Application of the Theory of Functional Connections to the Perturbed Lambert's Problem

TL;DR

This paper introduces a novel numerical method based on the Theory of Functional Connections to solve the perturbed Lambert's problem, improving robustness and efficiency in orbital transfer calculations.

Contribution

It applies the Theory of Functional Connections to derive a constrained functional for Lambert's problem, enabling analytical boundary condition satisfaction and handling perturbations effectively.

Findings

Demonstrates robustness and accuracy on Earth and Sun-centered orbits.

Shows improved speed and robustness over traditional methods.

Handles perturbations like Earth's oblateness and solar radiation pressure.

Abstract

A numerical approach to solve the perturbed Lambert's problem is presented. The proposed technique uses the Theory of Functional Connections, which allows the derivation of a constrained functional that analytically satisfies the boundary values of Lambert's problem. The propagation model is devised in terms of three new variables to mainly avoid the orbital frequency oscillation of Cartesian coordinates. Examples are provided to quantify robustness, efficiency, and accuracy on Earth and Sun centered orbits with various shapes and orientations. Differential corrections and a robust Lambert solver are used to validate the proposed approach in various scenarios and to compare it in terms of speed and robustness. Perturbations due to Earth's oblateness, third-body, and Solar radiation pressure are introduced, showing the algorithm's flexibility. Multi-revolution solutions are obtained. Finally, a polynomial analysis is conducted to show the dependence of convergence time on polynomial type and degree.