Optimal trajectory design has been extensively studied across multiple disciplines adopting different techniques for implementation and execution. It has been utilized in past space trajectory missions to either optimize the amount of fuel spent or minimize the time of flight to meet mission requirements. Coupled Radial Basis Functions (CRBFs) are a new way to solve these optimal control problems, and this thesis applies CRBFs to spacecraft trajectory optimization design problems. CRBFs are real-valued radial basis functions (RBFs) that utilize a conical spline while also not being affected by the value of the shape parameter. The CRBF approach is applied to nonlinear optimal control problems. We adopt the indirect formulation so that the necessary and boundary conditions are derived from the system dynamical equations. As a result, a set of nonlinear algebraic equations (NAEs) is generated. The NAEs are then solved using a standard solver in MATLAB and the results are produced. CRBFs do not rely heavily on initial extensive analysis of the problem, which makes it very intuitive to use. The states, control, and co-states are defined as the equations to be solved and approximated using CRBFs. The results show that CRBFs can be applied to space trajectory optimization problems to produce accurate results across state and costate variables on uniform user defined nodes across the simulation time.
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Master of Science in Aerospace Engineering (M.S.A.E.)
College of Engineering and Computer Science
Mechanical and Aerospace Engineering
Aerospace Engineering; Space System Design and Engineering
Length of Campus-only Access
Masters Thesis (Open Access)
Roy, Kyler, "Trajectory Design Optimization Using Coupled Radial Basis Functions (CRBFs)" (2023). Electronic Theses and Dissertations, 2020-. 1767.