1. Jeremy Straub 1, Corey Bergsrud 2 1 Department of Computer Science, University of North Dakota 2 Department of Electrical Engineering, University of North Dakota

2. Introduction Background Solar Power Satellites and Power Transfer Spacecraft Control Orbital Services Model System Considerations Mission Scenarios Service Optimization versus Fuel Consumption Graceful Degradation Re-Transmission Service Types Control Approach Methodology Algorithm Overview Qualitative Evaluation Methodology and Performance Computational Requirements Division of Computing Conclusions and Future Work

3. A constellation of solar power spacecraft (SPS) to provide power to orbital assets or ground locations (on Earth or another planet) is proposed It requires software to determine what the most efficient configuration of the spacecraft is (to service all required clients with the required service level) and how to achieve this configuration This paper presents a brief overview of several mission concepts that involve the use of multiple spacecraft to collect and transmit solar power to other consumer spacecraft An algorithm for control of these spacecraft is presented and evaluated The orbital-serving-orbital model is expanded upon in two different directions: The option of retransmission is considered Mission concepts where ground locations are serviced (in addition to orbital ones) are also considered Introduction

4. Power Transfer & Space Solar Power The concept of wireless power transfer was developed by Hertz and Tesla and refined to support transmission at microwave frequencies the 1930s. Glaser, in 1968, documented the concept of the SPS in a patent application. In the 1970s through the 1990s, space solar power (SSP) was investigated by the United States National Aeronautics and Space Administration (NASA) and Department of Energy (DoE). CubeSats In the late 1990s, Jordi Puig-Suari and Robert Twiggs created the concept of the CubeSat, a 10 cm x 10 cm x 10 cm, 1.33 kg spacecraft form factor The CubeSat Standard has been refined through twelve successive revisions; a recently-proposed thirteenth revision introduces the ability to use some propulsion systems to the CubeSat specification. Background: Solar Power Satellites

5. The earliest spacecraft were largely teleoperated Mission needs, including latency introduced by spacecraft’s distance from Earth, have driven the development of autonomous control technologies The use of autonomy for reducing communications through the use of a beacon methodology has been demonstrated Under this approach, a spacecraft sends status updates at regular intervals It will either advise a controller that it doesn’t require assistance or advise a level of urgency of the assistance required This approach reduces routine status data transmissions Successful autonomous control has also been demonstrated for: Entry, descent and landing Docking Planning Command health assessment and remediation Control of coordination between multiple spacecraft Background: Spacecraft Control

6. Several are considered: A SPS (or SPCS) collects power throughout its orbit and sends it to one or more ground stations when it overflies them. This energy is received and injected into the regional/national power grid or used to power a particular facility Space-to-space transfer Space-to-space system adapted to service both space-based and Earth-based locations SSP to service lunar industry and exploration SSP to power to craft in Mars orbit or sites on the Martian surface The use of SSP to create a powered corridor from the Earth to Mars System Considerations: Mission Scenarios

7. A SSP utility-style provider will experience changes in its customer base from time-to-time: Customer mission commencement and conclusion Changing mission needs If multiple SSP providers exist, customers may switch from one to another, creating similar potential to re-optimize. The new optimal service approach may require a change in the spacecraft’s orbit The onboard propellant will limit the service life of the spacecraft A trade study between the benefits of moving to the new optimal configuration must be compared to the cost (the reduced ability to conduct orbit-raising or make other System Considerations: Optimization vs. Fuel

8. The SSP system will experience both planned and unplanned failures and impairments during its operations SPS units will need to be taken off line and de-orbited (or otherwise disposed of) at planned intervals SPS units may experience unanticipated failures, component failures or irregularities As a SSP utility provider will have service level agreements (SLAs) to maintain and a SSP system serving other owned craft will have a requirement to keep these craft operational Graceful degradation of the SSP constellation is required. This requirement limits the solution space Redundancy must be maintained for each point-of-service This precludes some configurations which might be optimal in terms of key metrics System Considerations: Graceful Degradation

9. In some cases it may be desirable for a SPS to receive and retransmit power. If a SPS is in eclipse and has insufficient stored power to meet the needs of a given consumer craft Another craft with sufficient stored power or current generation capability could transmit this power to the SPS unit with a line-of-transmission to the consumer craft. Retransmission is expensive: It ties up two SPSs Incurs more loss to inefficiency than a single collector and transmitter. Given this: The ability for retransmission should be considered when planning A significant penalty (commensurate with the undesirability of this approach) should be incorporated System Considerations: Re-Transmission

10. A critical consideration in control decision making will be whether the SSP system is serving only orbital consumers or both orbital and ground consumers In the case of the later, the relative priority of the two may bear consideration For planning, the configuration to serve the ground may be different (particularly if SPSs are serving spacecraft in orbit above them) Also, some SPS units may be better equipped (due to collection capabilities, antenna configuration, etc.) to serve ground locations than others. System Considerations: Orbital vs. Orbital & Ground

11. The basic premise of the control algorithm proposed is that it will operate on the basis of decomposing a value cost comparison function. Several elements must be considered: Value cannot simply be divided by the cost and the one with the highest resulting value selected It may be desirable to generate more value, even though a higher- than-proportionate level of cost is incurred Because of the fixed fuel level, incurring fuel-cost at present may prevent other actions in the future. The need to maximize lifetime spacecraft value Each time propellant is used to change the spacecraft’s orbit this positions the spacecraft to take advantage of a current opportunity to generate value. May remove the opportunity to generate value available from the previous orbit Limits Lifetime Need to predict the needs and locations of future customers Weightings between all of the different factors for consideration Need to Act like a Responsible Utility Control Approach: Methodology

12. Determine: The power and propellant consumption of the proposed maneuver Its impact on goodwill The revenue it will generated Projected value of this maneuver for generating future revenue. All of these are computationally intensive. Cost Metric Determined from the power and propellant consumption as well as the goodwill impact Present value of future revenue must now be determined The value-metric value can be determined The tradeoff result value can be determined In the version of the algorithm shown, this is compared to a cutoff value based on a revenue-need projection This value could also be used to rank, for selection purposes, multiple prospective maneuver options. Control Approach: Algorithm

13. A limited qualitative evaluation of the proposed algorithm is now conducted: First the performance of the algorithm and methodology are assessed. Next, computational requirements are considered. Finally, the impact of the proposed approach on the prospective division of computing is considered. Qualitative Evaluation

14. A quantitative characterization of the performance of the proposed algorithm will not be possible until all of the components have been developed Current analysis has focused on eliminating duplicate calculations E.g., Goodwill impact, though listed in two separate categories, has been calculated and used for both the cost and value calculations Revenue need cutoff value serves as a heuristic to prevent the need to store and compare multiple solutions over time for decision making Model and weighting value heuristics have also been created and stored to prevent the need to repeatedly calculate these values Significant storage will exist onboard (relative to storage needs). Because of this, a focus on calculating, storing and updating (possibly out-of- process) a value will be utilized, instead of repetitively re-calculating the value. This trades a reduction in processing time for a reduction in accuracy. The frequency of recalculating various values will be a subject for future study. Qualitative Evaluation: Algorithm/Methodology Performance

15. A level of computational resources commensurate with a typical 6U CubeSat has been presumed. Current assessment is based on a projected configuration of two GumStix units; however, this may need to be refined over time as greater certainty regarding computational needs exists. Under any model, one processor would serve as a primary node and have the ability to control the power of the other nodes to conserve electrical power when their capabilities are not required. Qualitative Evaluation: Computational Requirements

16. The proposed algorithm is designed to be highly parallelizable. Initially, at least five separate threads can be utilized (potentially on different processors, should the capability exist). Some of these calculations may be further parallelizable, allowing even greater levels of parallel processing. Note that these parallelized items are the most computationally intensive. Once these are done, the number of prospective concurrent threads reduces to two (one for cost and one for value) while the metrics are calculated. Once this is done, a single thread combines these two metrics and performs decision making. Given the generally limited computational requirements of the proposed SPCS, it is likely that this parallelization (for the initial task set) will exceed the number of physical onboard processors. Qualitative Evaluation: Division of Computing

17. Preliminary work on an algorithm for the control of a 6U CubeSat SPS as part of a SSP system has been presented Five relevant factors that shape system design have been presented and a control algorithm and methodology, responsive to these design criteria has been presented A qualitative assessment of this prospective algorithm has been conducted and performance, computational requirements and its impact on the prospective division of computing have been assessed From the foregoing, it is not possible to assert that the proposed algorithm will adequately serve system needs; however, the qualitative evaluation suggests that the algorithm is responsive and that it (if not now serving needs) could be adapted to do so. Work on the development of this algorithm is ongoing. Future work will involve continued work on and completion of the designs for a 6U SPCS. The potential to use a larger CubeSat form factor (such as 12U) is also under consideration. The finalized algorithm will need to be adapted to the specifics of the final system and tested through simulation and, subsequently, on-orbit. Conclusions & Future Work

18. Small satellite development work at the University of North Dakota is or has been supported by the North Dakota Space Grant Consortium, North Dakota NASA EPSCoR, the University of North Dakota Faculty Research Seed Money Committee, North Dakota EPSCoR (NSF Grant # EPS- 814442), the Department of Computer Science, the John D. Odegard School of Aerospace Sciences and the National Aeronautics and Space Administration. Jeremy's work on the autonomous control of spacecraft and other robots has been supported by a Grant-In-Aid of Research from Sigma Xi, The Scientific Research Society, North Dakota EPSCoR (NSF # EPS-814442) and a Summer Doctoral Fellowship from University of North Dakota School of Graduate Studies. Presentation of this paper at the 64 th International Astronautical Congress has been supported by the United States National Aeronautics and Space Administration.