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.

This paper investigates the use of structured robust techniques for the control design of the aerodynamic descent phase of a reusable rocket. A unified control strategy based on the use of linear-time-invariant structured [ ] controllers for both attitude and position is proposed and verified in both frequency and time domains. The architecture of the controller and the observed performance are discussed. Moreover, the nonlinear behavior of the control strategy is analyzed by looking at both the gain-scheduling law in conditions of plant-controller misalignment through the use of misalignment matrices, and simulation results obtained with a high-fidelity, nonlinear six-degree-of-freedom closed-loop model in perturbed conditions. All the results are based on Cooperative Action Leading to Launcher Innovation in Stage Tossback Operations (CALLISTO), a reusable rocket demonstrator jointly developed by German Aerospace Center (DLR), Japan Aerospace Exploration Agency (JAXA), and National Centre for Space Studies (CNES).

JAXA, CNES and DLR have decided to join their force to develop and fly a scaled reusable VTVL rocket stage called CALLISTO (Cooperative Action Leading to Launcher Innovation in Stage Toss - back Operations). This vehicle will pave the way for future reusable launch vehicles. One of its main goals is to demonstrate the mastering of key techniques and technologies that will be needed later by operational reusable launch vehicles. Indeed in the frame of CALLISTO numerous challenging technologies are being matured for the specific case of reusable launch vehicles. The challenges of a selection of key technologies developed for CALLISTO are discussed and the solutions retained for CALLISTO are presented.

While there is a strong current interest in and an increasing body of the latest numerical work on fuel-optimal powered descent inside an atmosphere, little recent analytical understanding of the problem has been reported. This paper analyzes the endo-atmospheric fuel-optimal rocket landing problem in three-dimensional motion. The necessary conditions for the problem that account for both propulsive and aerodynamic forces are derived. They include the full set of costate equations and the optimality conditions of the body attitude in terms of the angle of attack and sideslip angle. In contrast to a long-standing assumption of coordinated flight in the literature, it is shown that in general coordinated flight is not optimal if sideslip modulation is allowed. Special cases, such as small-angle and in-plane motion, are analyzed and harmonized with the previous results that are well known in the literature. The analytical conditions derived in this paper can also serve as independent verification for numerical solutions obtained by direct methods in optimal control or can be exploited for trajectory-design purposes.