Duality-Based Near-Fuel-Optimal Impulsive Trajectory Computation for Spacecraft Rendezvous Under Perturbations

In this study, a novel impulsive trajectory optimization algorithm for near-fuel-optimal rendezvous under perturbations is presented. The algorithm, called algorithm for impulsive rendezvous trajectory optimization under perturbations (AIRTOP), is designed such that the accuracy of rendezvous constraints is improved as much as possible while retaining the first-order optimality, under high-fidelity dynamics models that encompass various orbital perturbations (e.g., nonspherical gravity, air drag, luni-solar gravity, and solar radiation pressure). To eliminate rendezvous constraint errors, AIRTOP solves the linearized impulsive rendezvous problem recursively using the nonsingular dual-primal optimization algorithm. To improve the computational efficiency, AIRTOP applies the approximate analytical gradient of the constraint error norm during its error elimination process. We present three numerical simulations near circular and elliptical orbits. The simulation results show that i) AIRTOP can successfully solve impulsive rendezvous problems under realistic orbital perturbations with minimal user intervention, and ii) it can generate more fuel-efficient solutions in similar or shorter computation time than two other methods, namely, the differential corrector of the General Mission Analysis Tool and the global optimization approach, which can also take complex perturbations into account.