Convex optimization of launch vehicle ascent trajectories

This thesis investigates the use of convex optimization techniques for the ascent trajectory design and guidance of a launch vehicle. An optimized mission design and the implementation of a minimum-propellant guidance scheme are key to increasing the rocket carrying capacity and cutting the costs of access to space. However, the complexity of the launch vehicle optimal control problem (OCP), due to the high sensitivity to the optimization parameters and the numerous nonlinear constraints, make the application of traditional optimization methods somewhat unappealing, as either significant computational costs or accurate initialization points are required. Instead, recent convex optimization algorithms theoretically guarantee convergence in polynomial time regardless of the initial point. The main challenge consists in converting the nonconvex ascent problem into an equivalent convex OCP. To this end, lossless and successive convexification methods are employed on the launch vehicle problem to set up a sequential convex optimization algorithm that converges to the solution of the original problem in a short time. Motivated by the computational efficiency and reliability of the devised optimization strategy, the thesis also investigates the suitability of the convex optimization approach for the computational guidance of a launch vehicle upper stage in a model predictive control (MPC) framework. Being MPC based on recursively solving onboard an OCP to determine the optimal control actions, the resulting guidance scheme is not only performance-oriented but intrinsically robust to model uncertainties and random disturbances thanks to the closed-loop architecture. The characteristics of real-world launch vehicles are taken into account by considering rocket configurations inspired to SpaceX's Falcon 9 and ESA's VEGA as case studies. Extensive numerical results prove the convergence properties and the efficiency of the approach, posing convex optimization as a promising tool for launch vehicle ascent trajectory design and guidance algorithms

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

This paper presents a convex programming approach to the optimization of a multistage launch vehicle ascent trajectory, from the liftoff to the payload injection into the target orbit, taking into account multiple nonconvex constraints, such as the maximum heat flux after fairing jettisoning and the splash-down of the burned-out stages. Lossless and successive convexification are employed to convert the problem into a sequence of convex subproblems. Virtual controls and buffer zones are included to ensure the recursive feasibility of the process and a state-of-the-art method for updating the reference solution is implemented to filter out undesired phenomena that may hinder convergence. A hp pseudospectral discretization scheme is used to accurately capture the complex ascent and return dynamics with a limited computational effort. The convergence properties, computational efficiency, and robustness of the algorithm are discussed on the basis of numerical results. The ascent of the VEGA launch vehicle toward a polar orbit is used as case study to discuss the interaction between the heat flux and splash-down constraints. Finally, a sensitivity analysis of the launch vehicle carrying capacity to different splash-down locations is presented.Comment: 2020 AAS/AIAA Astrodynamics Specialist Virtual Lake Tahoe Conferenc

Stochastic Control of Launch Vehicle Upper Stage with Minimum-Variance Splash-Down

This paper presents a novel synthesis method for designing an optimal and robust guidance law for a non-throttleable upper stage of a launch vehicle, using a convex approach. In the unperturbed scenario, a combination of lossless and successive convexification techniques is employed to formulate the guidance problem as a sequence of convex problems that yields the optimal trajectory, to be used as a reference for the design of a feedback controller, with little computational effort. Then, based on the reference state and control, a stochastic optimal control problem is defined to find a closed-loop control law that rejects random in-flight disturbance. The control is parameterized as a multiplicative feedback law; thus, only the control direction is regulated, while the magnitude corresponds to the nominal one, enabling its use for solid rocket motors. The objective of the optimization is to minimize the splash-down dispersion to ensure that the spent stage falls as close as possible to the nominal point. Thanks to an original convexification strategy, the stochastic optimal control problem can be solved in polynomial time since it reduces to a semidefinite programming problem. Numerical results assess the robustness of the stochastic controller and compare its performance with a model predictive control algorithm via extensive Monte Carlo campaigns

GTOC X: Solution Approach of Team Sapienza-PoliTo

This paper summarizes the solution approach and the numerical methods developed by the joint team Sapienza University of Rome and Politecnico di Torino (Team Sapienza-PoliTo) in the context of the 10th Global Trajectory Optimization Competition. The proposed method is based on a preliminary partition of the galaxy into several small zones of interest, where partial settlement trees are developed, in order to match a (theoretical) optimal star distribution. A multi-settler stochastic Beam Best-First Search, that exploits a guided multi-star multi-vessel transition logic, is proposed for solving a coverage problem, where the number of stars to capture and their distribution within a zone is assigned. The star-to-star transfers were then optimized through an indirect procedure. A number of refinements, involving settle time re-optimization, explosion, and pruning, were also investigated. The submitted 1013-star solution, as well as an enhanced 1200-point rework, are presented

Autonomous Upper Stage Guidance with Robust Splash-Down Constraint

This paper presents a novel algorithm, based on model predictive control (MPC), for the optimal guidance of a launch vehicle upper stage. The proposed strategy not only maximizes the performance of the vehicle and its robustness to external disturbances, but also robustly enforces the splash-down constraint. Indeed, uncertainty on the engine performance, and in particular on the burn time, could lead to a large footprint of possible impact points, which may pose a concern if the reentry points are close to inhabited regions. Thus, the proposed guidance strategy incorporates a neutral axis maneuver (NAM) that minimizes the sensitivity of the impact point to uncertain engine performance. Unlike traditional methods to design a NAM, which are particularly burdensome and require long validation and verification tasks, the presented MPC algorithm autonomously determines the neutral axis direction by repeatedly solving an optimal control problem (OCP) with two return phases, a nominal and a perturbed one, constrained to the same splash-down point. The OCP is transcribed as a sequence of convex problems that quickly converges to the optimal solution, thus allowing for high MPC update frequencies. Numerical results assess the robustness and performance of the proposed algorithm via extensive Monte Carlo campaigns.Comment: arXiv admin note: text overlap with arXiv:2210.1461

A Convex Optimization Approach for Finite-Thrust Time-Constrained Cooperative Rendezvous

This paper presents a convex approach to the optimization of a cooperative rendezvous, that is, the problem of two distant spacecraft that simultaneously operate to get closer. Convex programming guarantees convergence towards the optimal solution in a limited, short, time by using highly efficient numerical algorithms. A combination of lossless and successive convexification techniques is adopted to handle the nonconvexities of the original problem. Specifically, a convenient change of variables and a constraint relaxation are performed, while a successive linearization of the equations of motion is employed to handle the nonlinear dynamics. A filtering technique concerning the recursive update of the reference solution is proposed in order to enhance the algorithm robustness. Numerical results are presented and compared with those provided by an indirect method