Study of optimal control and trajectory optimization with direct methods

This Master’s Thesis presents the design and validation of an own MATLAB code that solves optimal trajectory problems, aimed primarily at gliders but extendable to thrust-powered vehicles. The core goal is to maximize range. A direct transcription strategy is adopted: system dynamics are discretized...

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Detalles Bibliográficos
Autor: Pozo Díaz, Xavier
Tipo de recurso: tesis de maestría
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/447084
Acceso en línea:https://hdl.handle.net/2117/447084
Access Level:acceso abierto
Palabra clave:Trajectory optimization
Optimal control
FALCON
Pontryagin
Optimització de la trajectòria
Àrees temàtiques de la UPC::Aeronàutica i espai::Aerodinàmica
Descripción
Sumario:This Master’s Thesis presents the design and validation of an own MATLAB code that solves optimal trajectory problems, aimed primarily at gliders but extendable to thrust-powered vehicles. The core goal is to maximize range. A direct transcription strategy is adopted: system dynamics are discretized with a trapezoidal collocation scheme, turning the continuous problem into a sparse nonlinear programming (NLP) solved with f mincon. The implementation is benchmarked against the FALCON.m toolbox. Three test cases of increasing complexity are addressed: 1. Drag-free projectile launch, which has a closed-form solution; 2. Optimal glide of an unpowered vehicle under nonlinear aerodynamic forces; 3. Maximizing range of a flight with limited thrust and fuel management. Beyond verifying optimal solutions, the thesis discusses key technical choices—such as the use of trapezoidal collocation and finite-difference gradient estimates—and assesses their impact on computational cost. Future improvements are outlined: integrating faster, specialized solvers (e.g. IPOPT, multiple shooting), enriching the model with 3-D dynamics, wind and operational constraints, and supplying analytical gradients to boost convergence speed. Overall, the project delivers a versatile, validated tool for aircraft trajectory optimization and lays a solid foundation for further research in flight-path planning and control.