Bounded Motions near Contact Binary Asteroids by Hamiltonian Structure-Preserving Control

Abstract

This paper is devoted to stabilizing motions near a special type of equilibrium point of contact binary asteroids by Hamiltonian structure-preserving control. Aiming at noncollinear equilibrium points of the asteroid 1996 HW1, a Hamiltonian structure-preserving controller is built up using stable and unstable manifolds. Compared with traditional Hamiltonian structure-preserving controllers, it is capable of stabilizing the motion near a special kind of equilibrium point only using stable or unstable manifolds. The analytical solution of controlled motions is approximated by a nonlinear series using the method of variation of parameters. An optimization strategy is proposed including the numerical optimization of control gains by maximum-likelihood and the global optimization of initial deviation analytically. To achieve collision avoidance, the concept of an artificial potential function is introduced to the controller, which still has the capability to change equilibrium points’ topological type to elliptic without breaking the system’s Hamiltonian structure.