This thesis’s work serves as proof of concept for the Next Generation Space Weather Prediction Mission, a multi-spacecraft mission at various libration points whose objective is to forecast Space Weather hazards with a 12day warning time. This thesis deals with the design and control of orbits of spacecraft formations at different libration points. The systems studied are SunEarth, SunVenus, SunMercury, and SunMars. The orbit design and formation keeping control of the spacecraft are solved simultaneously using an optimization software called DIDO. Initial conditions are obtained through two different strategies. The first one, by placing the spacecraft in a tetrahedral formation and using Monte Simulations to find the initial velocities. The second strategy suggests holding velocities fixed while initial locations of the spacecraft are chosen randomly. All results are verified and validated by applying Pontryagin’s principle to the optimal control problem by “hand”, and then comparing the results with the outputs from the optimization software.
L4 and L5 points of any systems are the easiest to work with due to their inherent stability. In most cases, the use of the L1norm of control as the cost function yields the lowest station-keeping cost. The culminating remark is that the Next Generation Space Weather Prediction Mission is feasible from an astrodynamics perspective.
","abstract_html":"<p>This thesis’s work serves as proof of concept for the Next Generation Space Weather Prediction Mission, a multi-spacecraft mission at various libration points whose objective is to forecast Space Weather hazards with a 12day warning time. This thesis deals with the design and control of orbits of spacecraft formations at different libration points. The systems studied are SunEarth, SunVenus, SunMercury, and SunMars. The orbit design and formation keeping control of the spacecraft are solved simultaneously using an optimization software called DIDO. Initial conditions are obtained through two different strategies. The first one, by placing the spacecraft in a tetrahedral formation and using Monte Simulations to find the initial velocities. The second strategy suggests holding velocities fixed while initial locations of the spacecraft are chosen randomly. All results are verified and validated by applying Pontryagin’s principle to the optimal control problem by “hand”, and then comparing the results with the outputs from the optimization software.</p> <p>L4 and L5 points of any systems are the easiest to work with due to their inherent stability. In most cases, the use of the L1norm of control as the cost function yields the lowest station-keeping cost. The culminating remark is that the Next Generation Space Weather Prediction Mission is feasible from an astrodynamics perspective.</p>","abstract_has_math":false,"creators":["Rangel, Roberto Cuéllar"],"institution":null,"degree_name":"Master of Science in Aerospace Engineering","degree_level":"Thesis - Open Access","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-07-01T07:00:00Z","date_published":"2020-07-01T07:00:00Z","updated_at":"2026-07-27T19:25:29Z","subjects":["spacecraft","Lagrange points","space weather","Aerospace Engineering","Oceanography and Atmospheric Sciences and Meteorology","Space Vehicles"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/539","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Rangel, Roberto Cuéllar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Aerospace Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["spacecraft","Lagrange points","space weather","Aerospace Engineering","Oceanography and Atmospheric Sciences and Meteorology","Space Vehicles"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/539"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis’s work serves as proof of concept for the Next Generation Space Weather Prediction Mission, a multi-spacecraft mission at various libration points whose objective is to forecast Space Weather hazards with a 12day warning time. This thesis deals with the design and control of orbits of spacecraft formations at different libration points. The systems studied are SunEarth, SunVenus, SunMercury, and SunMars. The orbit design and formation keeping control of the spacecraft are solved simultaneously using an optimization software called DIDO. Initial conditions are obtained through two different strategies. The first one, by placing the spacecraft in a tetrahedral formation and using Monte Simulations to find the initial velocities. The second strategy suggests holding velocities fixed while initial locations of the spacecraft are chosen randomly. All results are verified and validated by applying Pontryagin’s principle to the optimal control problem by “hand”, and then comparing the results with the outputs from the optimization software.
L4 and L5 points of any systems are the easiest to work with due to their inherent stability. In most cases, the use of the L1norm of control as the cost function yields the lowest station-keeping cost. The culminating remark is that the Next Generation Space Weather Prediction Mission is feasible from an astrodynamics perspective.
"]},{"key":"dc:title","label":"Title","values":["Optimization of Spacecraft Formations about Lagrange Points for the Next Generation Space Weather Prediction Mission"]}]}],"canonical_facts":{"dc:creator":["Rangel, Roberto Cuéllar"],"dc:description.abstract":["This thesis’s work serves as proof of concept for the Next Generation Space Weather Prediction Mission, a multi-spacecraft mission at various libration points whose objective is to forecast Space Weather hazards with a 12day warning time. This thesis deals with the design and control of orbits of spacecraft formations at different libration points. The systems studied are SunEarth, SunVenus, SunMercury, and SunMars. The orbit design and formation keeping control of the spacecraft are solved simultaneously using an optimization software called DIDO. Initial conditions are obtained through two different strategies. The first one, by placing the spacecraft in a tetrahedral formation and using Monte Simulations to find the initial velocities. The second strategy suggests holding velocities fixed while initial locations of the spacecraft are chosen randomly. All results are verified and validated by applying Pontryagin’s principle to the optimal control problem by “hand”, and then comparing the results with the outputs from the optimization software.
L4 and L5 points of any systems are the easiest to work with due to their inherent stability. In most cases, the use of the L1norm of control as the cost function yields the lowest station-keeping cost. The culminating remark is that the Next Generation Space Weather Prediction Mission is feasible from an astrodynamics perspective.
"],"dc:identifier":["https://commons.erau.edu/edt/539"],"dc:subject":["spacecraft","Lagrange points","space weather","Aerospace Engineering","Oceanography and Atmospheric Sciences and Meteorology","Space Vehicles"],"dc:title":["Optimization of Spacecraft Formations about Lagrange Points for the Next Generation Space Weather Prediction Mission"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Aerospace Engineering"]},"updated_at":"2026-07-27T19:25:29Z"}