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

arXiv:2605.11043 · astro-ph.IM, astro-ph.EP · Submitted 2026-05-11 · Read on arXiv

Dario Izzo, Harry Holt, Giacomo Acciarini, Laurent Beauregard, Yuri Shimane

astro-ph.IM, astro-ph.EP

Submitted: 2026-05-11

Comments: Work presented at the 30th International Symposium on Space Flight Dynamics (ISSFD)

License: http://creativecommons.org/licenses/by/4.0/

The gist: 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

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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 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.

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