Nonsingular Dual–Primal Algorithm for Fuel-Optimal Impulsive Rendezvous

This paper addresses a fuel-optimal impulsive rendezvous problem for minimizing the total characteristic velocity. In previous research, the authors proposed an efficient dual-primal optimization algorithm for this problem, taking advantage of the primal and dual formulations at once. Although the dual-primal optimization algorithm is capable of computing the accurate global-optimal trajectory for most cases, it cannot solve the nontrivial primer vector cases in which the optimal impulse timings (that is, the time points at which the optimality conditions are satisfied) are not identical to the time points of the optimal impulses (that is, the time points at which the impulses are applied in the optimal trajectory). The main contributions of this paper are 1) development of a novel strategy resolving the nontrivial primer vectors for general dual-first approaches, and 2) development of a new nonsingular dual-primal optimization algorithm adopting the strategy. The new algorithm generates an impulse sequence set including the possible combinations of time points of impulses, and then it searches through the impulse sequence set to find the primal root. To demonstrate its nontriviality resolution capability, the rendezvous problems near circular and elliptical orbits are solved for five test cases, and the newly developed algorithm succeeds in resolving nontrivial primer vectors.