Efficient Iteration Adjustment Method for Solving Optimal Multiple-Impulse Rendezvous

In this study, an efficient iteration adjustment method is proposed for addressing the problem of optimal two-body multiple-impulse fixed-time rendezvous based on the primer vector theory. The method initiates with a two-impulse Lambert trajectory and gradually increases the number of impulses through a set of well-defined adjustment criteria to ultimately obtain the optimal impulsive trajectory associated with the optimal impulse number. The proposed algorithm comprises two components: internal iteration and external adjustment. The internal iteration employs a hybrid iterative algorithm that combines the Newton method and steepest descent search. The external adjustment, based on the results of the internal iteration and the shape of its primer vector curve, involves operations such as adding, moving, or deleting impulses until the necessary conditions are fully met. In various tested scenarios, the method rapidly finds solutions that satisfy the necessary conditions using fewer internal iterations and external adjustments. Solution experiments with random boundary conditions further demonstrate the method’s efficiency and applicability. The proposed method offers a robust framework for a broader spectrum of multiple-impulse trajectory optimization problems grounded in the primer vector theory.