Autonomous Constellation Fault Monitoring with Inter-satellite Links: A Rigidity-Based Approach

TL;DR

This paper introduces a rigidity-based fault detection framework for lunar satellite constellations using inter-satellite links, enabling fault detection without ground-based stations through graph theory and matrix analysis.

Contribution

It presents a novel graph-theoretic approach leveraging vertex redundantly rigid graphs and GCEDM singular values for fault detection in lunar satellite networks.

Findings

Effective fault detection demonstrated in lunar constellation simulations

Method does not require precise ephemeris or ground stations

Applicable to various satellite configurations around the Moon

Abstract

To address the need for robust positioning, navigation, and timing services in lunar environments, this paper proposes a novel fault detection framework for satellite constellations using inter-satellite ranging (ISR). Traditionally, navigation satellites can depend on a robust network of ground-based stations for fault monitoring. However, due to cost constraints, a comprehensive ground segment on the lunar surface is impractical for lunar constellations. Our approach leverages vertex redundantly rigid graphs to detect faults without relying on precise ephemeris. We model satellite constellations as graphs where satellites are vertices and inter-satellite links are edges. We identify faults through the singular values of the geometric-centered Euclidean distance matrix (GCEDM) of 2-vertex redundantly rigid sub-graphs. The proposed method is validated through simulations of constellations around the Moon, demonstrating its effectiveness in various configurations. This research contributes to the reliable operation of satellite constellations for future lunar exploration missions.