Impulsive Spacecraft Formation Maneuvers with Optimal Firing Times

摘要

Necessary and sufficient conditions for minimizing impulsive thrust vectors and application times have been derived, and a novel method for their calculation has been demonstrated. Given an initial guess of application times, t_0 = [t_1, ..., t_N], the proposed method converges to a local minimum, although not necessarily a global minimum. Global minimization could be achieved by applying our method to a series of different initial guesses. In the context of the formation-flying problem, the presented optimal timing theory is well suited for application to the linear time-varying dynamics of mean differential elements. Although in this Note, the classical orbital element set has been employed, which is suitable for e ≠ 0 deg and i ≠ 0 deg, the optimal timing conditions presented are applicable to alternative orbital element sets as well. The method has been shown to yield smaller ΔV costs for formation keeping than existing nonoptimal strategies, particularly for formations in highly elliptical orbits. It has also been shown to improve upon previous optimal formation reconfiguration results, for some cases.