Generalized Potter–Stern Algorithm for Impulsive Minimum-Fuel Fixed-Time Rendezvous

In 1965, at the times of the celebrated Edelbaum's question (how many impulses?) and the birth of Primer Vector Theory, Potter and Stern presented a systematic pruning procedure to reduce rendezvous maneuver sequences of [Formula: see text] impulses to an equivalent, at least suboptimal, [Formula: see text]-impulse one, building on the results by Neustadt. This work revisits and generalizes the Potter-Stern algorithm for all [Formula: see text]-fuel optimal linear rendezvous problems. The aforementioned procedure is shown to constitute an incomplete particularization of the simplex method, the well-known systematic Linear Programming optimization technique. In view of such connection, which appears to have remained unnoticed, the performance and convergence of the Potter-Stern algorithm is analyzed, and several improvements are proposed. As a result, the original method is extended beyond the original [Formula: see text] fuel-consumption metric to both the unconstrained and constrained [Formula: see text] cases, thus rendering the algorithm independent of the fuel-consumption proxy used. Given its low computational footprint and non-specialized implementation (requiring only linear algebra machinery), the algorithm stands as a solid candidate for onboard, real-time, embedded guidance applications. Several realistic Keplerian rendezvous mission test cases are presented to demonstrate the performance of the proposed generalized method against state-of-the-art solvers.