Finite-Element Collocation Based Successive Convexification for Powered Landing Guidance of Reusable Rockets

The problem of powered landing guidance of reusable rockets is formulated in the presence of aerodynamic drag forces. This problem is challenging for onboard guidance applications due to non-convex thrust constraints and nonlinearities introduced by aerodynamic drag, mass-depletion dynamics, and free final time. Convex programming, which is characterized by deterministic convergence, is becoming increasingly attractive to address such problems. Lossless convexification is used to deal with the non-convex thrust constraints to make this guidance problem tractable. In addition, other non-convexities are eliminated by finite-element collocation based successive convexification, which relies on finite-element collocation discretization, linearization, trust region, and relaxation. Through successive convexification, a sequence of second-order cone programming problems is solved in each iteration by a state-of-the-art interior-point algorithm. The proposed approach is verified and compared with a direct method associated with an efficient nonlinear programming algorithm by numerical simulation.