Last updated: 03-Sep-2001
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One of the significant challenges to successful formation flight of
spacecraft is maintenance of the formation, i.e., control of the motion of the individual
spacecraft to maintain the overall formation. This includes both stabilization of a
given formation and reconfiguring of the formation. While the dynamics and control a
single spacecraft is well understood, a formation of spacecraft effectively acts a
deformable body due to control forces which restore it to its desired formation. As a
deformable body, the formation is capable of exhibit complex dynamic behavior. Effective
control strategies must exploit this behavior as well as the natural dynamics of the
system to achieve goals such as formation error minimization and minimal fuel consumption
during formation reconfiguration. An additional concern is the impact a decentralized
control structure would have control algorithm design and formation controllability.
Spacecraft dynamics are mechanical, meaning they admit a Lagrangian or Hamiltonian
formulation. We are investigating the dynamics and control of formation flight by
exploiting the mechanical structure of the dynamical system in conjunction with proven
methods of linearization and structured uncertainty. At Caltech, we have developed
analytical tools such as the energy-momentum method for assessing the stability of a
mechanical system, as well as methodologies for control of mechanical systems. One
important property of mechanical systems is the ability of small changes in the internal
shape of the system to effect global motion of the system. Exploiting this phenomenon,
termed geometric phase, in conjunction with the inherent nonlinear instability of
a formation in certain regimes of its cluster of orbits, may yield methods for
reconfiguring the formation which rely solely on internal motions of the formation, and
hence are simple algorithmically and are amenable to a decentralized control architecture.
Another relevant area of research at Caltech is in trajectory generation for mechanical
systems. We are also developing approaches to solving optimal control problems for
mechanical systems which exploit the mechanical structure and which are computationally
tractable.
The following individuals are supported under this project: