Campaign-level dynamic network modelling for spaceflight logistics for the flexible path concept
Introduction
As space becomes more and more accessible through technology development, space systems design has also become increasingly complex. Thus, we need a campaign-level perspective for space systems design in addition to the conventional mission-level perspective. A campaign contains multiple missions that may or may not be for the same destinations. A design method taking the whole campaign into consideration can enable efficient and flexible space systems.
We can see a transition from mission-level design into campaign-level design in our history of space exploration. In the Apollo project, all missions used a carry-along strategy, where they transported everything they needed by themselves. This was possible due to their short mission durations (e.g., 2 weeks) and small demands in consumables and equipment. However, that type of mission-level strategy is not necessarily desirable for long-term missions. For example, the International Space Station (ISS) programme could not use a mission-level strategy because it aimed to have a human presence in space over the long term. Instead, it used a campaign-level resupply strategy, where the vehicles are launched regularly to resupply the hardware and consumables and even replace the crew.
The campaign-level strategies include uses of technologies and infrastructure considering the whole campaign. Particularly, a combination of pre-deployment, carry-along, and resupply strategies will be very important for interplanetary missions over the long term. In addition, effective uses of different technologies and infrastructures such as advanced propulsion system [1], [2], propellant depot [3], [4], [5], [6], and in-situ resource utilization (ISRU) [7], [8], [9], [10], [11] have also been proposed to be useful.
Given that background, we aim to find an efficient optimization framework to consider a campaign-level mission planning for future human and robotic space exploration. This paper particularly intends to improve and extend the most advanced work we recognize in space logistics optimization literature, which uses time-expanded generalized multi-commodity network flow (GMCNF) approach for space logistics modelling [12], [13], [14], [15]. In the previous work, dynamic linear programming (LP) based network optimization approach has been proposed to be effective [12], [13], [14], [15]. However, using continuous variables for all flows might not provide a realistic solution. For example, a crew member can be split into multiple pieces in the optimal solution. In order to avoid that situation, this paper proposes a mixed-integer linear programming (MILP) formulation. A more important contribution of this paper is about the time-expanded network. The previous work used a bi-scale time-expanded network for dynamic optimization [14], [15]. This method was useful in providing a logistics flow over time and provided a more realistic solution than static optimization, but it required a large computational resources. In this paper, a new efficient approximate method, a partially static time-expanded network, is proposed. This method combines the ideas from both static and bi-scale time-expanded network approaches, which enables significant improvement in computational effort.
The resulting efficient dynamic optimization formulation is proposed and applied to a case study containing human exploration of a near-Earth object (NEO) and Mars, related to the concept of the Flexible Path. This case study shows that a design from a campaign-level perspective would significantly improve the performance. This is the very reason why we need to pursue campaign-level space mission planning, and the proposed method can be a very strong support and evaluation tool for that purpose.
The rest of the paper is organized in the following: Section 2 shows the past research in space logistics modelling, and Section 3 shows the detailed method. Section 4 applies the proposed method to the case study. Section 5 concludes the discussions.
Section snippets
Literature review
Space logistics has been studied recently in the context of the efficient human exploration of Mars. A detailed literature review and motivation behind space logistics research can be found in the past papers [14], [15], but a few important studies are shown here.
Network modelling has been proposed to be an effective technique for efficient optimization of space logistics. It converts the space logistics map into a mathematical graph as shown in Fig. 1. Here, the nodes correspond to physical
Campaign-level dynamic space logistics modelling
This chapter summarizes the mathematics for campaign-level dynamic space logistics modelling. There are two important components in the mathematics of space logistics modelling: MILP formulation and the partially static time-expanded network. The details of these two components are shown in the next sections.
Case study: Flexible Path
This chapter applies the proposed method to a case study. The objective of the case study is (1) to show the usefulness of the newly proposed MILP-based partially static time-expanded network and (2) to evaluate the benefits of campaign-level system design compared with the mission-level system design.
Conclusions
In this paper, a campaign-level dynamic logistics network formulation for lifecycle optimization of human-robotic mission sequences is proposed and applied to the Flexible Path case study. The proposed method using a partially static time-expanded network can find the optimal combination of technologies and operations to be used at each stage of the campaign. The idea is to combine the GMCNF with a time-expanded network to model the dynamic movement of commodities and infrastructure elements
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