Dynamics and control of an elastic dumbbell spacecraft in a central gravitational field

The dynamics of a dumbbell shaped spacecraft are modeled as two identical mass particles connected by a linear elastic spring. The equations of motion of the spacecraft in a planar orbit in a central gravitational field are presented. The equations of motion characterize orbit, attitude, and shape (or elastic deformation) degrees of freedom and the coupling between them. Relative equilibria, corresponding to circular planar orbits, are obtained from these equations of motion. Linear equations of motion that describe perturbations from these relative equilibria are presented. New dynamics and control problems are introduced for these linear equations. Controllability results are presented for various actuation assumptions, based on the linear equations.

[1]  DJ SCHEERES,et al.  Stability of Relative Equilibria in the Full Two‐Body Problem , 2004, Annals of the New York Academy of Sciences.

[2]  R. Skelton.  Dynamic Systems Control: Linear Systems Analysis and Synthesis , 1988 .

[3]  Daniel J. Scheeres.  Stability in the Full Two-Body Problem , 2002 .

[4]  John P. Moran,et al.  Effects of Plane Librations on the Orbital Motion of a Dumbbell Satellite , 1961 .

[5]  N. H. McClamroch,et al.  Attitude control of a tethered spacecraft , 2003, Proceedings of the 2003 American Control Conference, 2003..

[6]  Ilya V. Kolmanovsky,et al.  Nonlinear attitude and shape control of spacecraft with articulated appendages and reaction wheels , 2000, IEEE Trans. Autom. Control..

[7]  Mahmut Reyhanoglu,et al.  Planar Reorientation Maneuvers of Space Multibody Systems Using Internal Controls , 1992 .

[8]  Mahmut Reyhanoglu,et al.  Dynamics of multibody vehicles and their formulation as nonlinear control systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[9]  Daniel J. Scheeres,et al.  Stability in the Full Two-Body Problem , 2002 .

[10]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[11]  N. Harris McClamroch,et al.  Translational and Rotational Maneuvers of an Underactuated Space Robot using Prismatic Actuators , 2002, Int. J. Robotics Res..

[12]  Alan J. Laub,et al.  Controllability and observability criteria for multivariable linear second-order models , 1984 .

[13]  Sangbum Cho,et al.  Optimal orbit transfer of a spacecraft with fixed length tether , 2003 .

[14]  L. Fu,et al.  Controllability of spacecraft systems in a central gravitational field , 1994, IEEE Trans. Autom. Control..

[15]  Arun K. Misra,et al.  Dynamics and control of tethered satellite systems , 2008 .