Modeling and Optimizing Space Networks for Improved Communication Capacity by Sara C. Spangelo A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Aerospace Engineering) in the University of Michigan 2013 Doctoral Committee: Assistant Professor James W. Cutler, Chair Associate Professor Ella M. Atkins Professor Dennis S. Bernstein Associate Professor Amy E. M. Cohn ©Sara C. Spangelo 2013 My family and friends. ii TABLE OF CONTENTS Dedication ....................................... ii List of Figures ..................................... iv List of Tables ...................................... v List of Appendices ................................... vi List of Abbreviations ................................. vii Abstract ......................................... viii Chapter 1 Introduction ..................................... 1 1.1 Emerging Trends in Satellite Communication...............2 1.1.1 Small Satellites: Trends and Challenges..............3 1.1.2 Federated Ground Station Networks................4 1.1.3 Protocol Modernization......................6 1.1.4 Model-Based Systems Engineering................6 1.1.5 Summary of Emerging Trends...................8 1.2 Literature Review and Areas for Extension.................8 1.2.1 Space Communication Modeling and Simulation.........8 1.2.2 Spacecraft Modeling and Simulation................ 10 1.2.3 Scheduling............................. 12 1.2.4 Frameworks and Architectures for Space Operations....... 19 1.3 Thesis Contributions............................ 23 1.4 Intellectual Innovations........................... 25 1.4.1 Spacecraft Modeling Framework as Optimization Formulation.. 25 1.4.2 Coupling Operational Planning with Design............ 27 1.5 Thesis Outline................................ 28 2 Model and Simulation Framework and Applications .............. 29 2.1 Operational Modeling Framework..................... 29 2.1.1 Model Elements.......................... 30 2.1.2 Framework Formulation...................... 30 2.1.3 Block Diagram Representation.................. 32 2.2 Framework Application to Communication-Focused Model........ 33 iii 2.2.1 Definitions............................. 33 2.2.2 Ground Station Network Model.................. 36 2.2.3 Communication-Focused Spacecraft Model............ 41 2.3 Data Sets and Simulator........................... 47 2.3.1 Satellite and Ground Station Data................. 47 2.3.2 Simulator Description....................... 51 2.4 Application of Model and Simulator.................... 52 2.5 Summary.................................. 53 3 Constraint-Based Capacity Assessment ...................... 58 3.1 Network Constraints............................ 59 3.1.1 Orbit and Ground Station Coverage................ 59 3.1.2 Availability of Download Time.................. 63 3.2 Energy Constraints............................. 77 3.3 Comparison to Download Requirements.................. 78 3.4 Summary.................................. 81 4 Deterministic Optimization: Formulation and Results .............. 84 4.1 Problem Description and System Dynamics................ 85 4.1.1 Energy Dynamics.......................... 87 4.1.2 Data Dynamics........................... 88 4.1.3 System Optimization........................ 88 4.2 Problem Formulation............................ 89 4.2.1 Notation.............................. 89 4.2.2 Under-Constrained Formulation (UCF).............. 91 4.3 A Special Case: Linear Dynamics..................... 92 4.3.1 Real-World Computational Experiments.............. 94 4.3.2 General Case Computational Experiments............. 98 4.3.3 Non-Integral Solutions Resulting in Branching.......... 102 4.4 Applications to Non-Linear Dynamics................... 107 4.4.1 Algorithm for Solving Non-Linear SMSPs ............. 110 4.4.2 Special Case: Piece-wise Linear Dynamics............ 111 4.5 Summary.................................. 119 5 Deterministic Optimization: Extensions and Applications ............ 121 5.1 Generalized Under-Constrained Formulation (GUCF)........... 122 5.1.1 Notation.............................. 122 5.1.2 Formulation............................. 124 5.2 Single Operational Satellite Problem (SOSP)................ 126 5.2.1 Problem Description........................ 126 5.2.2 Problem Formulation........................ 127 5.3 Diverse LEO CubeSat Missions Application................ 128 5.3.1 Optimal Results for Realistic CubeSat Missions.......... 130 5.3.2 Sensitivity to Deterministic Problem Parameters......... 131 5.4 Interplanetary Mission Application..................... 138 iv 5.4.1 Mission Description and Proposed Communication Architectures 138 5.4.2 Mission Assessment........................ 142 5.4.3 Optimization Results........................ 145 5.5 Summary.................................. 150 6 Sensitivity to Stochasticity in Download Efficiency ................ 155 6.1 Scheduling and Collecting Download Efficiency Data........... 157 6.2 Modeling Download Efficiency Data.................... 160 6.3 Summary and Future Directions...................... 165 7 Conclusions and Future Work ........................... 167 7.1 Conclusions................................. 167 7.2 Future Work................................. 169 7.2.1 Verification and Validation (V&V)................. 169 7.2.2 Operational Planning for Complex Spacecraft........... 170 7.2.3 Applications to Multi-Satellite Missions.............. 171 7.2.4 Stochasticity in Operational Scheduling Problem......... 172 7.2.5 Coupled Vehicle and Operations Optimization.......... 173 7.2.6 Applications to Interplanetary Missions.............. 173 7.2.7 Summary.............................. 175 Appendices ....................................... 176 Bibliography ...................................... 184 v LIST OF FIGURES 1.1 Small satellite launch trends demonstrating a growing number of launched and projected missions................................3 2.1 A generic representation of the subsystem function Zs;j = gs;j(Ys;j; U; Ps;j; t) for s = 1 and j = 1; 2; 3. All values are time dependent............. 32 2.2 Elements and dynamics of the system model represented with a conventional feedback control loop diagram. The non-italicized labels are the conventional elements of a control feedback loop. The italicized labels are the elements of the modeling framework............................. 34 2.3 Schematic with increasingly higher fidelity ground station models within smaller ellipses, where the ellipse area represents network capacity. Note this diagram is not to scale.................................... 41 2.4 Global locations and projected visibility cones of stations in N2 and N3 as- suming a satellite altitude of 500 km and an elevation mask of 0◦........ 50 2.5 Time histories of on-board stored energy and total data downloaded for an in- stance of the RAX-2 mission with psol = 5:5 W and maximum eclipse duration of 35 % of orbit.................................. 54 2.6 Time histories of on-board stored energy and total data downloaded for an instance of the RAX-2 mission with psol = 3 W and zero eclipse duration (all 97 minutes of orbital period are in sunlight)................... 55 2.7 Data downloaded for variable solar power collection values (psol) for an in- stance of the RAX-2 mission. Results are compared when there is maximum eclipse, with an eclipse fraction of 0.35 (34 minutes of a 97 minute orbital period), and zero eclipse (always in sunlight). Note data is not plotted for infeasible mission scenarios........................... 56 3.1 Percentage of satellite passes which have ground station coverage for different space node inclinations and ground node latitudes with a ground node mini- mum communication elevation of 0◦....................... 61 3.2 Percentage of satellite passes which have ground station coverage for different space node inclinations and ground node latitudes with a ground node mini- mum communication elevation of 10◦....................... 62 3.3 Earth coverage of latitude ranges for different numbers of ground stations (Ngs) and satellite inclinations assuming a circular orbit at an altitude of 500 km. See Figure 2.4 for the locations and footprints of the stations........ 64 vi 3.4 Average daily access time as a function of satellite inclination and ground station latitude for 650 km altitude circular orbits using SGP4 propagation method in STK................................... 66 3.5 Communication capacity as a function of diverse orbital properties and a range of ground network sizes for a one year simulation................ 67 3.6 CubeSat survey of existing ground stations [1].................. 69 3.7 Effects of variation in AFSCN ground station latitudes from Table 3.2 on net- work capacity for the AeroCube 3 satellite with 99◦ inclination and 715 km altitude orbit.................................... 70 3.8 2009 Minotaur-1 launched CubeSat group relative to Ann Arbor ground sta- tion (42:27◦N; 83:76◦W ) following epoch, the time the satellite emerges from the launch vehicle................................. 72 3.9 Total network capacity for 2009 Minotaur-1 launched CubeSat group relative to entire AFSCN with 15 antennas........................ 74 3.10 Effects of growing family of satellites on network utilization for a fixed ground station network. The CubeSats are launched into 400 to 800 km random orbits, and access time is computed relative to the 15 ground station antennas in the AFSCN. Excess access time is the time where