Sub-Optimal Fast Fourier Series Approximation for Initial Trajectory Design

TL;DR

This paper extends the Finite Fourier Series Shape-Based trajectory approximation method to generate sub-optimal initial trajectories by incorporating time of flight minimization, providing feasible solutions for trajectory design.

Contribution

It introduces a modified NLP objective to produce sub-optimal trajectories that include time of flight considerations, expanding the original FFS SB approach.

Findings

Generated feasible sub-optimal trajectories with minimized time of flight.

Solutions differ from original FFS SB trajectories, offering alternative initial guesses.

Trajectories are suitable for use with direct solvers in trajectory optimization.

Abstract

The Finite Fourier Series (FFS) Shape-Based (SB) trajectory approximation method has been used to rapidly generate initial trajectories that satisfy the dynamics, trajectory boundary conditions, and limitation on maximum thrust acceleration. The FFS SB approach solves a nonlinear programming problem (NLP) in searching for feasible trajectories. This paper extends the development of the FFS SB approach to generate sub optimal solutions. Specifically, the objective function of the NLP problem is modified to include also a measure for the time of flight. Numerical results presented in this paper show several solutions that differ from those of the original FFS SB ones. The sub-optimal trajectories generated using a time of flight minimization are shown to be physically feasible trajectories and potential candidates for direct solvers.