Close approach analysis method considering attitude and shape using dual quaternions

This paper proposes a close approach analysis method considering object attitude change. Implementing a detailed close approach analysis is important for space situational awareness. Conventional conjunction assessment methods assume the shape of the object as a encompassing sphere, which excludes considering the attitude change. However, most of the spacecraft are not spherical, and conventional methods result in overestimation. The proposed method in this paper consists of two steps: 1) calculation of the time of close approach with two objects as point masses and 2) interpolation of the first and last states in the time duration when the close distance is less than a given threshold. Dual quaternions are employed to express the translational and rotational motions, which ensures the uniqueness of the interpolation. Numerical simulations are performed to verify the proposed method and compare it with a conventional method.