Differentiable Satellite Constellation Configuration via Relaxed Coverage and Revisit Objectives

TL;DR

This paper presents a fully differentiable pipeline for satellite constellation design that optimizes coverage and revisit objectives using novel continuous relaxations, outperforming traditional black-box optimization methods.

Contribution

It introduces four continuous relaxations enabling gradient-based optimization of satellite constellations, including the first differentiable orbit propagator for mission-level objectives.

Findings

Successfully recovers Walker-Delta geometry from irregular initializations.

Discovers elliptical Molniya-like orbits with high latitude dwell using gradients.

Outperforms simulated annealing, genetic algorithm, and differential evolution in evaluations.

Abstract

Satellite constellation design requires optimizing orbital parameters across multiple satellites to maximize mission specific metrics. For many types of mission, it is desirable to maximize coverage and minimize revisit gaps over ground targets. Existing approaches to constellation design either restrict the design space to symmetric parametric families such as Walker constellations, or rely on metaheuristic methods that require significant compute and many iterations. Gradient-based optimization has been considered intractable due to the non-differentiability of coverage and revisit metrics, which involve binary visibility indicators and discrete max operations. We introduce four continuous relaxations: soft sigmoid visibility, noisy-OR multi-satellite aggregation, leaky integrator revisit gap tracking, and LogSumExp soft-maximum, which when composed with the $\partial$SGP4 differentiable orbit propagator, yield a fully differentiable pipeline from orbital elements to mission-level objectives. We show that this scheme can recover Walker-Delta geometry from irregular initializations, and discovers elliptical Molniya-like orbits with apogee dwell over extreme latitudes from only gradients. Compared to simulated annealing (SA), genetic algorithm (GA), and differential evolution (DE) baselines, our gradient-based method recovers Walker-equivalent geometry within ${\sim}750$ evaluations, whereas the three black-box baselines plateau at with significantly worse revisit even with roughly four times the evaluation budget.