Computational graph construction of adjoint sensitivities for low-thrust trajectory optimization and desensitized optimal control

Low-thrust trajectory problems are becoming more frequent with the widespread adoption of electric propulsion systems for spacecraft. As the thrust acceleration is reduced and the size of the subsequent optimization problem grows, the traditional formulations become numerically ill-conditioned. At the same time, classical optimal control problems suffer from cumbersome notation when many function compositions are present. To address these issues, several numerical innovations are introduced for low-thrust orbital transfers spanning parametrization (nested B-spline control compressed via singular value decomposition), regularization (a new monotonic independent variable for the (h, e) orbital elements), and constraint handling. These together allow for the optimization of orbital maneuvers in cislunar space with thrust levels lower than existing frameworks. To streamline notations, the functional dependencies are indicated on a separate computational graph. The performance index is viewed as the output of an evaluation procedure dependent on its inputs. This allows unfolding the chain rule for differentiation in order to design efficient algorithms for trajectory optimization. The methods in this dissertation include adjoint sensitivities (extended to objectives that already contain a sensitivity cost, i.e. desensitized optimal control), a multiple-shooting framework, and a vectorization-based matrix calculus. A key finding is an alternative evaluation of desensitized objectives whose system of differential equations scales only with the number of states. Numerical demonstrations include a standard Zermelo navigation problem, a benchmark Earth-Mars orbital transfer, a Mars pinpoint landing scenario, and an unusually lengthy low-thrust orbit raising from a geostationary transfer orbit to a near-rectilinear halo orbit subject to launcher and eclipse duration constraints. Furthermore, a numerical experiment on integration schemes and two minimum-propellant scenarios are provided. Lastly, a proof confirming that the solution of a shooting formulation satisfies the first-order necessary conditions of optimality is formulated for a Bolza problem.

Author

• Arustei, Adrian

Identifier

hdl:10057/56106

OAI identifier oai:identifier

oai:soar.wichita.edu:10057/56106