Propellant Balancing Method for Formation Maintenance Considering Remaining Propellant

Abstract

This paper presents a method of propellant balancing to maximize the mission lifetime in spacecraft formation flying. The proposed method considers the initial remaining propellant, which was not considered in previous studies. This method optimizes the reference orbit for the virtual chief spacecraft so that the control effort of the deputy spacecraft is adjusted to balance the remaining propellant. The authors formulate the problem as an optimization problem and build new algorithms for propellant balancing, including the coordinate transformation for the chief spacecraft. A propellant-optimal solution is also analytically derived for an equilateral triangle of three spacecraft. The analytical solution is computationally inexpensive since it can be calculated using only the remaining propellant at the desired time and some pre-computed parameters. Finally, the analytical solution was compared with the results of numerical optimization, and the analytical solution was confirmed to be sufficiently practical.