Onboard Guidance for Reusable Rockets: Aerodynamic Descent and Powered Landing

Abstract

This paper describes a novel general on-board guidance strategy which can be applied to both the aerodynamically-controlled descent and the powered landing phase of reusable rockets. The proposed guidance method is based on sequential convex optimization applied to a Cartesian representation of the equations of motion. The contributions are an exploitation of convex and non-convex contributions, which are processed separately to maximize the computational efficiency of the approach, the inclusion of highly nonlinear terms represented by aerodynamic accelerations, a complete reformulation of the problem based on the use of Euler angle rates as control means, an improved transcription based on the use of a generalized hp pseudospectral method, and a dedicated formulation of the aerodynamic guidance problem for reusable rockets. The problem is solved for a 40 kN-class reusable rocket. Results show that the proposed technique is a very effective methodology able to satisfy all the constraints acting on the system, and can be potentially employed online to solve the entire descent phase of reusable rockets in real-time.

Convex Optimization of Launch Vehicle Ascent Trajectory with Heat-Flux and Splash-Down Constraints

“…In particular, Eqs. (48)(49)(50)(51) are grouped into a constraint vector χ 0 and then relaxed as χ w, where w are free variables, referred to as virtual buffers. Like virtual control, the virtual buffers should be used only when necessary, so a penalty term is defined:…”

“…[35,41,46], or (ii) a soft quadratic trust region, such as in Refs. [47,48]. Both trust regions were applied only on the control variables, because this was observed to be the most effective strategy for the problem under investigation.…”

“…This is because, in general, trust regions work better when the initial reference trajectory is closer to the optimal solution, while in this application an accurate guess is not available and is quite hard to design. Even though advanced trust region implementation demonstrated to be highly effective without particularly good initial guesses in diverse applications, including atmospheric entry [35,60] and rocket landing [28,48], a proper tuning of the involved parameters (such as initial radius of the hard trust region or penalty weights of the soft trust region) may require a significant effort. Instead, the filtering approach is much easier to set up, as the method sensitivity to the values of the weights is low; indeed, high success rates are achieved by every considered family as long as K ≥ 3.…”

“…Also, the typical lossless convexification strategy originally proposed for powered descent problems [45] is slightly modified by preserving the original state variables and thus preventing accuracy issues related to the large variation between the liftoff and payload mass when a logarithmic scale is used [41]. Finally, additional algorithmic robustness is provided by an original method, named filtering, for the recursive update of the reference solution that avoids the use of trust region constraints [46][47][48], which may limit the search space or modify the objective function and thus require a careful implementation, as well as initialization strategies based on homotopy [7][8][9], which can significantly increase the computational burden. When using filtering, the update of the reference solution is devised as a weighted sum of the previously found solutions, rather than being based only on the last one.…”

Successive Chebyshev pseudospectral convex optimization method for nonlinear optimal control problems

“…In References 29 and 30, successive convex optimization technology was used to solve the space rendezvous and docking problem to seek the most economical fuel consumption. In Reference 31, an on‐board guidance strategy for landing phase of reusable rocket was proposed based on sequential convex optimization. The highly nonlinear aerodynamic acceleration term is considered.…”