Optimal Impulsive Rendezvous Under Target Flyby Constraint Based on Primer Vector Theory

This paper investigates the two-body fuel-optimal impulsive rendezvous problem with a target flyby constraint. Firstly, by defining the corresponding impulsive trajectory parameters, the constraint is implicitly incorporated into the problem formulation, and the feasibility of the constrained impulsive trajectory is ensured through solving the Lambert two-point boundary value problem. Secondly, to solve for the optimal impulsive trajectory, the constrained cost gradient and impulse addition criteria are derived based on the calculus of variations. In this derivation process, the constrained primer vector is defined, with the conventional primer vector proven to be a special form of the former in the unconstrained case. As a key conclusion of this paper, under the framework of the constrained primer vector, both the impulse addition method and the optimality necessary conditions can be formulated in forms analogous to those in the unconstrained case, thereby revealing the intrinsic connection between constrained and unconstrained problems. Finally, in the typical scenarios analyzed, the optimal flyby-rendezvous trajectory is successfully solved using the constrained cost gradient, and its optimality is verified via the necessary conditions. Meanwhile, a comparison with results obtained via the direct method demonstrates the advantage of the proposed method in terms of optimality and solution efficiency.