Optimal Satellite-Formation Collision-Avoidance Maneuver Based on Relative E/I Vectors

The optimal satellite-formation collision-avoidance maneuver problem is investigated in terms of relative eccentricity and inclination vectors (E/I vectors) in relative E/I vectors plane. Using the relative E/I vectors theory and under the relative inclination vector unchanged assumption, first, the fuel-optimal collision-avoidance maneuver problem to maneuver the final target configuration with predefined passive safety parameters using minimal fuel is transferred to the geometrical problem to find the shortest distance from the initial point determined by the current relative eccentricity vector to the hyperbolic curve, which is determined by a predefined passive safety parameter in the relative E/I vectors plane. This case is solved using the Newton interaction method. Second, the optimal collision-avoidance maneuver problem to maneuver the final target configuration having maximum passive safety parameter under limiting fuel constraint is interpreted as the geometrical problem to find the optimal curve that has maximum passive safety parameter and is tangent to the maneuverable circle, whose center and radius are the initial point determined by the current relative eccentricity vector and the limited fuel, respectively. The equivalent geometrical problem is solved by applying a simple heuristic search method. The validities of the proposed optimal collision-avoidance methods in terms of relative E/I vectors are confirmed by numerical simulations.