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Optimal Placement of On-Orbit Servicing Depots for Satellite Constellations


Core Concepts
The core message of this work is to propose a novel optimization framework, called the Orbital Facility Location Problem (OFLP), to determine the optimal placement and number of on-orbit servicing depots for satellite constellations in high-altitude orbits, such as Medium Earth Orbit (MEO). The OFLP simultaneously optimizes the number of facilities, their orbital positions, and the allocation of client satellites to each facility, while accounting for the costs of establishing and operating the depots.
Abstract
This work proposes an adaptation of the Facility Location Problem (FLP) for the optimal placement of on-orbit servicing depots for satellite constellations in high-altitude orbits, such as Medium Earth Orbit (MEO). The high-altitude regime poses unique challenges, as low-thrust propulsion systems are required to conduct plane-change maneuvers between the various orbital planes of the constellation. The key aspects of the proposed Orbital Facility Location Problem (OFLP) are: Formulation as a binary linear program that optimizes the number of facilities, their orbital positions, and the allocation of client satellites to each facility. Incorporation of the costs associated with establishing and operating the depots, including the launch and orbit insertion costs, as well as the costs of the low-thrust transfers between the facilities and the client satellites. Use of a Lyapunov feedback controller (Q-Law) to compute the low-thrust transfer costs between the facilities and the clients. Expression of the objective function in terms of the Effective Mass to Low Earth Orbit (EMLEO), which provides a standardized metric to compare the costs of different depot architectures. Refinement of the facility locations in continuous space after the OFLP solution is obtained, to further optimize the depot placements. The proposed approach is applied to designing on-orbit servicing depot architectures for the Galileo and GPS constellations, demonstrating the effectiveness of the OFLP framework.
Stats
The Galileo constellation consists of 28 satellites on 4 orbital planes. The GPS constellation consists of 31 satellites on 6 orbital planes. The maximum launch mass capability of the Ariane 64 launch vehicle is 12,950 kg. The servicer vehicle's thrust is 0.1 N and its specific impulse is 3,000 s.
Quotes
"On-orbit servicing, assembly, and manufacturing (OSAM) is a key piece of technology gaining attention from both commercial and governmental players alike." "Conceptualized OSAM needs span multiple activities, including refueling, repair/refurbishment/mission extension by retrofitting additional modules, inspection, assembly, or end of life (EOL) services, typically consisting of de-orbiting or tugging to graveyard orbits."

Deeper Inquiries

How can the OFLP framework be extended to consider other types of servicing activities beyond just mass drop-off, such as robotic manipulation or assembly tasks

To extend the OFLP framework to consider other types of servicing activities beyond mass drop-off, such as robotic manipulation or assembly tasks, several modifications and additions can be made. Firstly, the cost metrics in the optimization objective would need to be adjusted to account for the specific tasks involved in these activities. For example, the cost of robotic manipulation or assembly could be based on factors like the complexity of the task, the precision required, and the time taken to complete the task. Secondly, the constraints in the OFLP formulation would need to be expanded to include the requirements and limitations of the specific servicing activities. For robotic manipulation, constraints related to the reach, dexterity, and payload capacity of the robotic manipulator would need to be incorporated. Similarly, for assembly tasks, constraints related to the compatibility of components, the assembly sequence, and the workspace requirements would need to be considered. Additionally, the facility locations and configurations optimized in the OFLP would need to be tailored to support the specific requirements of the robotic manipulation or assembly tasks. This could involve optimizing the placement of facilities to minimize travel distances for the robotic manipulator or to provide adequate space and resources for assembly tasks. Overall, extending the OFLP framework to include other types of servicing activities would require a detailed understanding of the specific tasks involved, as well as collaboration with experts in robotics, assembly, and space operations to ensure the optimization model accurately reflects the needs and constraints of these activities.

What are the potential drawbacks or limitations of the assumption that servicing needs for client satellites within the same constellation are independent and do not require coordinated visits

The assumption that servicing needs for client satellites within the same constellation are independent and do not require coordinated visits has several potential drawbacks and limitations. One major limitation is that it may not reflect the reality of operational scenarios where multiple satellites within a constellation may require servicing simultaneously or within close time frames. If servicing needs are not coordinated, there could be inefficiencies in the deployment of servicing resources, leading to increased costs, longer wait times for satellite maintenance, and potential disruptions in constellation operations. Additionally, without coordination, there may be missed opportunities to optimize servicing missions by bundling multiple client visits into a single trip, which could result in cost savings and improved operational efficiency. Furthermore, the assumption of independent servicing needs may overlook the interconnected nature of satellite operations within a constellation. For example, if one satellite experiences a critical issue that affects the entire constellation, it may be more efficient to address the issue holistically rather than on a satellite-by-satellite basis. To address these limitations, a more flexible and adaptive approach to servicing coordination could be implemented within the OFLP framework. This could involve incorporating dynamic scheduling algorithms, real-time monitoring of satellite health, and predictive maintenance strategies to optimize servicing missions and ensure timely and efficient support for all client satellites within the constellation.

How could the OFLP be adapted to address servicing needs for constellations with faster technology refresh rates, where bundling multiple client visits into a single servicing trip may be more beneficial

Adapting the OFLP to address servicing needs for constellations with faster technology refresh rates, where bundling multiple client visits into a single servicing trip may be more beneficial, would require several key adjustments to the optimization model. One approach could be to introduce a dynamic scheduling component to the OFLP that takes into account the varying needs and priorities of client satellites over time. This could involve optimizing facility locations and resource allocations based on real-time data on satellite health, maintenance requirements, and technology refresh cycles. Additionally, the OFLP could be modified to include constraints and objectives related to maximizing the efficiency of servicing missions by bundling multiple client visits into a single trip. This could involve optimizing the sequencing of client visits, considering factors such as proximity in orbital elements, similarity in servicing tasks, and overall mission duration. Furthermore, the adaptation could involve incorporating predictive maintenance strategies and proactive servicing plans into the optimization model. By anticipating future servicing needs and scheduling missions accordingly, the OFLP could help minimize downtime, reduce operational costs, and ensure the continuous functionality of the constellation. Overall, adapting the OFLP for constellations with faster technology refresh rates would require a more dynamic and responsive approach to servicing optimization, focusing on agility, adaptability, and efficiency in meeting the evolving needs of the satellite fleet.
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