The use of Coulomb force has been analyzed in recent years to provide propulsion in space for various applications. Coulomb formation can also be utilized to make close formation spacecraft missions fuel efficient. In this study, the Coulomb formation of two craft is studied in elliptic chief orbits for two formation geometries. The first formation requires both spacecraft to be aligned along the nadir (radial) direction and the second formation requires both spacecraft to maintain a constant separation distance relative to each other while each spacecraft rotates freely on the surface of a sphere with the ratio of the radii being inversely proportional to the ratio of the masses. Two nonlinear optimal feedback control techniques are implemented to stabilize the dynamics of the Coulomb formation and maintain the desired formation while minimizing the energy costs. The control accelerations are compared to the analytical constraint accelerations obtained using the Udwadia-Kalaba equations for constrained motion. Due to the effects of plasma shielding, a Debye length model is incorporated in the nonlinear dynamics as a linear function of altitude of the formation's center of mass. The integrated thruster efforts are calculated for both optimal and analytical techniques and the fuel costs are determined and compared for both formations. The results demonstrated that the use of Coulomb force increases fuel efficiency for formation achievement and maintenance. The numerical analysis is performed on a) the highly eccentric Molniya orbit and b) the near-circular near-GEO orbit of the ERS-21.
","abstract_html":"<p>The use of Coulomb force has been analyzed in recent years to provide propulsion in space for various applications. Coulomb formation can also be utilized to make close formation spacecraft missions fuel efficient. In this study, the Coulomb formation of two craft is studied in elliptic chief orbits for two formation geometries. The first formation requires both spacecraft to be aligned along the nadir (radial) direction and the second formation requires both spacecraft to maintain a constant separation distance relative to each other while each spacecraft rotates freely on the surface of a sphere with the ratio of the radii being inversely proportional to the ratio of the masses. Two nonlinear optimal feedback control techniques are implemented to stabilize the dynamics of the Coulomb formation and maintain the desired formation while minimizing the energy costs. The control accelerations are compared to the analytical constraint accelerations obtained using the Udwadia-Kalaba equations for constrained motion. Due to the effects of plasma shielding, a Debye length model is incorporated in the nonlinear dynamics as a linear function of altitude of the formation's center of mass. The integrated thruster efforts are calculated for both optimal and analytical techniques and the fuel costs are determined and compared for both formations. The results demonstrated that the use of Coulomb force increases fuel efficiency for formation achievement and maintenance. The numerical analysis is performed on a) the highly eccentric Molniya orbit and b) the near-circular near-GEO orbit of the ERS-21.</p>","abstract_has_math":false,"creators":["Memon, Muhammad Wasif"],"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":2019,"date_issued":"2019-12-01T08:00:00Z","date_published":"2019-12-01T08:00:00Z","updated_at":"2026-07-27T19:26:28Z","subjects":["fuel efficiency","constrained motion","spacecraft","coulomb formation","elliptic","Aeronautical Vehicles"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/490","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Memon, Muhammad Wasif"]}]},{"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":["fuel efficiency","constrained motion","spacecraft","coulomb formation","elliptic","Aeronautical Vehicles"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/490"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The use of Coulomb force has been analyzed in recent years to provide propulsion in space for various applications. Coulomb formation can also be utilized to make close formation spacecraft missions fuel efficient. In this study, the Coulomb formation of two craft is studied in elliptic chief orbits for two formation geometries. The first formation requires both spacecraft to be aligned along the nadir (radial) direction and the second formation requires both spacecraft to maintain a constant separation distance relative to each other while each spacecraft rotates freely on the surface of a sphere with the ratio of the radii being inversely proportional to the ratio of the masses. Two nonlinear optimal feedback control techniques are implemented to stabilize the dynamics of the Coulomb formation and maintain the desired formation while minimizing the energy costs. The control accelerations are compared to the analytical constraint accelerations obtained using the Udwadia-Kalaba equations for constrained motion. Due to the effects of plasma shielding, a Debye length model is incorporated in the nonlinear dynamics as a linear function of altitude of the formation's center of mass. The integrated thruster efforts are calculated for both optimal and analytical techniques and the fuel costs are determined and compared for both formations. The results demonstrated that the use of Coulomb force increases fuel efficiency for formation achievement and maintenance. The numerical analysis is performed on a) the highly eccentric Molniya orbit and b) the near-circular near-GEO orbit of the ERS-21.
"]},{"key":"dc:title","label":"Title","values":["Fuel Efficient Control Design and Constrained Motion Analysis for Spacecraft Coulomb Formation in Elliptic Chief Orbits"]}]}],"canonical_facts":{"dc:creator":["Memon, Muhammad Wasif"],"dc:description.abstract":["The use of Coulomb force has been analyzed in recent years to provide propulsion in space for various applications. Coulomb formation can also be utilized to make close formation spacecraft missions fuel efficient. In this study, the Coulomb formation of two craft is studied in elliptic chief orbits for two formation geometries. The first formation requires both spacecraft to be aligned along the nadir (radial) direction and the second formation requires both spacecraft to maintain a constant separation distance relative to each other while each spacecraft rotates freely on the surface of a sphere with the ratio of the radii being inversely proportional to the ratio of the masses. Two nonlinear optimal feedback control techniques are implemented to stabilize the dynamics of the Coulomb formation and maintain the desired formation while minimizing the energy costs. The control accelerations are compared to the analytical constraint accelerations obtained using the Udwadia-Kalaba equations for constrained motion. Due to the effects of plasma shielding, a Debye length model is incorporated in the nonlinear dynamics as a linear function of altitude of the formation's center of mass. The integrated thruster efforts are calculated for both optimal and analytical techniques and the fuel costs are determined and compared for both formations. The results demonstrated that the use of Coulomb force increases fuel efficiency for formation achievement and maintenance. The numerical analysis is performed on a) the highly eccentric Molniya orbit and b) the near-circular near-GEO orbit of the ERS-21.
"],"dc:identifier":["https://commons.erau.edu/edt/490"],"dc:subject":["fuel efficiency","constrained motion","spacecraft","coulomb formation","elliptic","Aeronautical Vehicles"],"dc:title":["Fuel Efficient Control Design and Constrained Motion Analysis for Spacecraft Coulomb Formation in Elliptic Chief Orbits"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Aerospace Engineering"]},"updated_at":"2026-07-27T19:26:28Z"}