An algorithm to improve the computational efficiency of the low-thrust escape trajectory is developed. The algorithm reduces computational effort while maintaining accuracy, making it desirable for use in computing optimal escape trajectory by direct method. As low-thrust ionic propulsion engines are considered for use in interplanetary missions, design and planning includes the optimization of the spacecraft trajectory. The low-thrust escape phase evolves in the form of a slowly unwinding spiral. The computational expense required to accurately propagate the dense spiraling trajectory of the planetocentric escape phase through the numerical integration of the ordinary differential equations is undesirable. Implementation of an algorithm that approximates the trajectory while maintaining accuracy and improving computational efficiency is beneficial. The algorithm developed is demonstrated with the optimization of a sample Earth-escape trajectory. An inexpensive trajectory calculation with little error is produced.
The escape parameters (time, range angle and position) are studied for achieving optimum escape missions using low-thrust vehicle . Results are compared with previously reported analytical and numerical calculations. The equations of motion in addition to Euler-Lagrange optimization equations were solved using an IBM 7090 Low-Thrust Digital Computer Program. Specific impulses were varied from 1,000 to 25,000 sec and electrical power outputs were varied from 100 KW to 100 MW. Planar orbits initially circular) were assumed. Results of the parametric investigation are presented both in tabular and graphical form. Analy is of generated escape data indicate that the analytical equations previously reporte have deviations ranging from approximately -25% to 44%. Numerical results previously reported are in general agreement with this study. (Author).
This paper provides a catalogue of brief descriptions of current lowthrust trajectory and mass computation programs. All known sources were contacted, and questionnaires were sent to those who indicated that they possessed such codes.
Inhaltsangabe:Abstract: This thesis presents improvements to FLOAT, a hybrid analytical/numerical algorithm for rapid generation of three dimensional, optimal launch vehicle ascent trajectories. Improvements have been made to the terminal constraints, which are now available in a more general form to allow for an optimal attachment point to the target orbit.The existing algorithm also has been extended with logic that allows for vehicles with low thrust to weight ratios in the upper stage and successful convergence of problems with path constraints for normal force and angle of attack Another major extension made to the code is the introduction of coasting arcs. Coasting arcs are implemented using a completely analytical solution for the prediction of states and costates as well as for the required sensitivity matrix. This allows for a very fast and accurate calculation even with long coasting arcs. Finally, an approach for the optimization of start and end time of coast arcs is presented.This approach was implemented and the results of a test case compare very well with results generated with OTIS for the same case. At the end, suggestions for future development are made. Inhaltsverzeichnis:Table of Contents: Summaryi Acknowledgementsii Contentsiii Nomenclaturev Figuresviii Introduction1 1.Problem description3 1.1Describing the final orbit3 1.2Coordinate frame5 1.3Dynamic system6 1.4Initial conditions7 1.5Path constraints7 1.6Performance index7 1.7Terminal constraints8 1.8Solution method8 1.9Non-dimensionalization of the variables9 2.Solving the two-point boundary value problem10 2.1Vacuumsolution10 2.1.1Simplified model equations10 2.1.2Optimal control for vacuum solution11 2.1.3Thrust integrals and closed form solution for ascent in vacuum12 2.2Atmospheric solution13 2.2.1Dynamic system and collocation variables13 2.2.2Optimality condition to solve for 1b14 2.2.3Differential equations for the costate variables16 2.3Terminal constraints16 2.3.1Attaching at perigee17 2.3.2Free attachment point17 2.4Transversality conditions18 2.4.1Final costates for attaching at perigee18 2.4.2Final costates for free attachment point19 2.4.3Equatorial orbits22 2.5Adjusting final time22 2.6Computation procedure23 2.7Numerical results24 3.Low thrust upper stages27 3.1Typical low thrust case27 3.2Problems with low thrust upper stages28 3.3Upper stage modification30 3.4Advantage of free attachment point for low thrust [...]
This thesis concerns the use of genetic algorithms in the optimization of the trajectories of low thrust spacecraft. Genetic algorithms are programming tools which use the principles of biological evolution and adaptation to optimize processes. These algorithms have been found to be very useful in many different engineering disciplines. The goal of this project is to determine their applicability to the generation and optimization of low thrust spacecraft trajectories. This thesis describes the basic operating principles of genetic algorithms and then applies them to two different missions.
