Trajectory Optimization and Guidance Design by Convex Programming

The field of aerospace guidance and control has recently been evolving from focusing on traditional laws and controllers to numerical algorithms with the aim of achieving onboard applications for autonomous vehicle systems. However, it is very difficult to perform complex guidance and control missions with highly nonlinear dynamic systems and many constraints onboard. In recent years, an emerging trend has occurred in the field of Computational Guidance and Control (CG&C). By taking advantage of convex optimization and highly efficient interior point methods, CG&C allows complicated guidance and control problems to be solved in real time and offers great potential for onboard applications. With the significant increase in computational efficiency, convex-optimization-based CG&C is expected to become a fundamental technology for system autonomy and autonomous operations. In this dissertation, successive convex approaches are proposed to solve optimal control programs associated with aerospace guidance and control, and the emphasis is placed on potential onboard applications. First, both fuel-optimal and time-optimal low-thrust orbit transfer problems are investigated by a successive second-order cone programming method. Then, this convex method is extended and improved to solve hypersonic entry trajectory optimization problems by taking advantage of line-search and trust-region techniques. Finally, the successive convex approach is modified to the design of autonomous entry guidance algorithms. Simulation results indicate that the proposed methodologies are capable of generating accurate solutions for low-thrust orbit transfer problems and hypersonic entry problems with fast computational speed. The proposed methods have great potential for onboard applications

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

Development of a Reachability Analysis Algorithm for Space Applications

In the last decades developments in space technology paved the way to more challenging missions like asteroid mining, space tourism and human expansion into the Solar System. These missions require difficult tasks such as real-time capable guidance schemes for re-entry, landing on celestial bodies and implementation of large angle maneuvers for spacecraft. There is a need for an analysis tool to increase the robustness and success of these missions. Reachability analysis contributes to this requirement by obtaining the set of all achievable states for a dynamical system starting from an initial condition with given admissible control inputs of the system. In this study, an optimal control based reachability analysis algorithm is developed for evaluating the performance of the guidance and control methods for space missions considering the desired performance index. The developed method considers a soft-landing problem for a Moon mission as the case study, and attainable area of the lander as the performance index. The method computes feasible trajectories for the lunar lander between the point where the terminal landing maneuver starts and points that constitutes the candidate landing region. The candidate landing region is discretized by equidistant points on a two dimensional plane, i.e. in downrange and crossrange coordinates, and for each grid point a distance function is defined. This distance function acts as an objective function for a related optimal control problem (OCP). Each infinite dimensional OCP is transcribed into a finite dimensional Nonlinear Programming Problem (NLP) by using Pseudo-Spectral Methods (PSM). The NLPs are solved using available tools to obtain feasible trajectories and approximated reachable sets with information about the states of the dynamical system at the grid points. The proposed method approximates reachable sets of the lander with propellant-to-reach and time-to-reach cost by solution of NLPs. A polynomial-based Apollo guidance scheme is used to compare the results for the developed method. The coefficients that define the position of the lander are obtained by solving a series of explicit equations for the given initial and final states. A model inversion based PD controller is designed to track the generated trajectory. Feasible solutions that satisfy safe landing conditions are filtered and the results are compared for the two different approaches. Finally, the uncertainties which are characterized by initial state error and system parameters are also considered. A multivariate trajectory interpolation tool is used to interpolate RS with different initial states. A Riccati equation-based controller is designed to track the previously obtained reference trajectories within presence of the uncertainties. Monte Carlo (MC) simulations are carried out to obtain safe attainable landing area of the lunar lander as probability maps. The same uncertainty set is used to verify these probability maps by propagating the uncertainties using unscented transform. The developed tool analyzes the different guidance and control methods, for the attainable landing area of the lander, under various landing scenarios, with different dynamical models and controller parameters. Numerous quality metrics are used to compare the change of characteristics of the attainable landing area and performance of the guidance and control methods, and selected design parameters

Numerical optimal control with applications in aerospace

This thesis explores various computational aspects of solving nonlinear, continuous-time dynamic optimization problems (DOPs) numerically. Firstly, a direct transcription method for solving DOPs is proposed, named the integrated residual method (IRM). Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct collocation, this new approach alternates between minimizing and constraining the squared norm of the dynamic constraint residuals integrated along the whole solution trajectories. The method is capable of obtaining solutions of higher accuracy for the same mesh compared to direct collocation methods, enabling a flexible trade-off between solution accuracy and optimality, and providing reliable solutions for challenging problems, including those with singular arcs and high-index differential-algebraic equations. A number of techniques have also been proposed in this work for efficient numerical solution of large scale and challenging DOPs. A general approach for direct implementation of rate constraints on the discretization mesh is proposed. Unlike conventional approaches that may lead to singular control arcs, the solution of this on-mesh implementation has better numerical properties, while achieving computational speedups. Another development is related to the handling of inactive constraints, which do not contribute to the solution of DOPs, but increase the problem size and burden the numerical computations. A strategy to systematically remove the inactive and redundant constraints under a mesh refinement framework is proposed. The last part of this work focuses on the use of DOPs in aerospace applications, with a number of topics studied. Using example scenarios of intercontinental flights, the benefits of formulating DOPs directly according to problem specifications are demonstrated, with notable savings in fuel usage. The numerical challenges with direct collocation are also identified, with the IRM obtaining solutions of higher accuracy, and at the same time suppressing the singular arc fluctuations.Open Acces