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Model order reduction for impact-contact dynamics simulations of flexible manipulators

Published online by Cambridge University Press:  05 January 2007

Ou Ma  and
Jiegao Wang
Ou Ma*
Affiliation:
New Mexico State University, Las Cruces, NM 88003, USA
Jiegao Wang
Affiliation:
MDA Space Missions, MD Robotics, Brampton, ON L6S 3J4, Canada
*
*Corresponding author. E-mail: oma@nmsu.edu
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Summary

Dynamic simulation of a flexible manipulator performing physical contact (including low-speed impact) tasks with stiff environment is very time consuming because very small integration step sizes have to be used for numerical stability. Existing model order reduction techniques cannot be readily applied due to the nonlinear nature of the contact dynamics. In this paper, a method is introduced to deal with this problem. The method first linearizes the contact force model on the right-hand side of the dynamics equations periodically. It then identifies the linear “stiffness” and “damping” terms from the linearized contact force model and combines them with the existing structural stiffness and damping matrices of the associated multibody system on the left-hand side of the equations. After such a process, the traditional modal analysis and reduction techniques for linear dynamic systems can be applied to reduce the order of the resulting dynamic system. Two numerical examples of flexible manipulators performing a contact task are presented to demonstrate the significant gain in computational efficiency and the improved output results.

Keywords

Model order reductionmodel reductioncontact dynamicssimulationflexible manipulators
Type
Article
Information
Robotica , Volume 25 , Issue 4 , July 2007 , pp. 397 - 407
Copyright
Copyright © Cambridge University Press 2007

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References

1. Ma, O., Buhariwala, K., Roger, N., Maclean, J. and Carr, R., “MDSF — a generic development and simulation facility for flexible, complex robotic systems,” Robotica 15, 49–62 (1997).CrossRefGoogle Scholar
2. Ma, O., “CDT – A General Contact Dynamics Toolkit,” Proceedings of the 31st International Symposium on Robotics, Montreal, Canada (2000) pp. 468–473.Google Scholar
3. Gilardi, G. and Sharf, I., “, Literature survey of contact dynamics modelling,” Mech. Mach. Theory 37, 1213–1239 (2002).CrossRefGoogle Scholar
4. Ascher, U. M., Pai, D. K. and Cloutier, B. P., “Forward dynamics, elimination methods, and formulation stiffness in robot simulation,” Int. J. Robot. Res. 16 (6), 749–758 (1997).CrossRefGoogle Scholar
5. Guyan, R. J., “Reduction of stiffness and mass matrix,” AIAA J. 3 (2), 380 (1965).CrossRefGoogle Scholar
6. Craig, R. R. and Bampton, M. C. C., “Coupling of substructures for dynamics analysis,” AIAA J. 6 (7), 1313–1319 (1968).CrossRefGoogle Scholar
7. Moore, B. C., “Principal component analysis in linear systems, controllability, observability and model reduction,” IEEE Trans. Autom. Control 26, 17–32 (1981).CrossRefGoogle Scholar
8. Rule, J., Richard, R. E. and Clark, R. L., “Design of an aero-elastic Delta wing model for active flutter control,” J. Guid. Control Dyn. 24 (5), 918–924 (2001).CrossRefGoogle Scholar
9. Kokotovic, P. V., O'Malley, R. E. Jr. and Sannuti, P., “Singular perturbations and order reduction in control theory—an overview,” Automatica 12, 123–132 (1976).CrossRefGoogle Scholar
10. Samar, R., Postlethwaite, I. and Gu, D. W., “Applications of the Singular Perturbation Approximation of Balanced Systems”, Proceedings of the 3rd IEEE Conference on Control Applications (1994) pp. 1823–1828.Google Scholar
11. Obinata, G. and Anderson, B. D. O., Model Reduction for Control System Design (Springer-Verlag, London, 2001).CrossRefGoogle Scholar
12. Glover, K., “All optimal Hankel-norm approximations of linear multivariable systems and their L∞-error bounds,” Int. J. Control 39 (6), 1115–1193 (1984).CrossRefGoogle Scholar
13. Sheu, C. H. et al. ., “Application of the substructuring technique to nonlinear dynamic structural analysis,” Comput. Struct. 35, 593–601.CrossRefGoogle Scholar
14. Friswell, M. I., Penny, J. E. T. and Garvey, S. D., “Using linear model reduction to investigate the dynamics of structures with local non-linearities,” Mech. Syst. Signal Process. 9 (3), 317–328 (1995).CrossRefGoogle Scholar
15. Hardy, M., Whole Vehicle Refinement, Automotive Modeling and NVH: Techniques and Solutions (IMechE Seminar Publication No. 15, London, 1997).Google Scholar
16. Kirkpatrick, S. W., “Development and validation of high fidelity vehicle crash simulation models,” SAE Transactions, 109, No. 6, pp. 872–881 (2000).Google Scholar
17. Cyril, X., Jaar, G. and St-Pierre, J., “Advanced Space Robotics Simulation for Training and Operations,” AIAA Modeling and Simulation Technologies Conference, Denver, CO (August 14–17 2000).Google Scholar
18. Wood, W. L., Practical Time-Stepping Schemes (Clarendon, London, 1990).Google Scholar
19. Fung, T. C., “Complex-time-step Newmark methods with controllable numerical dissipation,” Int. J. Numer. Methods Eng. 41, 65–93 (1998).3.0.CO;2-F>CrossRefGoogle Scholar
20. Marhefka, D. W. and Orin, D. E., “A compliant contact model with nonlinear damping for simulation of robotic systems,” IEEE Trans. Syst. Man Cybern. 29 (6), 566–572 (1999).CrossRefGoogle Scholar
21. Angeles, J., Rational Kinematics (Springer-Verlag, New York, 1989).Google Scholar
22. Skelton, R. E., Hughes, P. and Hablani, H. B., “Order reduction for models of space structures using modal cost analysis,” J. Guid. Control Dyn. 5 (4), 351–357 (1982).CrossRefGoogle Scholar
23. Gregory, C. Z. Jr., “Reduction of large flexible spacecraft models using internal balancing theory,” J. Guid. Control Dyn. 7 (6), 725–732 (1984).CrossRefGoogle Scholar
24. Cogan, S., Lallement, G., Ayer, F. and Ben-Haim, Y., “Model order reduction by selective sensitivity,” AIAA J. 35 (3), 557–562 1997).CrossRefGoogle Scholar
25. Woods, R. L. and Lawrence, K. L., Modeling and Simulation of Dynamic Systems (Prentice-Hall, Englewood Cliffs, NJ, 1997).Google Scholar
26. Singiresu, S. R., Mechanical Vibrations, 4th ed. (Prentice Hall, Englewood Cliffs, NJ, 2003).Google Scholar
27. Wang, J., Mukherji, R., Ficocelli, M., Ogilvie, A., Liu, M. and Rice, C., “Modeling and Simulation of Robotic System for Servicing Hubble Space Telescope,” Proceedings of the 2006 IEEE International Conference on Intelligent Robots and Systems, Beijing, China (October 9–15, 2006) pp. 1026–1031.Google Scholar