Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal Satellite Constellation Configuration Design: A Collection of Mixed Integer Linear Programs

David O. Williams Rogers, Dongshik Won, Dongwook Koh, Kyungwoo Hong, Hang Woon Lee

Abstract

Designing satellite constellation systems involves complex multidisciplinary optimization in which coverage serves as a primary driver of overall system cost and performance. Among the various design considerations, constellation configuration, which dictates how satellites are placed and distributed in space relative to each other, predominantly determines the resulting coverage. In constellation configuration design, coverage may be treated either as an optimization objective or as a constraint, depending on mission goals. State-of-the-art literature addresses each mission scenario on a case-by-case basis, employing distinct assumptions, modeling techniques, and solution methods. While such problem-specific approaches yield valuable insights, users often face implementation challenges when performing trade-off studies across different mission scenarios, as each scenario must be handled distinctly. In this paper, we propose a collection of five mixed-integer linear programs that are of practical significance, extensible to more complex mission narratives through additional constraints, and capable of obtaining provably optimal constellation configurations. The framework can handle various metrics and mission scenarios, such as percent coverage, average or maximum revisit times, a fixed number of satellites, spatiotemporally varying coverage requirements, and static or dynamic targets. The paper presents several case studies and comparative analyses to demonstrate the versatility of the proposed framework.

Optimal Satellite Constellation Configuration Design: A Collection of Mixed Integer Linear Programs

Abstract

Designing satellite constellation systems involves complex multidisciplinary optimization in which coverage serves as a primary driver of overall system cost and performance. Among the various design considerations, constellation configuration, which dictates how satellites are placed and distributed in space relative to each other, predominantly determines the resulting coverage. In constellation configuration design, coverage may be treated either as an optimization objective or as a constraint, depending on mission goals. State-of-the-art literature addresses each mission scenario on a case-by-case basis, employing distinct assumptions, modeling techniques, and solution methods. While such problem-specific approaches yield valuable insights, users often face implementation challenges when performing trade-off studies across different mission scenarios, as each scenario must be handled distinctly. In this paper, we propose a collection of five mixed-integer linear programs that are of practical significance, extensible to more complex mission narratives through additional constraints, and capable of obtaining provably optimal constellation configurations. The framework can handle various metrics and mission scenarios, such as percent coverage, average or maximum revisit times, a fixed number of satellites, spatiotemporally varying coverage requirements, and static or dynamic targets. The paper presents several case studies and comparative analyses to demonstrate the versatility of the proposed framework.

Paper Structure

This paper contains 21 sections, 1 theorem, 41 equations, 17 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Constellation Configuration Design Optimization Problem Formulations
  4. Notation and Definitions
  5. Common Parameters in Illustrative Examples
  6. Set Covering Location Problem
  7. Partial Set Covering Location Problem
  8. Maximal Covering Location Problem
  9. Minimal Maximum Revisit Time Problem
  10. Minimal Average Revisit Time Problem
  11. Comparative Analyses, Mix and Match, and Extensions
  12. Comparative Analyses of the Five Formulations
  13. Mix and Match
  14. Maximum Revisit Time as a Mission Requirement
  15. Average Revisit Time as a Mission Requirement
  16. ...and 6 more sections

Key Result

Theorem 1

Let $G$ be a simple graph with $n \ge 3$, then $G$ is Hamiltonian if $d(\nu) \ge n/2$ for all $\nu \in \mathcal{V}(G)$.

Figures (17)

  • Figure 1: Satellite constellation configuration design optimization flow. The proposed MILP formulations are categorized by whether coverage is treated as a requirement or an objective.
  • Figure 2: Flowchart for the optimal constellation configuration design.
  • Figure 3: SCLP formulation results.
  • Figure 4: PSCLP formulation results.
  • Figure 5: MCLP formulation results.
  • ...and 12 more figures

Theorems & Definitions (11)

  • Remark 1: PSCLP as a Generalization of SCLP
  • Remark 2: Mean Percent Coverage
  • Remark 3: MCLP with Budget Constraint
  • Remark 4: Cyclic Property
  • Remark 5: Minimizing the Sum of MRTs
  • Remark 6: Cyclic Property
  • Remark 7
  • Remark 8
  • Theorem 1: Dirac's Theorem Dirac
  • Remark 9: One-Satellite Fault-Tolerant ISL Network Topology
  • ...and 1 more