# Browsing by Subject "Trajectory design"

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Item Automatic algorithm for accurate numerical gradient calculation in general and complex spacecraft trajectories(2010-12) Restrepo, Ricardo Leon; Ocampo, Cesar; Hull, David G.Show more An automatic algorithm for accurate numerical gradient calculations has been developed. The algorithm is based on both finite differences and Chebyshev interpolation approximations. The novelty of the method is an automated tuning of the step size perturbation required for both methods. This automation guaranties the best possible solution using these approaches without the requirement of user inputs. The algorithm treats the functions as a black box, which makes it extremely useful when general and complex problems are considered. This is the case of spacecraft trajectory design problems and complex optimization systems. An efficient procedure for the automatic implementation is presented. Several examples based on an Earth-Moon free return trajectory are presented to validate and demonstrate the accuracy of the method. A state transition matrix (STM) procedure is developed as a reference for the validation of the method.Show more Item Low-thrust trajectory design techniques with a focus on maintaining constant energy(2014-08) Hernandez, Sonia, active 21st century; Akella, Maruthi Ram, 1972-Show more Analytical solutions to complex trajectory design problems are scarce, since only a few specific cases allow for closed-form solutions. The main purpose of this dissertation is to design simple algorithms for trajectory design using continuous thrust, with a focus on low-thrust applications. By “simple” here we seek to achieve algorithms that either admit an analytical solution, or require minimal input by the user and minimal computation time. The three main contributions of this dissertation are: designing Lyapunov-based closed-loop guidance laws for orbit transfers, finding semi-analytical solutions using a constant magnitude thrust, and perturbation theory for approximate solutions to low-thrust problems. The technical aspect that these problems share in common is that they all use, fully or partially, a thrusting model in which the energy of the system is kept constant. Many orbit transfer problems are shown to be solved with this thrusting protocol.Show more Item Preliminary interplanetary trajectory design tools using ballistic and powered gravity assists(2015-08) Brennan, Martin James; Fowler, Wallace T.; Russell, Ryan; Bettadpur, Srinivas; Lightsey, E G; Olsen, CarrieShow more Preliminary interplanetary trajectory designs frequently use simplified two-body orbital mechanics and linked conics methodology to model the complex trajectories in multi-body systems. Incorporating gravity assists provides highly efficient interplanetary trajectories, enabling otherwise infeasible spacecraft missions. Future missions may employ powered gravity assists, using a propulsive maneuver during the flyby, improving the overall trajectory performance. This dissertation provides a complete description and analysis of a new interplanetary trajectory design tool known as TRACT (TRAjectory Configuration Tool). TRACT is capable of modeling complex interplanetary trajectories, including multiple ballistic and/or powered gravity assists, deep space maneuvers, parking orbits, and other common maneuvers. TRACT utilizes an adaptable architecture of modular boundary value problem (BVP) algorithms for all trajectory segments. A bi-level optimization scheme is employed to reduce the number of optimization variables, simplifying the user provided trajectory information. The standardized optimization parameter set allows for easy use of TRACT with a variety of optimization algorithms and mission constraints. The dissertation also details new research in powered gravity assists. A review of literature on optimal powered gravity assists is presented, where many optimal solutions found are infeasible for realistic spacecraft missions. The need was identified for a mission feasible optimal powered gravity assist algorithm using only a single impulsive maneuver. The solution space was analyzed and a complete characterization was developed for solution types of the optimal single-impulse powered gravity assist. Using newfound solution space characteristics, an efficient and reliable optimal single-impulse powered gravity assist BVP algorithm was formulated. The mission constraints were strictly enforced, such as maintaining the closest approach above a minimum radius and below a maximum radius. An extension of the optimal powered gravity assist research is the development of a gravity assist BVP algorithm that utilizes an asymptote ΔV correction maneuver to produce ballistic gravity assist trajectory solutions. The efficient algorithm is tested with real interplanetary mission trajectory parameters and successfully converges upon ballistic gravity assists with improved performance compared to traditional methods. A hybrid approach is also presented, using the asymptote maneuver algorithm together with traditional gravity assist constraints to reach ballistic trajectory solutions more reliably, while improving computational performance.Show more Item A self-contained guidance and targeting algorithm for spacecraft applications(2012-08) Scarritt, Sara Kathryn; Marchand, Belinda G.; Hull, David G.; Ocampo, Cesar A.; D'Souza, Christopher N.; Weeks, Michael W.Show more The development of a self-contained, onboard, fully autonomous trajectory guidance tool for spacecraft is presented. To be considered completely autonomous requires the capability to both identify an appropriate startup solution, and then use that solution to target a set of user-defined path and endpoint constraints. To minimize the cost of flight software development and validation, both the generation of the startup solution and the targeting algorithm are designed to be as computationally efficient as possible. This study addresses both the determination of a startup arc and the subsequent targeting process. The first part of the investigation considers the targeting algorithm. Linear targeting through differential corrections is a well-known approach for identifying feasible solutions that meet specified mission and trajectory constraints. However, to date, these methods relied on the assumption that the associated control inputs were impulsive in nature. This research focuses on the theoretical development and numerical validation of a generalized linear targeting algorithm capable of accommodating finite periods of continuous control action for a wide range of applications. Examples are presented to illustrate the general concept and to contrast the performance of this new targeting process against more classical impulsive targeting methods. The second section of the study introduces a novel approach utilizing artificial potential function methods to identify suitable startup solutions. Although common in other types of path planning, these methods have not yet been used for orbital or interplanetary trajectory design, primarily due to their inherent suboptimality. However, results show that this issue can be addressed with relative ease by the targeting algorithm.Show more