{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/140806"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/140806","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Optimal Control in Aircraft Trajectory Planning","abstract":"Trajectory planning for autonomous and piloted aircraft must satisfy not only geometric constraints but also full six-degree-of-freedom dynamics, actuator limits, and mission- or safety-driven performance objectives. This thesis investigates optimal control as a refinement tool for trajectory-planning problems that are typically addressed using geometric or search-based methods. Two case studies are considered. The first addresses loss-of-thrust contingency landing for a fixed-wing aircraft, formulating a nonlinear optimal control problem that minimizes a population-density-weighted ground risk metric, with and without an explicit time penalty, subject to a six-degree-of-freedom Cessna 182 model and operational constraints. Initial trajectories are provided by discrete search and Dubins paths, and the refined solutions reduce risk and/or flight time while remaining dynamically feasible and trackable in closed-loop simulation. The second case study develops an energy-optimal trajectory generation framework for a Lift+Cruise QuadPlane small uncrewed aircraft system. Starting from spline-based reference paths, a six-degree-of-freedom QuadPlane model and power-based cost function are used to compute dynamically feasible trajectories that include hover--to--cruise mode transitions and multi-waypoint maneuvers. Results show consistent reductions in power and energy consumption, smoother attitude and angular-rate histories, and explicit characterization of trade-offs among energy use, maneuver aggressiveness, and operational constraints. Collectively, these case studies demonstrate how optimal control can bridge fast geometric planning and high-fidelity dynamics, supporting preflight design of risk-aware and energy-efficient trajectories for both contingency and nominal operations.","abstract_html":"Trajectory planning for autonomous and piloted aircraft must satisfy not only geometric constraints but also full six-degree-of-freedom dynamics, actuator limits, and mission- or safety-driven performance objectives. This thesis investigates optimal control as a refinement tool for trajectory-planning problems that are typically addressed using geometric or search-based methods. Two case studies are considered. The first addresses loss-of-thrust contingency landing for a fixed-wing aircraft, formulating a nonlinear optimal control problem that minimizes a population-density-weighted ground risk metric, with and without an explicit time penalty, subject to a six-degree-of-freedom Cessna 182 model and operational constraints. Initial trajectories are provided by discrete search and Dubins paths, and the refined solutions reduce risk and/or flight time while remaining dynamically feasible and trackable in closed-loop simulation. The second case study develops an energy-optimal trajectory generation framework for a Lift+Cruise QuadPlane small uncrewed aircraft system. Starting from spline-based reference paths, a six-degree-of-freedom QuadPlane model and power-based cost function are used to compute dynamically feasible trajectories that include hover--to--cruise mode transitions and multi-waypoint maneuvers. Results show consistent reductions in power and energy consumption, smoother attitude and angular-rate histories, and explicit characterization of trade-offs among energy use, maneuver aggressiveness, and operational constraints. Collectively, these case studies demonstrate how optimal control can bridge fast geometric planning and high-fidelity dynamics, supporting preflight design of risk-aware and energy-efficient trajectories for both contingency and nominal operations.","abstract_has_math":false,"creators":["Kim, Heejin S."],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Aerospace Engineering","degree_department":"Aerospace and Ocean Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Atkins, Ella M."],"committee_members":["Sultan, Cornel","Woolsey, Craig A."],"year":2025,"date_issued":"2025-12-03","date_published":"2025-12-03","updated_at":"2026-07-22T22:19:59Z","subjects":["optimal control","trajectory planning","aircraft dynamics and control"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10919/140806","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Atkins, Ella M."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Sultan, Cornel","Woolsey, Craig A."]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace and Ocean Engineering"]},{"key":"dc:creator","label":"Author","values":["Kim, Heejin S."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-01-14T18:42:44Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-01-14T18:42:44Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-12-03"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["optimal control","trajectory planning","aircraft dynamics and control"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/140806"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Trajectory planning for autonomous and piloted aircraft must satisfy not only geometric constraints but also full six-degree-of-freedom dynamics, actuator limits, and mission- or safety-driven performance objectives. This thesis investigates optimal control as a refinement tool for trajectory-planning problems that are typically addressed using geometric or search-based methods. Two case studies are considered. The first addresses loss-of-thrust contingency landing for a fixed-wing aircraft, formulating a nonlinear optimal control problem that minimizes a population-density-weighted ground risk metric, with and without an explicit time penalty, subject to a six-degree-of-freedom Cessna 182 model and operational constraints. Initial trajectories are provided by discrete search and Dubins paths, and the refined solutions reduce risk and/or flight time while remaining dynamically feasible and trackable in closed-loop simulation. The second case study develops an energy-optimal trajectory generation framework for a Lift+Cruise QuadPlane small uncrewed aircraft system. Starting from spline-based reference paths, a six-degree-of-freedom QuadPlane model and power-based cost function are used to compute dynamically feasible trajectories that include hover--to--cruise mode transitions and multi-waypoint maneuvers. Results show consistent reductions in power and energy consumption, smoother attitude and angular-rate histories, and explicit characterization of trade-offs among energy use, maneuver aggressiveness, and operational constraints. Collectively, these case studies demonstrate how optimal control can bridge fast geometric planning and high-fidelity dynamics, supporting preflight design of risk-aware and energy-efficient trajectories for both contingency and nominal operations."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Modern aircraft and drones must plan their flight paths in ways that are not only efficient, but also safe and realistic for the vehicle to follow. This thesis studies how advanced mathematical tools, known as optimal control methods, can refine simple “first guess” paths into more practical and reliable flight trajectories. The first part of this work focuses on emergency landings for a small airplane that suddenly loses engine power. In this situation, the aircraft must glide to a safe landing site while avoiding highly populated areas on the ground. Starting from basic paths generated by fast search methods, the thesis uses optimal control to adjust the route so that it respects the true motion limits of the aircraft and reduces the overall risk to people on the ground. The results show that these refined routes can lower risk and, in some cases, shorten the time it takes to reach a landing site. The second part examines a hybrid electric aircraft called a Lift+Cruise QuadPlane, which uses multiple rotors for vertical takeoff and landing and a wing for efficient forward flight. Here, optimal control is used to design energy-efficient paths that include transitions between hovering and forward flight and motion through multiple waypoints. The study demonstrates that these optimized trajectories can save energy and produce smoother motions while still satisfying limits on the aircraft’s attitude and control effort. Together, these two case studies highlight how optimal control can help bridge the gap between simple, fast planning methods and the complex realities of safe, efficient flight in both emergency and routine operations."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Optimal Control in Aircraft Trajectory Planning"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Atkins, Ella M."],"dc:contributor.committeemember":["Sultan, Cornel","Woolsey, Craig A."],"dc:contributor.department":["Aerospace and Ocean Engineering"],"dc:creator":["Kim, Heejin S."],"dc:date.accessioned":["2026-01-14T18:42:44Z"],"dc:date.available":["2026-01-14T18:42:44Z"],"dc:date.issued":["2025-12-03"],"dc:description.abstract":["Trajectory planning for autonomous and piloted aircraft must satisfy not only geometric constraints but also full six-degree-of-freedom dynamics, actuator limits, and mission- or safety-driven performance objectives. This thesis investigates optimal control as a refinement tool for trajectory-planning problems that are typically addressed using geometric or search-based methods. Two case studies are considered. The first addresses loss-of-thrust contingency landing for a fixed-wing aircraft, formulating a nonlinear optimal control problem that minimizes a population-density-weighted ground risk metric, with and without an explicit time penalty, subject to a six-degree-of-freedom Cessna 182 model and operational constraints. Initial trajectories are provided by discrete search and Dubins paths, and the refined solutions reduce risk and/or flight time while remaining dynamically feasible and trackable in closed-loop simulation. The second case study develops an energy-optimal trajectory generation framework for a Lift+Cruise QuadPlane small uncrewed aircraft system. Starting from spline-based reference paths, a six-degree-of-freedom QuadPlane model and power-based cost function are used to compute dynamically feasible trajectories that include hover--to--cruise mode transitions and multi-waypoint maneuvers. Results show consistent reductions in power and energy consumption, smoother attitude and angular-rate histories, and explicit characterization of trade-offs among energy use, maneuver aggressiveness, and operational constraints. Collectively, these case studies demonstrate how optimal control can bridge fast geometric planning and high-fidelity dynamics, supporting preflight design of risk-aware and energy-efficient trajectories for both contingency and nominal operations."],"dc:description.abstractgeneral":["Modern aircraft and drones must plan their flight paths in ways that are not only efficient, but also safe and realistic for the vehicle to follow. This thesis studies how advanced mathematical tools, known as optimal control methods, can refine simple “first guess” paths into more practical and reliable flight trajectories. The first part of this work focuses on emergency landings for a small airplane that suddenly loses engine power. In this situation, the aircraft must glide to a safe landing site while avoiding highly populated areas on the ground. Starting from basic paths generated by fast search methods, the thesis uses optimal control to adjust the route so that it respects the true motion limits of the aircraft and reduces the overall risk to people on the ground. The results show that these refined routes can lower risk and, in some cases, shorten the time it takes to reach a landing site. The second part examines a hybrid electric aircraft called a Lift+Cruise QuadPlane, which uses multiple rotors for vertical takeoff and landing and a wing for efficient forward flight. Here, optimal control is used to design energy-efficient paths that include transitions between hovering and forward flight and motion through multiple waypoints. The study demonstrates that these optimized trajectories can save energy and produce smoother motions while still satisfying limits on the aircraft’s attitude and control effort. Together, these two case studies highlight how optimal control can help bridge the gap between simple, fast planning methods and the complex realities of safe, efficient flight in both emergency and routine operations."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/10919/140806"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["optimal control","trajectory planning","aircraft dynamics and control"],"dc:title":["Optimal Control in Aircraft Trajectory Planning"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:59Z"}