Differentiable Satellite Constellation Configuration via Relaxed Coverage and Revisit Objectives

2026-04-21

AI Summary

This work addresses the challenge that coverage and revisit metrics in satellite constellation design are non-differentiable due to their reliance on binary visibility checks and discrete max operations, hindering gradient-based optimization. The authors propose the first end-to-end differentiable framework for constellation optimization by introducing continuous relaxations: soft sigmoid visibility modeling, noisy-OR aggregation for multi-satellite coverage, leaky integrator-based revisit tracking, and LogSumExp as a smooth approximation to the maximum operator. Integrated with a differentiable orbit propagator (partialSGP4), this approach enables fully differentiable modeling of coverage and revisit objectives. It overcomes limitations of conventional symmetric configurations or black-box optimizers, reproducing Walker-Delta constellations in approximately 750 evaluations and discovering high-latitude-persistent Molniya-like elliptical orbits that significantly outperform traditional methods such as simulated annealing and genetic algorithms with fewer evaluations.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• satellite constellation design
• coverage optimization
• revisit time minimization
• non-differentiable objectives
• orbital parameter optimization

Innovation

• differentiable constellation design
• continuous relaxation
• gradient-based optimization
• coverage and revisit metrics
• partialSGP4