A practical guide to implementing zero-order-hold interplanetary trajectory legs

TL;DR

This paper presents a comprehensive approach for implementing zero-order-hold transcriptions in interplanetary trajectory optimization, emphasizing robustness and broad applicability across various dynamical models.

Contribution

It introduces a set of design principles, a novel shooting construction, a redundant throttle parameterization, a differentiable time-grid encoding, and a benchmark suite for trajectory optimization.

Findings

The ZOH method is robust across multiple dynamical models.

The throttle parameterization removes control singularities.

The benchmark suite enables standardized testing of trajectory problems.

Abstract

We study the practical implementation of zero-order-hold (ZOH) transcriptions for spacecraft trajectory optimisation, identifying a set of design principles that render them robust across a broad class of dynamical settings without problem-specific tuning. The contributions are fourfold: (i) a thorough study of the forward--backward shooting construction, denoted $\mathrm{ZOH}_\alpha$; (ii) a redundant four-dimensional throttle parameterization that eliminates the singularity of the control influence matrix along ballistic arcs; (iii) a softmax time-grid encoding that avoids ordering constraints on segment durations while preserving full differentiability; and (iv) the TOPS benchmark (Trajectory Optimisation Problems in Space), a suite of 28 problems spanning four dynamical models, two-body Cartesian, modified equinoctial elements, circular restricted three-body, and solar sailing, designed to be extended over time.