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Order-N Formulation and Dynamics of Multi-Unit Flexible Space Manipulators

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Abstract

As robotic manipulators gain more importance in space operations, it is becoming imperative to understand their distinctive dynamics and control characteristics. With the increasing complexity of space robots, efficient algorithms are now required for their simulation. The present study uses an order-N algorithm, based on the Lagrangian approach and velocity transformations, to simulate the planar dynamics of a novel orbiting manipulator with arbitrary number of slewing and deployable flexible links. The relatively general formulation accounts for interactions between orbital, librational, slewing, deployment, and vibrational degrees of freedom, and thus is applicable to a large class of manipulator systems of contemporary interest. A parametric analysis of the system dynamics is carried out to investigate the effects of initial disturbances, variation of system parameters and maneuver profiles. The study suggests significant coupling between the rigid body motion and structural vibrations. As a result, the system's flexibility can significantly affect the manipulator's performance.

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References

  1. Modi, V. J., ‘Attitude dynamics of satellites with flexible appendages ‐ A brief review’, Journal of Spacecraft and Rockets 11, 1974, 743‐751.

    Google Scholar 

  2. Modi, V. J. and Shrivastava, S. K., ‘Satellite attitude dynamics and control in the presence of environmental torques ‐ A brief survey’, Journal of Guidance, Control, and Dynamics 6, 1983, 461‐471.

    Google Scholar 

  3. Meirovitch, L. and Kwak, M. K., ‘On the maneuvering and control of space structures’, in Proceedings of the First International Conference on the Dynamics of Flexible Structures in Space, Cranfield, U.K., C. L. Kirk and J. L. Junkins (eds.), 1990, pp. 3‐17.

  4. Nagata, T., Modi, V. J., and Matsuo, H., ‘An approach to dynamics and control of flexible systems’, in A Collection of Technical Papers, AIAA/AAS Astrodynamics Conference, Scottsdale, AZ, AIAA, Washington, DC, 1994, Paper No. AIAA-94-3756CP, pp. 366‐375.

    Google Scholar 

  5. Chu, M. S. T., ‘Design, construction, and operation of a variable geometry manipulator’, M.A.Sc. Thesis, The University of British Columbia, Vancouver, B.C., Canada, 1997.

    Google Scholar 

  6. Dubowski, S. and Papadopoulos, E., ‘The kinematics, dynamics, and control of free-flying and free-floating space robotic systems’, IEEE Transactions on Robotics and Automation 5, 1993, 531‐543.

    Google Scholar 

  7. Hokamoto, S., Modi, V. J., and Misra, A. K., ‘Dynamics and control of mobile flexible manipulators with slewing and deployable links’, Astrodynamics 1995, Advances in the Astronautical Sciences 90, 1996, 339‐357.

    Google Scholar 

  8. Fu, K. S., Gonzalez, R. C., and Lee, C. S. G., Robotics: Control, Sensing, Vision, and Intelligence, McGraw-Hill, New York, 1987, pp. 82‐84 and 103‐124.

    Google Scholar 

  9. 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 11, 1980, 730‐736.

    Google Scholar 

  10. Keat, J. E., ‘Multibody system order n dynamics formulation based on velocity transform method’, Journal of Guidance, Control, and Dynamics 2, 1990, 207‐212.

    Google Scholar 

  11. Rosenthal, D. E., ‘An order n formulation for robotic systems’, The Journal of the Astronautical Sciences 4, 1990, 511‐529.

    Google Scholar 

  12. Jain, A. and Rodriguez, G., ‘Recursive flexible multibody system dynamics using spatial operators’, Journal of Guidance, Control, and Dynamics 6, 1992, 1453‐1466.

    Google Scholar 

  13. Bae, D. S. and Haug, E. J., ‘A recursive formulation for constrained mechanical system dynamics: Part I, Open loop systems’, Mechanics of Structures and Machines 3, 1987, 359‐382.

    Google Scholar 

  14. Kurdila, A. J., Menon, R. G., and Sunkel, J.W., ‘Nonrecursive order N formulation of multibody dynamics’, Journal of Guidance, Control, and Dynamics 5, 1993, 838‐844.

    Google Scholar 

  15. Pradhan, S., Modi, V. J., and Misra, A. K., ‘Order N formulation for flexible multibody systems in tree topology ‐ The Lagrangian approach’, in A Collection of Technical Papers, AIAA/AAS Astrodynamics Conference, San Diego, CA, AIAA, Washington, DC, 1996, Paper No. 96-3624-CP, pp. 480‐489.

    Google Scholar 

  16. Caron, M., ‘Planar dynamics and control of space-based flexible manipulators with slewing and deployable links’, M.A.Sc. Thesis, The University of British Columbia, Vancouver, B.C., Canada, 1996.

    Google Scholar 

  17. Sellapan, R. and Bainum, P. M., ‘Dynamics of spin-stabilized spacecraft during deployment of telescopic appendages’, Journal of Spacecraft and Rockets 10, 1976, 605‐610.

    Google Scholar 

  18. Modi, V. J. and Ibrahim, A. M., ‘Dynamics of the orbiter-based WISP experiment’, Acta Astronautica 11, 1992, 749‐761.

    Google Scholar 

  19. Meirovitch, L., Elements of Vibration Analysis, 2nd edn., McGraw-Hill, New York, 1986, pp. 255‐256 and 282‐290.

    Google Scholar 

  20. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in FORTRAN, 2nd edn., Cambridge University Press, Delhi, India, 1992, pp. 727‐744.

    Google Scholar 

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Caron, M., Modi, V.J. & Misra, A.K. Order-N Formulation and Dynamics of Multi-Unit Flexible Space Manipulators. Nonlinear Dynamics 17, 347–368 (1998). https://doi.org/10.1023/A:1008314211138

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  • DOI: https://doi.org/10.1023/A:1008314211138

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