In this paper, we explore the topic of in-space manufacturing, focusing on optimizing the logistic activities revolving around the production mix of Earth-supplied and space-debris recycled input material. We outset a baseline model for the internal and external logistic operations, putting an accent on the specific needs that out-of-atmosphere environment applications require. While the operations happening on the factory-in-space focus on efficient resource utilization, time management, and energy saving, the external ones deal with optimizing debris recovery missions. We discuss the key points of such a formulation, in terms of reliability, accuracy, and computational efficiency, that these recycling systems should strive to achieve for a successful implementation.
Although the idea of being able to see what lies beyond the sky tracks back to the beginning of
civilization [
So far, the manned space missions that have taken place over the years have been planned in such a
way that tools, repairing materials, and overall equipment need to be sent together with the
astronauts. In order to ensure the safety of the crew and increase the chance of mission success,
critical equipment is characterized by redundancy [
In 2014, a partnership between NASA and Made In Space, Inc. resulted in the Zero-G 3D Printing
initiative, where the astronauts boarding the ISS were supplied with a fused filament fabrication 3D
printer to study the capabilities of additive manufacturing in microgravity environments [
Enabling manufacturing in space is not solely related to space exploration: asteroids and near-Earth
objects contain minerals and metals, which may constitute a supply of raw materials.
While the current unfeasibility of space mining is acknowledged [
Apart from natural resources found in space, anthropical materials such as space debris are abundant.
Accumulated over decades of space missions, this debris -- particularly in low-orbit areas -- represents a potential resource pool for recycling, supporting both in-space and Earth-based manufacturing activities.
In this work, we focus on the specific problem of conceptualizing an optimization logistic system for the factory-in-space (FIS) manufacturing processes, whose raw materials input can be fed by recycled (mostly) metal debris. We divide the analysis into internal and external logistics and discuss each individually. For each of them, we provide the baseline for a Decision Support System (DSS) based on modeling a suitable optimization problem. Differently from the usual logistic system, we put an accent on the particular requirement of OOA infrastructure, mostly revolving around the critical management of resources and their remoteness from Earth.
The need to differentiate space logistics and planning from their terrestrial counterparts arises due to the distinctly challenging operational conditions posed by OOA environments.
Due to the nature of the goods being moved or the specific environment in which operations occur,
logistics has been divided into sub-fields, each characterizing specific aspects of the task to be
accomplished. For instance, the practices regarding handling dangerous material (e.g., explosives,
corrosive, or toxic substances) have been formalized in the so-called dangerous good logistics [
Internal logistics affect all the operations that occur within the boundaries of the factory, i.e., in our case, the FIS facility. An overview of (a part of) the FIS production chain is depicted in Figure 1. Let be the set of products either to be manufactured or serving as input material. Moreover, let be the set of time steps constituting the planning temporal window. We assume that consecutive time steps are evenly spaced by . We consider the step size to be constant. Note that input materials are themselves the resulting product of some manufacturing process, i.e., we consider them as contained in . This formulation considers both processes that comprise the transformation of input items and assembly steps. Let be the bill-of-materials matrix, so that indicates the number of instances of material needed for producing . Clearly, for all . The materials in might come from a recycling process or the Earth supply: let items of material be the production mix matrices, such that — indicate the amount of
— being supplied from Earth or produced from scrap recycling, respectively, . After ordering, each item will take time steps to be produced, while when supplied from Earth, it will take FIS warehouse buffer matrix, so that
time steps to reach the FIS. Let denotes all stored instances of item be the destined to produce .
Moreover, let be such that indicates the amount of instances of item ready at time , i.e., the production targets of . Therefore, we can express the buffer state as to be Note that and indicate the items supplied, taken from the warehouse, and produced to meet the production target, respectively. Equation (1) reads as follows: the buffer is composed by the buffering state at the previous time step, the added items whose production and supply were ordered steps in the past, respectively, and the withdrawn items. For , the latter corresponds to the production target; for , such a quantity corresponds to the items that are needed for producing . Ordering the production or supply of an item has its impacts in terms of resources: we denote such costs with and , respectively. For the sake of generality, we will not define them specifically; we reserve further discussion for Section 3. Moreover, each ordering decision leads to a certain amount of energy consumption: we denote with the unitary energy amount needed to carry out scrap recycling and from-Earth supply2 activities. The overall energy load the FIS power system is required to satisfy at time is denoted with , whose dynamics is described as follows, 2Although it might be reasonable to consider , we remark that external supply operations still require a minimum of power from the FIS side, e.g., items internal transportation and handling. where and is the maximum amount of deliverable energy at time . The equality in (2) indicates that the energy load comprises the amount used for handling just-supplied items and for the ones that are still under processing. Term represents a safety coefficient that limits the total energy drawn in order to guarantee a critical capacity for vital tasks. Finally, we can state the optimization problem for the internal logistic operations where the objective function to minimize in (3) represents the overall cost, in terms of resources, for both the recycling processes and from-Earth supply. 2.2.
Although some works have investigated the logistics of space transportation [
Let be the set of observable debris, i.e., the ones whose trajectory can be predicted. Let be the position of the -th debris at time . Moreover, let be the position of the debris probe at time . Its dynamics can be described by the following set of equations where equation (4) describes the position of the probe in space as a function of the velocity vector . The speed of the probe is constrained by (4b). Moreover, (4c) constraints the acceleration in terms of module and directional shift. The probe can take the -th debris if for some , i.e., if the probe intercepts it. The occurrence of this condition is indicated by the binary vector
, defined as
Note that (5) is a logical constraint that can be easily converted into a set of linear inequalities, using
well-known transformations [
3.
The presented logistic model is characterized by a considerable degree of extensibility. The limiting
condition for any extension should be the guarantee of convexity for the derived formulations. In
fact, the problems in (3) and (7) are, respectively, linear and (convex) quadratic problems. The model
presented in Section 2.1 presents the computationally worst-case scenario, i.e., the non-separability
of item quantities. Clearly, many production materials are characterized by real-valued quantities.
However, we chose to consider integer values to test the scenario, which would maximally burden
the computational infrastructure of the FIS. Several precautions can be taken in order to reduce the
computational burden, e.g. imposing that , for some . For
convexity, we refer to problems comprising convex objectives and constraints sets, apart from the
(potentially) non-convex variables domain, e.g., integral [
This work was supported in part by the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.3 - Call for tender No. 341 of March 15, 2022, of Italian Ministry of University and Research (funded by the European Union – NextGenerationEU) under the project “MICS (Circular and Sustainable Made-in-Italy)” (project code: PE00000004).
Declaration on Generative AI The author(s) have not employed any Generative AI tools.