A practical guide to implementing zero-order-hold interplanetary trajectory legs
Dario Izzo, Harry Holt, Giacomo Acciarini, Laurent Beauregard, Yuri Shimane
TLDR
This paper provides a practical guide and design principles for robust zero-order-hold (ZOH) transcriptions in spacecraft trajectory optimization.
Key contributions
- Thorough study of ZOHα, a forward-backward shooting construction for trajectory optimization.
- Redundant 4D throttle parameterization to eliminate control influence matrix singularity on ballistic arcs.
- Softmax time-grid encoding to avoid duration ordering constraints while maintaining differentiability.
- Introduces TOPS benchmark, a suite of 28 trajectory optimization problems across four dynamical models.
Why it matters
This work makes ZOH trajectory optimization more robust and practical across diverse space dynamics. It solves common implementation issues and provides a new benchmark, advancing space mission design.
Original 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 $\mathrm{ZOH}_α$; (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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