Capturing a spacecraft around a flyby asteroid using Hamiltonian-structure-preserving control.

*(English)*Zbl 07274903Summary: The potentially hazardous asteroid is not only the target of planetary defense missions but also an ideal one for scientific exploration of near-Earth objects due to minimal launching budget during its close encounter with Earth. The flyby segment of asteroid shows to be hyperbolic in an Earth-centred inertial frame. To guide the spacecraft captured by the asteroid under the common Earth’s gravity, the Hamiltonian-structure-preserving (HSP) controller, based only on the feedback of relative positions, is constructed to transform the topological structure of the equilibrium point from hyperbolic to elliptic. On account of the small mass of flyby asteroid, a hyperbolic two-body model is used to derive the form of controller. The controller is also proved to work effectively in the hyperbolic three-body model. Critical control gains for both transient and long-term stabilities are investigated, as well as the controlled frequencies caused by different gains. To avoid collision with an asteroid, the artificial potential function (APF) is employed to improve the HSP controller.

##### MSC:

70F | Dynamics of a system of particles, including celestial mechanics |

93 | Systems theory; control |

##### Keywords:

Hamiltonian-structure-preserving control; formation flying; flyby asteroid; hyperbolic restricted three-body problem
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\textit{M. Xu} et al., Commun. Nonlinear Sci. Numer. Simul. 93, Article ID 105500, 10 p. (2021; Zbl 07274903)

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