Six-Degree-of-Freedom Rocket Landing Optimization via Augmented Convex–Concave Decomposition

In this paper an augmented convex–concave decomposition (ACCD) method for treating nonlinear equality constraints in an otherwise convex problem is proposed. This augmentation improves greatly the feasibility of the problem when compared to the original convex–concave decomposition approach. The effectiveness of the ACCD is demonstrated by solving a fuel-optimal six-degree-of-freedom rocket landing problem in atmosphere, subject to multiple nonlinear equality constraints. Compared with known approaches such as sequential convex programming, where conventional linearization (with or without slack variables) is employed to treat those nonlinear equality constraints, it is shown that the proposed ACCD leads to more robust convergence of the solution process and a more interpretable behavior of the sequential convex algorithm. The methodology can also be applied effectively in the case where the determination of discrete controls or decision-making variables needs to be made, such as the on–off use of reaction control system thrusters in the rocket landing problem, without the need for a mixed integer solver. Numerical results are shown for a representative, reusable rocket benchmark problem.