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

Violation learning differential evolution-based hp-Adaptive pseudospectral method for trajectory optimization of Space Maneuver Vehicle

The sensitivity of the initial guess in terms of optimizer based on hp-adaptive pseudospectral method for solving Space Maneuver Vehicles (SMV) trajectory optimization problem has long been recognised as a difficult problem. Because of the sensitivity with regard to the initial guess, it may cost the solver a large amount of time to do the Newton iteration and get the optimal solution or even the local optimal solution. In this paper, to provide the optimizer a better initial guess and solve the SMV trajectory optimization problem, an initial guess generator using violation learning deferential evolution algorithm is introduced. A new constraint-handling strategy without using penalty function is presented to modify the fitness values so that the performance of each candidate can be generalized. In addition, a learning strategy is designed to add diversity for the population in order to improve the convergency speed and avoid local optima. Several simulation results are conducted by using the combination algorithm; Simulation results indicated that using limited computational efforts, the method proposed to generate initial guess can have better performance in terms of convergency ability and convergency speed compared with other approaches. By using the initial guess, the combinational method can also enhance the quality of the solution and reduce the number of Newton iteration and computational time. Therefore, The method is potentially feasible for solving the SMV trajectory optimization problem

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

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

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

Onboard Guidance for Reusable Rockets: Aerodynamic Descent and Powered Landing

This paper describes a novel general on-board guidance strategy which can be applied toboth 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 Cartesianrepresentation of the equations of motion. The contributions are an exploitation of convexand non-convex contributions, which are processed separately to maximize the computationalefficiency of the approach, the inclusion of highly nonlinear terms represented by aerodynamicaccelerations, a complete reformulation of the problem based on the use of Euler angle rates ascontrol means, an improved transcription based on the use of a generalized hp pseudospectralmethod, 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 proposedtechnique 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 inreal-time

A review of optimization techniques in spacecraft flight trajectory design

For most atmospheric or exo-atmospheric spacecraft flight scenarios, a well-designed trajectory is usually a key for stable flight and for improved guidance and control of the vehicle. Although extensive research work has been carried out on the design of spacecraft trajectories for different mission profiles and many effective tools were successfully developed for optimizing the flight path, it is only in the recent five years that there has been a growing interest in planning the flight trajectories with the consideration of multiple mission objectives and various model errors/uncertainties. It is worth noting that in many practical spacecraft guidance, navigation and control systems, multiple performance indices and different types of uncertainties must frequently be considered during the path planning phase. As a result, these requirements bring the development of multi-objective spacecraft trajectory optimization methods as well as stochastic spacecraft trajectory optimization algorithms. This paper aims to broadly review the state-of-the-art development in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning techniques for spacecraft flight operations. A brief description of the mathematical formulation of the problem is firstly introduced. Following that, various optimization methods that can be effective for solving spacecraft trajectory planning problems are reviewed, including the gradient-based methods, the convexification-based methods, and the evolutionary/metaheuristic methods. The multi-objective spacecraft trajectory optimization formulation, together with different class of multi-objective optimization algorithms, is then overviewed. The key features such as the advantages and disadvantages of these recently-developed multi-objective techniques are summarised. Moreover, attentions are given to extend the original deterministic problem to a stochastic version. Some robust optimization strategies are also outlined to deal with the stochastic trajectory planning formulation. In addition, a special focus will be given on the recent applications of the optimized trajectory. Finally, some conclusions are drawn and future research on the development of multi-objective and stochastic trajectory optimization techniques is discussed

Autonomous Trajectory Planning and Guidance Control for Launch Vehicles

This open access book highlights the autonomous and intelligent flight control of future launch vehicles for improving flight autonomy to plan ascent and descent trajectories onboard, and autonomously handle unexpected events or failures during the flight. Since the beginning of the twenty-first century, space launch activities worldwide have grown vigorously. Meanwhile, commercial launches also account for the booming trend. Unfortunately, the risk of space launches still exists and is gradually increasing in line with the rapidly rising launch activities and commercial rockets. In the history of space launches, propulsion and control systems are the two main contributors to launch failures. With the development of information technologies, the increase of the functional density of hardware products, the application of redundant or fault-tolerant solutions, and the improvement of the testability of avionics, the launch losses caused by control systems exhibit a downward trend, and the failures induced by propulsion systems become the focus of attention. Under these failures, the autonomous planning and guidance control may save the missions. This book focuses on the latest progress of relevant projects and academic studies of autonomous guidance, especially on some advanced methods which can be potentially real-time implemented in the future control system of launch vehicles. In Chapter 1, the prospect and technical challenges are summarized by reviewing the development of launch vehicles. Chapters 2 to 4 mainly focus on the flight in the ascent phase, in which the autonomous guidance is mainly reflected in the online planning. Chapters 5 and 6 mainly discuss the powered descent guidance technologies. Finally, since aerodynamic uncertainties exert a significant impact on the performance of the ascent / landing guidance control systems, the estimation of aerodynamic parameters, which are helpful to improve flight autonomy, is discussed in Chapter 7. The book serves as a valuable reference for researchers and engineers working on launch vehicles. It is also a timely source of information for graduate students interested in the subject