Optimal Trajectory Design for On-orbit Optical Inspection Using Spherical Gaussian

This study presents an optimal relative trajectory that maximizes the observable area of a target using an optical camera. On-orbit servicing missions have highlighted the importance of visual inspection for extending the functionality and lifespan of satellites. Existing trajectory design methods often rely on discrete or numerical evaluation of observation conditions, which limit analytical tractability and optimization performance. To address this issue, the evaluation function is formulated using spherical Gaussian (SG) functions, which describe directional distributions on a unit sphere. Considering a sphere encompassing the target, the observation area is modeled with SG continuously and analytically. Furthermore, SG is used to express the illumination condition as well, enabling integration of light conditions into trajectory planning. The optimal trajectory is obtained by an analytical impulsive satellite formation reconfiguration method in terms of relative eccentricity and inclination vectors. Numerical simulations are conducted under various conditions for on-orbit inspection in a geostationary orbit to validate the proposed method.