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Reducing the dynamics of a space robot modeled with quaternions

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper begins by describing the dynamical modeling of a two-link space manipulator using a constrained Lagrangian approach to mechanics. The dynamics of the space robot are obtained as a system of index-3 differential algebraic equations due to the use of quaternions as rotation operators. These equations are converted into a system of ordinary differential equations. A computed torque technique is utilized, based on the ordinary differential equation model, to reduce the size of the dynamical equations. The limitations of the technique are discussed. Specifically, it is shown that the input forces cannot be completely decoupled. As an example of how the composite system might be used, a proportional-derivative controller is implemented. The current limitations in analysis for this type of system are also described.
Czasopismo
Rocznik
Strony
49--57
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
  • University of North Carolina at Charlotte, Department of Electrical and Computer Engineerimg, 9201 University City Blvd, NC 28223 Charlotte, USA, drisenbe@uncc.edu
Bibliografia
  • [1] Isenberg D.R., Kakad Y.P., Computed Torque Control of a Quaternion Based Space Robot, Proceedings of 19th International Conference on Systems Engineering, 2008, pp. 59-64.
  • [2] Kane T.R., Wang C.F., On the Derivation of Equations of Motion, SIAM Journal of Applied Mathematics, Vol. 13, No. 2, 1965.
  • [3] Banerjee A.K., Contributions of Multibody Dynamics to Space Flight: A Brief Review, Journal of Guidance, Control, and Dynamics, Vol. 26, No. 3, 2003.
  • [4] Morton H.S. Jr., Hamilton and Lagrangian Formulations of Rigid-Body Rotational Dynamics Based on the Euler Parameters, The Journal of the Astronautical Sciences, Vol. 41, No. 4, 1993, pp. 569-591.
  • [5] Kuipers J.B., Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality, Princeton University Press, Princeton, NJ, 2002
  • [6] Isenberg D.R., Kakad Y.P., Simulating the Effects of a Non-Uniform Gravitational Field on a Space Robot, accepted for publication by Journal of Computers.
  • [7] Kunkel P., Mehrman V., Differential-Algebraic Equations: Analysis and Numerical Solution, European Mathematical Society, Zurich, 2006
  • [8] Chou J.C., Wu S.D., Constraint Violation Stabilization Using Input-Output Feedback Linearization in Multibody Dynamic Analysis, Journal of Guidance, Control, and Dynamics, Vol. 21, No. 2, 1998.
  • [9] Negrut D., Haug E.J., German H.C., An Implicit Runge-Kutta Method for Integration of Differential Algebraic Equations of Multibody Dynamics, Multibody System Dynamics, Vol. 9, 2003, p. 121-142.
  • [10] Baumgarte J., Stabilization of Constraints and Integrals of Motion in Dynamical Systems, Computer Methods in Applied Mechanics and Engineering, Vol. 1, 1972, pp. 1-16.
  • [11] Goldstein H., Classical Mechanics, Addison Wesley Reading, MA, 1959.
  • [12] Spong M.W., Vidyasagar M., Robot Dynamics and Control, John Wiley and Sons, New York, NY, 1989.
  • [13] Slotine J.E., Li W., Applied Nonlinear Control, Prentice Hall International Inc., Upper Saddle River, NJ., 1991.
  • [14] Khalil H.K., Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, 2002
  • [15] Tarraf D.C., Asada H.H., On the Nature and Stability of Differential-Algebraic Systems, Proceedings of the American Control Conference, 2002, pp. 3546-3551.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0062-0006
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