3), 1987, 359-382.
6. Bae, D.S. and Haug, E.J., 'A recursive formation for constrained mechanical systems dynamics: Part II, Closed loop systems', Mechanisms, Structures, and Machines, 15(4), 1987, 481-506.
7. Banerjee, A.K., 'Block-diagonal equations for multibody elastodynamics with geometric stiffness and constraints', Journal of Guidance, Control, and Dynamics 16(6), 1993, 1092-1100.
8. Baraff, D., 'Linear-time dynamics using Lagrange multipliers', in Proceedings of the ACM SIGGRAPH Conference on Computer Graphics, August 4-9, ASME, New York, 1996, 137-146.
9. Baumgarte, J., 'Stabilization of constraint and integrals of motion in dynamical systems', Computer Methods in Applied Mechanics and Engineering 1, 1972, 1-16.
10. Brenan, K.E., Campbell, S.L. and Petzold, L.R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York, 1989.
11. Chace, M.A., 'Method and experience in computer aided design of large-displacement mechanical systems', in Computer Aided Analysis and Optimizations of Mechanical System Dynamics, E.J. Haug (ed.), Springer-Verlag, Berlin, 1984, 233-259.
12. Featherstone, R., 'The calculation of robotic dynamics using articulated body inertias', International Journal of Robotics Research 2(1), 1983, 13-30.
13. Featherstone, R., Robotic Dynamics Algorithms, Kluwer Academic Publishers, Dordrecht, 1987.
14. Garcia de Jalon, J. and Bayo, E., Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge, Springer-Verlag, New York, 1994.
15. Hollerbach, J.M., 'A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity,' IEEE Transactions on Systems, Man, and Cybernetics SMC-10(11), 1980, 730-736.
16. Jain, A. and Rodriguez, G., 'Linearization of manipulator dynamics using spatial operators', IEEE Transactions on Systems, Man and Cybernetics, 23(1), 1993, 239-248.
17. Jain, A. and Rodriguez, G., 'Diagonalized Lagrangian robot dynamics', IEEE Transactions on Robotics and Automation 11(4), 1995, 571-584.
18. Kane, T.R. and Levinson, D.A., Dynamics: Theory and Application, McGraw Hill, New York, 1985.
19. Lubich, C., Nowak, U., Pohle, U. and Engstler, C., 'MEXX-numerical software for the integration of constrained mechanical systems', Berlin, SC92-12, 1992.
20. Nielan, P.E., 'Efficient computer simulation of motions of multibody systems', Ph.D. Dissertation, Stanford University, 1986.
21. Orlandea, N., Chace, M.A. and Calahan, D.A., 'A sparsity-oriented approach to the dynamics analysis and design of mechanical systems - Parts 1 & 2', Journal of Engineering for Industry 43, 1977, 773-784.
22. Park, K.C. and Chiou, J.C., 'Stabilization of computational procedures for constrained dynamical systems', Journal of Guidance, Control and Dynamics 11(4), 1988, 365-370.
23. Petzold, L.R., 'Differential/algebraic equations are not ODE's', SIAM Journal of Science, Statistics and Computation 3(3), 1982, 367-384.
24. Petzold, L.R. and Lotstedt, P., 'Numerical solution of nonlinear differential equations with algebraic constraints II: Practical implications', SIAM Journal of Science, Statistics and Computation 7(3), 1986, 720-733.
25. Rosenthal, D.E. and Sherman, M.A., 'High performance multibody simulations via symbolic equation manipulation and Kane's method', Journal of the Astronautical Sciences 34(3), 1986, 223-239.
26. Rosenthal, D.E., 'An order n formulation for robotic systems', Journal of Astronautical Sciences 38(4), 1990, 511-529.
27. Saha, S.K. and Schiehlen, W.O., 'Recursive kinematics and dynamics for parallel structured closed-loop multibody systems', Mechanical Structures and Machines 29(2), 2001, 143-175.
28. Schwertassek, R., 'Reduction of multibody simulation time by appropriate formulation of dynamical system equations', in Proceedings of the NATO Advanced Study Institute on Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, Troia, Portugal, June 27-July 9, M.S. Pereira and J.A.C. Ambrósio (eds.) Kluwer Academic Publishers, Dordrecht, 1993, 447-482.
29. Stajskal, V. and Valášek, M., Kinematics and Dynamics of Machinery, Marcel Dekker, New York, 1996.
30. Vereshchagin, A.F., 'Gauss principle of least constraint for modeling the dynamics of automatic manipulators using a digital computer', Soviet Physics - Doklady 20(1), 1975, 33-34.
31. Walker, M.W. and Orin, D.E., 'Efficient dynamic computer simulation of robotic mechanisms', Journal of Dynamic Systems, Measurements, and Control 104, 1982, 205-211.
32. Wehage, R.A. and Haug, E.J., 'Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems', Journal of Mechanical Design 104, 1982, 247-255.
33. Wehage, R.A., 'Application of matrix partitioning and recursive projection to O(n) solution of constrained equations of motion', in ASME Design Engineering Division (Publication) DE, Vol. 15-2, Trends and Developments in Mechanisms, ASME, New York, 1988, 221-230.