A New, General Perturbative Guidance for Space Vehicles

Abstract

Perturbative guidance techniques are aimed at driving a space vehicle along a prescribed, nominal path, leading to fullfilling the boundary conditions associated with the mission specifications. This work describes and applies the recently introduced, general-purpose perturbative guidance termed variable-time-domain neighboring optimal guidance, which assumes the optimal spacecraft trajectory as the nominal path. Minimization of the second differential of the objective function along the perturbed trajectory leads to deriving all the corrective maneuvers, in the context of an iterative closed-loop guidance scheme. Original analytical developments, based on optimal control theory and adoption of a variable time domain, constitute the theoretical foundation for several original features. The real-time feedback guidance at hand is exempt from the main disadvantages of similar algorithms proposed in the past, such as the occurrence of singularities for the gain matrices. The variable-time-domain neighboring optimal guidance algorithm is applied to two space maneuvers: (i) minimum-time exoatmospheric interception of moving targets and (ii) fast lunar ascent and orbit injection. Perturbations arising from nonnominal propulsive thrust or from errors in the initial conditions are included in the dynamical simulations. Extensive Monte Carlo campaigns are performed, and unequivocally prove the effectiveness and accuracy of the variable-time-domain neighboring optimal guidance algorithm.