Advanced Automation for Space Missions/Chapter 5.3

5.3 Feasibility

The design and construction of a fully self-replicating factory system will be a tremendously complicated and difficult task. It may also be fairly expensive in the near-term. Before embarking upon such an ambitious undertaking it must first be shown that machine self-replication and growth is a fundamentally feasible goal.

5.3.1 Concept Credibility

The plausibility of the theoretical notion of self-replicating machines already has been reviewed at length (see sec. 5.2). It remains only to demonstrate concept credibility in an engineering sense (Bradley, 1980, unpublished memorandum, and see appendix 5A; Cliff, 1981; Freitas, 1980a; von Tiesenhausen and Darbro, 1980) - that is, is it credible to consider building real physical machines able to replicate themselves?

The credibility of any design proposed for such a machine or machine system depends first and foremost upon whether that design is consistent with reasonably foreseeable automation and materials processing technologies. These technologies need not necessarily be well established or even state-of-the-art, but should at least be conceivable in the context of a dedicated R&D effort spanning the next two decades. It is interesting to note that computer programs capable of self-replication have been written in many different programming languages (Burger et al., 1980; Hay, 1980), and that simple physical machines able to replicate themselves in highly specialized environments have already been designed and constructed (Jacobson, 1958; Morowitz, 1959; Penrose,1959).

Another major requirement for concept credibility is a plausible system configuration. Proposed designs for selfreplicating systems (SRS) must be sufficiently detailed to permit the generation of work breakdown structures, subsystem operational flowcharts, mass and energy throughput calculations, and at least preliminary closure (see sec.5.3.6) analyses.

A related requirement is plausible mission scenarios. Research and development costs for the proposed design should be many orders of magnitude less than the Gross National Product. The mission must not require launch and support facilities which cannot or will not be available in the next two or three decades. The mission must entail reasonable flight times, system lifetimes, growth rates, production rates, and so forth. The problems of reliability and repair should be addressed.

The final requirement for concept credibility is positive societal impact. A given SRS design must be economically, politically, and socially feasible, or else it may never be translated into reality even if the technology to do so exists. A general discussion of the implications of replicating systems appears in section 5.5, but the team has arrived at no firm conclusions regarding concept feasibility in this area. More research is clearly required.

5.3.2 Concept Definition

In order to demonstrate SRS concept credibility, specific system designs and mission scenarios must be subjected to a detailed feasibility analysis. The first step in this process is to conceptualize the notion of replicating systems in as broad an engineering context as possible. Many kinds of replicating machine systems have been proposed and considered during the course of the study. Some of these place emphasis on different types of behavior than others.

Consider a "unit machine" which is the automata equivalent of the atom in chemistry or the cell in biology - the smallest working system able to execute a desired function and which cannot be further subdivided without causing loss of that function. The unit machine may be comprised of a number of subunits, say, A, B, C, and D. These subunits may be visualized in terms of structural descriptions (girders, gearboxes, generators), functional descriptions (materials processing, parts fabrication, mining, parts assembly), or any other complete subset-level descriptions of the entire system.

SRS may be capable of at least five broad classes of machine behavior:

Production - Generation of useful output from useful input. The unit machine remains unchanged in the process. This is a "primitive" behavior exhibited by all working machines including replicating systems.

Replication - Complete manufacture of a physical copy of the original unit machine, by the unit machine.

Growth - Increase in mass of the original unit machine by its own actions, retaining the physical integrity of the original design.

Evolution - Increase in complexity of structure or function of the unit machine, by adding to, subtracting from, or changing the character of existing system subunits.

Repair - Any operation performed by a unit machine upon itself, which does not alter unit population, designed unit mass, or unit complexity. Includes reconstruction, reconfiguration, or replacement of existing subunits.

These five basic classes of SRS behavior are illustrated in figure 5.5.

Figure 5.5 - Five basic classes of SRS behavior.

Replicating systems, in principle, may be designed which can exhibit any or all of these machine behaviors. In actual practice, however, it is likely that a given SRS format will emphasize one or more kinds of behaviors even if capable of displaying all of them. The team has considered two specific replicating systems designs in some detail. The first (cf. von Tiesenhausen and Darbro, 1980), which may be characterized as a unit replication system, is described in section 5.3.3. The second (cf. Freitas, 1980a; Freitas and Zachary, 1981), which can be characterized as a unit growth system, is outlined in section 5.3.4. The team decided to concentrate on the possibility of fully autonomous or "unmanned" SRS, both because these are more challenging from a technical standpoint than either manned or teleoperated systems and also because the latter has already been detailed to some degree elsewhere in this report (see chap. 4).

5.3.3 Unit Replication: A Self-Replicating System Design

The SRS design for unit replication is intended to be a fully autonomous, general-purpose self-replicating factory to be deployed on the surface of planetary bodies or moons. The anatomy of an SRS is defined by two end conditions: (1) the type and quantity of products required within a certain time, and (2) the available material needed to manufacture these products as well as the SRS itself.

There are four major subsystems which comprise each SRS unit, as shown in figure 5.6. First, a materials processing subsystem acquires raw materials from the environment and prepares industrial feedstock from these substances. Second, a parts production subsystem uses the feedstock to make machines or other parts. At this point SRS output may take two forms. Parts may flow to the universal constructor subsystem, where they are used to construct a new SRS (replication). Or, parts may flow to a production facility subsystem to be made into commercially useful products. The SRS also has a number of other important but subsidiary subsystems, including a materials depot, parts depots, product depot, control and command, and an energy system.

Figure 5.6 - Functional schematic of unit replication SRS.

The work breakdown structure given in figure 5.7 lists all SRS elements studied, and each is briefly described below.

Figure 5.7 - Work breakdown structure for SRS.

Materials processing and feedstock production. In this system, raw materials are gathered by strip or deep milling. They are then analyzed, separated, and processed into industrial feedstock components such as sheets, bars, ingots, castings, and so forth, which are laid out and stored in the materials depot. The processing subsystem has a high degree of autonomy including self-maintenance and repair. It is linked to a central supervisory control system (see below).

The materials processing subsystem is shown schematically in figure 5.8.

Figure 5.8 - SRS materials processing subsystem.

Materials depot. The materials depot collects and deposits in proper storage locations the various feedstock categories according to a predetermined plan. This plan ensures that the subsequent fabrication of parts proceeds in the most efficient and expeditious manner possible. The depot also serves as a buffer during interruptions in normal operations caused by failures in either the materials processing subsystem (depot input) or in the parts production subsystem (at depot output).

Parts production plant. The parts production plant selects and transports industrial feedstock from the materials depot into the plant, then fabricates all parts required for SRS production or replication activities. Finished parts are stored in the production parts and the replication parts depots, respectively. The parts production plant is highly automated in materials transport and in distribution, production, control, and subassembly operations.

The parts production plant subsystem is shown schematically in figure 5.9.

Figure 5.9 - SRS parts production plant subsystem.

Parts depots. There are two parts depots in the present design. These are called the production parts depot and the replication parts depot.

Parts are stored in the production parts depot exclusively for use in the manufacture of useful products in the production facility. If certain raw materials other than parts and subassemblies are required for production, these materials are simply passed from the materials depot through the parts production plant unchanged. The parts production depot also acts as a buffer during interruptions in normal operations caused by temporary failures in either the parts production plant or the production facility.

Parts and subassemblies are stored in the replication parts depot exclusively for use in the replication of complete SRS units. Storage is in lots earmarked for specific facility construction sites. The replication parts depot also serves as buffer during interruptions in parts production plant or universal constructor operations.

Production facility. The production facility manufactures the desired products. Parts and subassemblies are picked up at the production parts depot and are transported to the production facility to be assembled into specific useful products. Finished products are then stored in the products depot. Ultimately these are collected by the product retrieval system for outshipment.

Universal constructor. The universal constructor manufactures complete SRS units which are exact duplicates of the original system. Each replica can then, in turn, construct more replicas of itself, and so on. The universal constructor retains overall control and command responsibility for its own SRS as well as its replicas, until the control and command functions have also been replicated and transferred to the replicas. These functions can be overridden at any time by external means.

The universal constructor subsystem consists of two major, separate elements - the stationary universal constructor (fig. 5.10) and the mobile universal constructors (fig. 5.11). This composite subsystem must successfully perform a number of fundamental tasks, including receiving, sorting, loading, and transporting parts and subassemblies; assembling, constructing, installing, integrating, and testing SRS systems; starting and controlling SRS operations; and copying and transferring instructions between system components.

Figure 5.10 - SRS stationary universal constructor.

Figure 5.11 - SRS mobile universal constructors.

Products depot. The outputs of the production facility are stored in the products depot, ready for retrieval. Major hardware components are neatly stacked for ready access by the product retrieval system. Consumables such as elemental oxygen are stored in reusable containers that are returned empty to the production facility. The products depot also serves as a buffer against variable output and retrieval rates.

Product retrieval system. The product retrieval system collects the outputs of all SRS units in an "SRS field" and carries them to an outside distribution point for immediate use or for subsequent outshipment. The dashed lines in figure 5.11 indicate one possible solution to this problem in a typical SRS field. Other solutions are possible - careful consideration must be given to SRS field configuration to arrive at an optimum product retrieval system design.

Command and control systems. The master control and command system, located within the stationary universal constructor, is programmed to supervise the total SRS operation and to communicate both with the peripheral controls of the mobile universal constructors during the selfreplication phase and with the replicated stationary universal constructor during the transfer of command and control for the operation of the new SRS unit.

The master control and command system operates its own SRS unit through individual communication links which address the local control and command systems of individual SRS elements. In this way the master control and command system supervises the condition and operations of its own system elements, from materials acquisition through end product retrieval.

Energy system. The power requirements for the present design may be in gigawatt range. Hence, a single energy source (such as a nuclear power plant) would be excessively massive, and would be difficult to replicate in any case. This leaves solar energy as the lone viable alternative. Daylight options include: (1) central photovoltaic with a ground cable network, (2) distributed photovoltaic with local distribution system, (3) individual photovoltaic, and (4) satellite power system, with microwave or laser power transmission to central, local, or individual receivers. Nighttime power options include MHD, thermionics, or turbogenerators using fuel generated with excess capacity during daytime. Oxygen plus aluminum, magnesium, or calcium could be used for fuel. A 155to efficient central silicon photovoltaic power station has been assumed in the reference design, with an output of tens of gigawatts and a size on the order of tens of square kilometers.

Each SRS produces, in addition to its scheduled line of regular products, a part of the photovoltaic energy system equal to the energy needs of its replicas. These are retrieved along with the regular products by the product retrieval system and are assembled on-site to increase energy system capacity according to demand during the self-replication phase.

SRS deployment and expansion. A complete SRS factory unit, erected on the surface of the Moon, might appear as illustrated in figure 5.12.

Figure 5.12 - Self-replicating lunar factory.

As a unit replication scheme, the multiplication of SRS units proceeds from a single primary system to many hundreds of replica systems. This expansion must be carefully planned to reach the desired factory output capacity without running out of space and materials. Figure 5.13 shows one possible detailed growth plan for the geometry of an SRS field. In this plan, each SRS constructs just three replicas, simultaneously, then abandons replication and goes into full production of useful output. After the three generations depicted, an SRS field factory network 40 units strong is busy manufacturing products for outshipment.

Figure 5.13 - Possible growth plan with simultaneous replica construction, suitable for geometry of an SRS field.

The routes taken by mobile universal constructors are shown as solid lines, the product retrieval routes as dashed lines.

Figure 5.14 shows another possible expansion geometry. Again, each SRS constructs just three replicas, but sequentially rather than simultaneously. The end result is a field of 326 individual units after nine cycles of replication. Output is collected by the product retrieval system and taken to an end product assembly/collection system where end products undergo final assembly and other operations preparatory to outshipment. A more detailed discussion of expansion scenarios for SRS fields may be found in von Tiesenhausen and Darbro (1980).

Figure 5.14 - SRS growth plan with sequential replication.

Proposed development and demonstration scenario. It is proposed that the practical difficulties of machine replication should be confronted directly and promptly by a dedicated development and demonstration program having four distinct phases.

In Phase A of the development scenario, a robot manipulator will be programmed to construct a duplicate of itself from supplied parts and subassemblies. The original robot then makes a copy of its own operating program and inserts this into the replica, then turns it on, thus completing the duplication process (see appendix 5J). To complete Phase A; the replica must construct a replica of itself, repeating in every way the actions of the original robot. The rationale for the second construction, called the Fertility Test, is to demonstrate that the capacity for self-replication has in fact been transmitted from parent machine to offspring.

In Phase B of the development and demonstration scenario, the robot manipulator will be supplied with numerous additional parts so it can assemble objects of interest other than replicas of itself. This is intended to show that the system is able to construct useful products in addition to the line of robot duplicates.

In Phase C the manipulator system is still required to construct replicas and useful products. However, the robot now will be supplied only with industrial feedstock such as metal ingots, bars, and sheets, and must fabricate all necessary parts and subassemblies on its own. Successful completion of Phase C is expected to be much more difficult than the two earlier phases. The reason is that the parts fabrication machines must themselves be constructed by the robot manipulator and, in addition, all parts and subassemblies comprising the newly introduced fabrication machines must also be made available to the manipulator. Fabricator machines thus must be programmed to make not only the parts required for robot manipulators and useful products, but also their own parts and subassemblies as well. This raises the issue of parts closure, a matter which is discussed in section 5.3.6.

In Phase D, the system developed in the previous phase is retained with the exception that only minerals, ores, and soils of the kind naturally occurring on terrestrial or lunar surfaces are provided. In addition to all Phase C capabilities, the Phase D system must be able to prepare industrial feedstock for input to the fabrication machines. Successful completion of Phase D is expected to be the most difficult of all because, in addition to the parts closure problem represented by the addition of materials processing machines, all chemical elements, process chemicals, and alloys necessary for system construction and operation must be extracted and prepared by the materials processing machines. This raises the issue of materials closure (see also sec. 5.3.6). The completion of Phase D will yield an automatic manufacturing facility which, beginning with "natural" substrate, can replicate itself.

This progressive development of a replicating factory will serve to verify concept feasibility, clarify the functional requirements of such a system, and identify specific technological problem areas where additional research in automation and robotics is needed. A minimum demonstration program should be designed to gain engineering under standing, confidence, and hands-on experience in the design A and operation of replicating systems. (See sec. 5.6.) The question of when the results of an Earth-based development and demonstration project should be translated to lunar requirements, designs, and construction remains open. On the one hand, it may be deemed most practical to complete Phase D before attempting a translation to a design better suited to a lunar or orbital environment. On the other hand, major system components for a lunar facility undoubtedly could be undertaken profitably earlier in concert with Phase C and D development. The proposed development and demonstration scenario is described in greater detail in von Tiesenhausen and Darbro (1980).

5.3.4 Unit Growth: A Growing Lunar Manufacturing Facility

The Lunar Manufacturing Facility (LMF) demonstrating SRS unit growth is intended as a fully automatic general purpose factory which expands to some predetermined adult size starting from a relatively tiny "seed" initially deposited on the lunar surface. This seed, once deployed on the Moon, is circular in shape, thus providing the smallest possible perimeter/surface area ratio and minimizing interior transport distances. Expansion is radially outward with an accelerating radius during the growth phase. Original seed mass is 100 tons.

The replicating LMF design encompasses eight fundamental subsystems. Three subsystems are external to the main factory (transponder network, paving, and mining robots). The LMF platform is divided into two identical halves, each comprised of three major production subsystems: (1) the chemical processing sector accepts raw lunar materials, extracts needed elements, and prepares process chemicals and refractories for factory use; (2) the fabrication sector converts these substances into manufactured parts, tools, and electronics components; and (3) the assembly sector, which assembles fabricated parts into complex working machines or useful products of any conceivable design. (Each sector must grow at the same relative rate for uniform and efficient perimeter expansion.) Computer facilities and the energy plant are the two remaining major subsystems. (See fig. 5.15.)

Figure 5.15 - Functional schematic of unit growth SRS.

Transponder network. A transponder network operating in the gigahertz range assists mobile LMF robots in accurately fixing their position relative to the main factory complex while they are away from it. The network, described briefly in appendix 5B, is comprised of a number of navigation and communication relay stations set up in a well defined regular grid pattern around the initial seed and the growing LMF complex.

Paving robots. In order to secure a firm foundation upon which to erect seed (and later LMF) machinery, a platform of adjoining flat cast basalt slabs is required in the baseline design. A team of five paving robots lays down this foundation in a regular checkerboard pattern, using focused solar energy to melt pregraded lunar soil in situ. (See app. 5C.)

Mining robots. As described in appendix SD, LMF mining robots perform six distinct functions in normal operation: (1) strip mining, (2) hauling, (3) landfilling, (4) grading, (5) cellar-digging, and (6) towing. Lunar soil is strip-mined in a circular pit surrounding the growing LMF. This material is hauled back to the factory for processing, after which the unused slag is returned to the inside edge of the annular pit and used for landfill which may later be paved over to permit additional LMF radial expansion. Paving operations require a well graded surface, and cellar digging is necessary so that the LMF computer may be partially buried a short distance beneath the surface to afford better protection from potentially disabling radiation and particle impacts. Towing is needed for general surface transport and rescue operations to be performed by the mining robots. The robot design selected is a modified front loader with combination roll-back bucket/dozer blade and a capacity for aft attachments including a grading blade, towing platform, and a tow bar.

Chemical processing sectors. Mining robots deliver raw lunar soil strip-mined at the pit into large input hoppers arranged along the edge of entry corridors leading into the chemical processing sectors in either half of the LMF. This material is electrophoretically separated (Dunning and Snyder, 1981; see sec. 4.2.2) into pure minerals or workable mixtures of minerals, then processed using the HF acid-leach method (Arnold et al., 1981; Waldron et al., 1979) and other specialized techniques to recover volatiles, refractories, metals, and nonmetallic elements. Useless residue and wastes are collected in large output hoppers for landfill. Buffer storage of materials output is on site. Chemical processing operations are shown schematically in figure 5.16, and are detailed in appendix SE.

Figure 5.16 - LMF chemical processing sector: Operations.

Fabrication sectors. The LMF fabrication sector outlined in appendix 5F is an integrated system for the production of finished aluminum or magnesium parts, wire stock, cast basalt parts, iron or steel parts, refractories, and electronics parts. Excepting electronics (Zachary, 1981) there are two major subsystems: (1) the casting subsystem, consisting of a casting robot to make molds, mixing and alloying furnaces for basalt and metals, and automatic molding machines to manufacture parts to low tolerance using the molds and alloys prepared; and (2) the laser machining and finishing subsystem, which performs final cutting and machining of various complex or very-close-tolerance parts. The basic operational flowchart for parts fabrication is shown in figure 5.17.

Figure 5.17 - LMF parts fabrication sector: Operations.

Assembly sectors. Finished parts flow into the automated assembly system warehouse, where they are stored and retrieved by warehouse robots as required. This subsystem provides a buffer against system slowdowns or temporary interruptions in service during unforeseen circumstances. The automated assembly subsystem requisitions necessary parts from the warehouse and fits them together to make subassemblies which are inspected for structural and functional integrity. Subassemblies may be returned to the warehouse for storage, or passed to the mobile assembly and repair robots for transport to the LMF perimeter, either for internal repairs or to be incorporated into working machines and automated subsystems which themselves may contribute to further growth. The basic operational flowchart for SRS parts assembly is shown in figure 5.18, and a more detailed presentation may be found in appendix 5G.

Figure 5.18 - LMF assembly sector: Operations.

Computer control and communications. The seed computers must be capable of deploying and operating a highly complex, completely autonomous factory system. The original computer must erect an automated production facility, and must be expandable in- order to retain control as the LMF grows to its full "adult" size. The computer control subsystem coordinates all aspects of production, scheduling, operations, repairs, inspections, maintenance, and reporting, and must stand ready to respond instantly to emergencies and other unexpected events. Computer control is nominally located at the hub of the expanding LMF disk, and commands in hierarchical fashion a distributed information processing system with sector computers at each node and sector subsystems at the next hierarchical level of control. Communications channels include the transponder network, direct data bus links, and E2ROM messenger chips (firmware) for large data block transfers.

Using ideas borrowed from current industrial practice, top-down structured programming, and biology, Cliff (1981) has devised a system architecture which could perform automated design, fabrication, and repair of complex systems. This architecture, presented in appendix SH, is amenable to straightforward mathematical analysis and should be a highly useful component of the proposed lunar SRS. Further work in this area should probably include a survey of industrial systems management techniques (Carson, 1959) and the theory of control and analysis of large-scale systems (Sandell et al., 1978).

In a practical sense, it is quite possible to imagine the lunar SRS operating nonautonomously (Johnsen, 1972). For instance, the in situ computer could be used simply as a teleoperation-management system for operations controlled directly by Earth-based workers. Material factory replication would proceed, but information necessary to accomplish this would be supplied from outside. An intermediate alternative would permit the on-site computer to handle mundane tasks and normal functions with humans retaining a higher-level supervisory role. Yet another possibility is that people might actually inhabit the machine factory and help it reproduce - manned machine economies can also self-replicate.

Solar canopy. The solar canopy is a "roof" of photovoltaic solar cells, suspended on a relatively flimsy support web of wires, crossbeams and columns perhaps 3-4 m above ground level. The canopy covers the entire LMF platform area and expands outward as the rest of the facility grows. The solar canopy and power grid provide all electrical power for LMF systems. Canopy components may be stationary or may track solar motions using heliostats if greater eff1ciency is required. A further discussion of canopy design and rationale may be found in appendix 5I.

Mass, power, and information requirements. Seed subsystem masses and power requirements scale according to the total system mass assumed. SRS can be reduced indefinitely in size until its components begin to scale nonlinearly. Once this physical or technological limit is reached for any subsystem component, comprehensive redesign of the entire factory may become necessary.

A seed mass of 100 tons was selected in the present study for a number of reasons. First, 100 tons is a credible system mass in terms of foreseeable NASA launch capabilities to the lunar surface, representing very roughly the lunar payload capacity of four Apollo missions to the Moon. Second, after performing the exercise of specifying seed components in some detail it is found that many subsystems are already approaching a nonlinear scaling regime for a 100-ton LMF. For instance, according to Criswell (1980, private communication) the minimum feasible size for a linear-scaling benchtop HF acid-leach plant for materials processing is about 1000 kg; in the present design, two such plants are required with a mass of 1250 kg each. Third, the results of a previous study (Freitas, 1980a) which argued the feasibility of 433-ton seed in the context of an interstellar mission (inherently far more challenging than a lunar factory mission) were compared with preliminary estimates of 15-107 tons for partially self-replicating lunar factories of several different types (O'Neill et al., 1980), and an intermediate trial value of 100 tons selected. The 100-ton figure has appeared in numerous public statements by former NASA Administrator Dr. Robert A. Frosch (lecture delivered at Commonwealth Club, San Francisco, Calif., 1979, and personal communication,1980) and by others in prior studies (Bekey and Naugle, 1980; Giacconi et al., working paper of the Telefactors Working Group, Woods Hole New Directions Workshop, 1979). Finally, it was decided to use a specific system mass rather than unscaled relative component mass fractions to help develop intuitive understanding of a novel concept which has not been extensively studied before.

For reasons similar to the above, an SRS strawman replication time of 1 year was taken as appropriate. The ranges given in table 5.1, drawn from the analysis presented in appendixes 5B-5I, are estimates of the mass and power requirements of an initial seed system able to manufacture 100 tons of all of its own components per working year, hence, to self-replicate. These figures are consistent with the original estimate of a 100 ton circular LMF seed with an initial deployed diameter of 120 m, so feasibility has been at least tentatively demonstrated. However, it must be emphasized that the LMF seed design outlined above is intended primarily as a proof of principle. Numerical values for system components are only crude estimates of what ultimately must become a very complex and exacting design.

Table 5.1. Seed Mass And Power Requirements Estimates

Seed subsystem	Estimated mass of 100 ton/yr seed, kg	Estimated power of 100 ton/yr seed, W	Computer processor, bits to operate	Computer memory, bits to describe
Transponder network	1,000	---	105 (100 Kbit; 12.5 Kbyte)	106 (1 Mbit; 125 Kbyte)
Paving robots	12000	Up to 104	106 - 107 (1 - 10 Mbit; 125 Kbyte - 1.25 Mbyte)	107 - 108 (10 - 100 Mbit; 1.25 - 12.5 Mbyte)
Mining robots	4,400	Up to 104	4 - 7×108 (400 - 700 Mbit; 50 - 87.5 Mbyte)	109 (1 Gbit; 125 Mbyte)
Chemical processing sector (S)	15,300 - 76,400	380,000 - 11,000,000	9.4×107 (94 Mbit; 11.75 Mbyte)	3.1×109 (3.1 Gbit; 387.5 Mbyte)
Fabrication sector (S)	.	.	.	.
... Electronics	(3000)	.	.	.
... Floor map	.	.	.	109 (1 Gbit; 125 Mbyte)
... Totals	137 - 20,000	270 - 345,000	1010 (10 Gbit; 1.25 Gbyte)	1011 (100 Gbit; 12.5 Gbyte)
Assembly sector (S)	.	.	.	.
... Assembly robots	83 - 1,150	83 - 19,600	109 (1 Gbit; 125 Mbyte)	1010 (10 Gbit; 1.25 Gbyte)
... Warehouse subsystem	1,000	10,000	107 (10 Mbit; 1.25 Mbyte)	108 (100 Mbit; 12.5 Mbyte)
Floor map	.	.	.	109 (1 Gbit; 125 Mbyte)
Automated transport vehicles	1,000	6,000	107 (10 Mbit; 1.25 Mbyte)	108 (100 Mbit; 12.5 Mbyte)
Mobile assembly and repair robots	4,000	40,000	4×109 (4 Gbit; 500 Mbyte)	4×1010 (40 Gbit; 5 Gbyte)
Computer central	2,200	37,000	1.6×1010 (16 Gbit; 2 Gbyte)	1.6×1010 (16 Gbit; 2 Gbyte)
... orbital site map	.	.	.	1011 (100 Gbit; 12.5 Gbyte)
Solar canopy	22,000	---	2×107 (20 Mbit; 2.5 Mbyte)	2×108 (200 Mbit; 25 Mbyte)
Totals	63,100 - 145,600	0.47 MW - 11.5 MW	15.5 - 15.8×109 (15.5 - 15.8 Gbit; 1.94 - 1.98 Gbyte)	272x109 (272 Gbit; 34 Gbyte)
Nominal annual seed output	100,000	1.7 MW	.	.

Information processing and storage requirements also have been collected and summarized in table 5.1, and lie within the state-of-the-art or foreseeable computer technologies. These calculations, though only rough approximations, quite likely overestimate real needs significantly because of the conservative nature of the assumptions employed. (See also sec.5.2.3.)

SRS mission overview. In the most general case of fully autonomous operation, a typical LMF deployment scenario might involve the following initial sequence:

1. The predetermined lunar landing site is mapped from orbit to 1-m resolution across the entire target ellipse.
2. Seed lands on the Moon, as close to dead center of the mapped target area as possible navigationally.
3. Mobile assembly and repair robots, assisted by mining robots, emerge from the landing pod and erect a small provisional solar array to provide interim power until the solar canopy is completed.
4. LMF robots, with the computer, select the precise site where erection of the original seed will commence. This decision will already largely have been made based on orbital mapping data, but ground truth will help refine the estimate of the situation and adjust for unexpected variations.
5. Mobile robots emplace the first three stations of the transponder network (the minimum necessary for triangulation), calibrate them carefully, and verify that the system is in good working order.
6. Mining robots equipped with grading tools proceed to the construction site and level the local surface.
7. Five paving robots disembark and begin laying down the seed platform in square grids. This requires one working year for completion.
8. When a sufficiently large platform section has been completed, seed mobile robots transfer the main computer to a place prepared for it at the center of the expanding platform disk.
9. Erection of the solar canopy begins, followed by each of the seed sectors in turn, starting with the chemical processing. Total time to unpack the landing pod after moonfall is one working year, conducted in parallel with paving and other activities. The completed seed factory unit, unfurled to a 120 m diam on the surface of the Moon 1 year after landing, might appear as shown in figure 5.19.

Figure 5.19 - Self-growing lunar factory.

The LMF has two primary operational phases - growth and production. The optimal program would probably be to "bootstrap" (grow) up to a production capacity matching current demand, then reconfigure for production until demand increases, thus necessitating yet further growth (O'Neill et al., 1980). Growth and production of useful output may proceed sequentially, cyclically, or simultaneously, though the former is preferred if large subsystems of the lunar factory must be reconfigured to accommodate the change.

The LMF also may exhibit replicative behavior if and when necessary. Replicas of the original seed could be constructed much like regular products and dispatched to remote areas, either to increase the total area easily subject to utilization or to avoid mortality due to depletion of local resources or physical catastrophes. The scheduling of factory operational phases is very flexible, as shown schematically in figure 5.20, and should be optimized for each mission and each intended use.

Figure 5.20 - Flexible scheduling of LMF operational phases.

5.3.5 Lunar SRS Growth and Productivity

As the study progressed, the team noted a developing convergence between the two designs for SRS described in sections 5.3.3 and 5.3.4. Both require three major subsystems - materials processing, fabrication, and assembly plus a variety of support systems, and each is capable of replication and useful production. Both display exponential expansion patterns.

Of course, in a finite environment exponential growth cannot continue indefinitely. Geometrical arguments by - Taneja and Walsh (1980, Summer Study document) suggest that planar packing of triangular, cubic, or hexagonal units can expand exponentially only for as many generations as each unit has sides, assuming that once all sides are used up no further doubling can occur by the enclosed unit.

Growth is quadratic from that time on. However, in real physical systems such as the developing LMF, enclosure need not preclude material communication with exterior units. Selected ramification of communication, control, and materials transportation channels or internal component rearrangement, reconfiguration, or specialization can prevent "starvation" in the inner regions of the expanding system. Hence, SRS exponential growth may continue until limited either by purposeful design or by the - specific configuration of the external environment. Assuming that a 100-ton seed produces 100 tons/year of the same materials of which it is composed, then if T is elapsed time and N is number of seed units or seed mass-equivalents generated during this time, T = I + log₂ N for simple exponential "doubling" growth. (There is no replication in the first year, the time required for initial setup.) If P is productivity in tons/year, then P = 100 log₂ N.

However, the above is valid only if each unit works only on its own replica. If two or more units cooperate in the construction of a single replica, still more rapid "fast exponential" growth is possible. This is because new complete replicas or LMF subsystems are brought on line sooner, and thence may begin contributing to the exponentiation earlier than before. Using the above notation, the "fast exponential" growth rate is given by T= 1 + 1/2 + ... + 1/N in the optimum case where all available machines contribute directly to the production of the next unit.

Growth rates and productivities are tabulated for exponential and "fast-exponential" expansion in table 5.2. Note that in just 10 years the output of such a facility could grow to approximately one million tons per year. If allowed to expand for 18 years without diversion to production, the factory output could exponentiate to more than 4 X 10⁹ tons per year, roughly the entire annual industrial output of all human civilization.

Table 5.2 Growth Rates And Productivity For Exponential SRS Expansion

Calendar years	Working years, T	Exponential growth, y = 1 yr		"Fast-exponential" growth, y = 1 yr
		Number of units, N	System productivity, tons/yr	Number of units, N	System productivity, tons/yr
0	0	0	0	0	0
2	1	1	100	1	100
4	2	2	200	4	400
6	3	4	400	11	1,100
8	4	8	800	31	3,100
10	5	16	1,600	83	8,300
12	6	32	3,200	227	22,700
14	7	64	6,400	616	61,600
16	8	128	12,800	1,674	167,400
18	9	256	25,600	4,550	455,000
20	10	512	51,200	12,367	1,236,700
22	11	1,024	102,400	33,617	3,361,700
24	12	2,048	204,800	91,380	9,138,000
26	13	4,096	409,600	248,398	24,839,800
28	14	8,192	819,200	675,215	67,521,500
30	15	16,384	1,638,400	1,835,426	183,542,600
32	16	32,768	3,276,800	4,989,205	498,920,500
34	17	65,536	6,553,600	13,562,066	1,356,206,600
36	18	131,072	13,107,200	36,865,517	3,686,551,700
38	19	262,144	26,214,400	100,210,865	10,021,086,500
40	20	524,288	52,428,800	272,401,372	27,240,137,200

(About 3 billion seed units would completely cover the entire lunar surface)

Useful SRS products may include lunar soil thrown into orbit by mass drivers for orbital processing, construction projects, reaction mass for deep space missions, or as radiation shielding; processed chemicals and elements, such as oxygen to be used in space habitats, as fuel for interorbital vehicles, and as reaction mass for ion thrusters and mass drivers; metals and other feedstock ready-made for space construction or large orbital facilities for human occupation (scientific, commercial, recreational, and medical); components for large deep-space research vessels, radio telescopes, and large high-power satellites; complex devices such as machine shop equipment, integrated circuits, sophisticated electronics gear, or even autonomous robots, teleoperators, or any of their subassemblies; and solar cells, rocket fuels, solar sails, and mass driver subassemblies. Also, a 100-ton seed which has undergone thousand-fold growth or replication represents a 2 GW power generating capacity, plus a computer facility with a 16,000 Gbit processing capability and a total memory capacity of 272,000 Gbits. These should have many useful applications in both terrestrial and space industry.

5.3.6 Closure in Self-Replicating Systems

Fundamental to the problem of designing self-replicating systems is the issue of closure.

In its broadest sense, this issue reduces to the following question: Does system function (e.g., factory output) equal or exceed system structure (e.g., factory components or input needs)? If the answer is negative, the system cannot independently fully replicate itself; if positive, such replication may be possible.

Consider, for example, the problem of parts closure. Imagine that the entire factory and all of its machines are broken down into their component parts. If the original factory cannot fabricate every one of these items, then parts closure does not exist and the system is not fully self-replicating .

In an arbitrary system there are three basic requirements to achieve closure:

1. Matter closure - can the system manipulate matter in all ways necessary for complete self-construction?
2. Energy closure - can the system generate sufficient energy and in the proper format to power the processes of self-construction?
3. Information closure can the system successfully command and control all processes required for complete self-construction?

Partial closure results in a system which is only partially self-replicating. Some vital matter, energy, or information must be provided from the outside or the machine system will fail to reproduce. For instance, various preliminary studies of the matter closure problem in connection with the possibility of "bootstrapping" in space manufacturing have concluded that 90-96% closure is attainable in specific nonreplicating production applications (Bock, 1979; Miller and Smith, 1979; O'Neill et al., 1980). The 4-10% that still must be supplied sometimes are called "vitamin parts." These might include hard-to-manufacture but lightweight items such as microelectronics components, ball bearings, precision instruments and others which may not be cost-effective to produce via automation off-Earth except in the longer term. To take another example, partial information closure would imply that factory-directive control or supervision is provided from the outside, perhaps (in the case of a lunar facility) from Earth-based computers programmed with human-supervised expert systems or from manned remote teleoperation control stations on Earth or in low Earth orbit.

The fraction of total necessary resources that must be supplied by some external agency has been dubbed the "Tukey Ratio" (Heer, 1980). Originally intended simply as an informal measure of basic materials closure, the most logical form of the Tukey Ratio is computed by dividing the mass of the external supplies per unit time interval by the total mass of all inputs necessary to achieve self-replication. (This is actually the inverse of the original version of the ratio.) In a fully self-replicating system with no external inputs, the Tukey Ratio thus would be zero (0%).

It has been pointed out that if a system is "truly isolated in the thermodynamic sense and also perhaps in a more absolute sense (no exchange of information with the environment) then it cannot be self-replicating without violating the laws of thermodynamics" (Heer,1980). While this is true, it should be noted that a system which achieves complete "closure" is not "closed" or "isolated" in the classical sense. Materials, energy, and information still flow into the system which is thermodynamically "open"; these flows are of indigenous origin and may be managed autonomously by the SRS itself without need for direct human intervention.

Closure theory. For replicating machine systems, complete closure is theoretically quite plausible; no fundamental or logical impossibilities have yet been identified. Indeed, in many areas automata theory already provides relatively unambiguous conclusions. For example, the theoretical capability of machines to perform "universal computation" and "universal construction" can be demonstrated with mathematical rigor (Turing, 1936; von Neumann, 1966; see also sec. 5.2), so parts assembly closure is certainly theoretically possible.

An approach to the problem of closure in real engineering-systems is to begin with the issue of parts closure by asking the question: can a set of machines produce all of its elements? If the manufacture of each part requires, on average, the addition of >1 new parts to product it, then an infinite number of parts are required in the initial system and complete closure cannot be achieved. On the other hand, if the mean number of new parts per original part is <1, then the design sequence converges to some finite ensemble of elements and bounded replication becomes possible.

The central theoretical issue is: can a real machine system itself produce and assemble all the kinds of parts of which it is comprised? In our generalized terrestrial industrial economy manned by humans the answer clearly is yes, since "the set of machines which make all other machines is a subset of the set of all machines" (Freitas et al.,1981). In space a few percent of total system mass could feasibly be supplied from Earth-based manufacturers as "vitamin parts." Alternatively, the system could be designed with components of very limited complexity (Heer, 1980). The minimum size of a self-sufficient "machine economy" remains unknown.

Von Tiesenhausen and Darbro (1980) similarly argue that a finite set of machines can produce any machine element . Their reasoning, outlined in figure 5.21, is as follows:

Figure 5.21 - Closure of SRS parts production.

1. If all existing machines were disassembled into their individual parts there would obviously be a finite number of parts, many of them identical, and a large number would be of common categories like shafts, motors, wiring, etc. The only differences between the machines would be a different selection, different arrangement, and different dimensions of this finite number of parts.
2. A finite number of parts involves a finite number of machine operations, this number being less than the number of parts because some machines can make more than one kind of parts.
3. Therefore, the number of machines is finite and less than the number of operations.

This reasoning can then be generalized to say: "Every existing machine can be reduced to a finite set of machine elements, and there exists a finite set of machine operations." (Still, of course, a limited number of standard elements should be developed and machine operations limited as much as practical by substitution, in order to minimize the number of parts and machine operations.)

Similar arguments may be applied to materials processing and feedstock production. There exists a finite number of different materials anywhere. There is a finite number of materials processes which is less than the number of materials because single processes result in various materials (e.g., silicon and oxygen). Hence, there is a finite number of materials processing robot systems needed for an SRS. Also, there is a finite and rather limited number of feedstock requirements such as bars, rods, ingots, plates, etc. The number of materials is much less than the number of parts; therefore, a finite number of parts fabrication robots is required for an SRS.

Closure engineering In actual practice, the achievement of full closure will be a highly complicated, iterative engineering design process. Every factory system, subsystem, component structure, and input requirement (Miller and Smith, 1979) must be carefully matched against known factory output capabilities. Any gaps in the manufacturing flow must be filled by the introduction of additional machines, whose own construction and operation may create new gaps requiring the introduction of still more machines.

The team developed a simple iterative procedure for generating designs for engineering systems which display complete closure. The procedure must be cumulatively iterated, first to achieve closure starting from some initial design, then again to eliminate overclosure to obtain an optimally efficient design. Each cycle is broken down into a succession of subiterations which ensure three additional dimensions of closure:

1. Qualitative closure - can, say, all parts be made?
2. Quantitative closure - can, say, enough parts be made?
3. Throughput closure - can parts be made fast enough?

In addition, each subiteration sequence is further decomposed into design cycles for each factory subsystem or component, as shown in figure 5.22.

Figure 5.22 - Generalized closure engineering design cycles.

The procedure as outlined, though workable in theory, appears cumbersome. Further work should be done in an attempt to devise a more streamlined, elegant approach.

Quantitative materials closure - numerical results In the context of materials processing, "closure" is a relationship between a given machine design and a given particular substrate from which the machine's elemental chemical constituents are to be drawn. Hence the numerical demonstration of closure requires a knowledge of the precise composition both of the intended base substrate to be utilized and of the products which the SRS must manufacture from that substrate. Following a method suggested by the work of Freitas (1980a), a modified "extraction ratio" R_n is defined as the mass of raw substrate material which must be processed (input stream) to obtain a unit mass of useful system output having the desired mass fraction of element n (output stream).

Consider the significance of the extraction ratio to the problem of materials closure. Assume that the final product is to be composed of elements x, y, and z. An R_x = 1 means that 1 kg of lunar soil contains exactly the mass of element x needed in the manufacture of 1 kg of the desired output product. On the other hand, R_y = 10 means that 10 kg of lunar regolith must be processed to extract all of element y required in 1 kg of final product. The difference between R_x and R_y may signify that y is more rare in lunar soil than x, or that the two elements are equally abundant but ten times more y than x is required (by weight) in the final product. When the output stream is identical to the machine processing system itself, then the system is manufacturing more of itself - self-replicating - and the extraction ratio becomes an index of system materials closure on an element-by-element basis.

The total net extraction ratio R is some function of the individual extraction ratios R_n, and depends on the methods of materials processing employed. At worst, if only one element is recovered from a given mass of input stream ("parallel processing"), then R is the sum of all R_n. At best, if the input stream is processed sequentially to extract all desired elements in the necessary amounts ("serial processing"), then R is driven solely by the R_n of the element most difficult to extract, say, element z. That is, R = (R_n)_max = R_z, which is always equal to or smaller than the sum of all R_n. As serial processing should dominate in the lunar factory the latter formula is assumed for purposes of the present calculations. Note that R_n can be less than 1 for individual elements, but for an entire machine system R must always be greater than or equal to 1.

As a general rule, a low value for R implies that the system is designed for low mass throughput rates and is built from relatively few different chemical elements. A high value of R implies that many more elements are necessary and that a higher mass throughput rate will be accommodated to obtain them.

The "closure" of a given output stream (product) relative to a specified input stream (substrate) is computed by treating R as an independent variable. If I_n is the concentration of element n in mineral form in the input stream of lunar soil (kg/kg), E_n is the efficiency of chemical extraction of pure element n from its mineral form which is present in lunar soil (kg/kg), and O_n is the concentration of element n in the desired factory output stream (kg/kg), then R_n = O_n/E_nI_n. Closure C_n for each element is defined as the mass of pure element n available in a system with a total net extraction ratio R per unit mass of output stream. For any given element, if R >= Rn then all pure element n needed is already available within the system. In this case, C_n = O_n. On the other hand, if R < R_n then the choice of R is too low; all the pure element n needed cannot be recovered, and more lunar soil must be processed to make up the difference if 100% closure is to be achieved. In this case, C_n = O_n(R/R_n), since the closure deficit is measured by the ratio of the chosen R to the actual R_n of the given element (i.e., how much the factory has, divided by how much the factory actually needs). Total net system closure C is simply the sum of all C_n for all elements n required in the output stream of the SRS factory (Freitas and Zachary, 1981)

To estimate the quantitative materials closure for the lunar SRS baseline designs proposed in sections 5.3.3 and 5.3.4, three different approaches were taken in an attempt to converge on a useful estimate of the composition of the output stream necessary for LMF selfreplication. First, the "seed" element distribution given by Freitas (1980a) in the context of a self-reproducing exploratory space probe was adopted. These figures are derived from published data on the material consumption of the United States (the world's largest factory) during the years 1972-1976 (U.S. Bureau of Mines, 1978; U.S. Bureau of the Census, 1977, 1978). A second but less comprehensive measure called "demandite" is based on 1968 U.S. consumption data (Goeller and Weinberg, 1976). A molecule of "nonfuel demandite" is the average nonrenewable resource used by humans, less fuel resources (Waldron et al., 1979). Third, the direct estimate of LMF elemental composition presented in appendix 5E was used to obtain additional trial values for O_n. (Appendix 5E also represents a first attempt to deal with qualitative materials closure for SRS.) In all cases the input stream was assumed to consist of lunar maria regolith, with values for I_n averaged from published data (Phinney et al., 1977) and listed in table 5.3. Following earlier work, for simplicity all efficiencies E_n were taken to be 0.93 (Rao et al., 1979; Williams et al.,1979).

Table 5.3. Average Chemical Element Abundances In Lunar Maria

Element	Abundance	Element	Abundance	Element	Abundance	Element	Abundance
Al	6.80%	Bi	3.19 ppb	Ho	3.73 ppm	Ru	0.231 ppm
Ca	7.88%	Br	0.178 ppm	I	2.00 ppb	Sb	22.1 ppb
Cr	0.264%	C	104 ppm	In	32.9 ppb	Sc	48.8 ppm
Fe	13.2%	Cd	0.197 ppm	Ir	6.32 ppb	Se	0.306 ppm
K	0.113%	Ce	48.8 ppm	La	17.2 ppm	Sm	10.9 ppm
Mg	5.76%	Cl	25.6 ppm	Li	12.9 ppm	Sn	0.900 ppm
Mn	0.174%	Co	40.3 ppm	Lu	1.22 ppm	Sr	167 ppm
Na	0.290%	Cs	0.392 ppm	Mo	0.520 ppm	Ta	1.26 ppm
O	41.3%	Cu	14.4 ppm	N	95.4 ppm	Tb	2.58 ppm
P	0.066%	Dy	15.3 ppm	Nb	19.6 ppm	Te	0.0545 ppm
S	0.125%	Er	19.24 ppm	Nd	38.2 ppm	Th	2.50 ppm
Si	20.4%	Eu	1.77 ppm	Ne	2.75 ppm	Tl	1.61 ppb
Ti	3.10%	F	174 ppm	Ni	169 ppm	Tm	1.42 ppm
Ag	45.2 ppb	Ga	4.99 ppm	Os	12.9 ppb	U	0.805 ppm
Ar	0.800 ppm	Gd	14.3 ppm	Pb	3.11 ppm	V	114 ppm
As	0.206 ppm	Ge	0.626 ppm	Pd	12.3 ppb	W	0.358 ppm
Au	2.66 ppb	H	54.8 ppm	Pr	7.20 ppm	Y	84.2 ppm
B	4.78 ppm	He	28.5 ppm	Rb	3.21 ppm	Yb	8.40 ppm
Ba	195 ppm	Hf	7.77 ppm	Re	1.36 ppb	Zn	23.4 ppm
Be	2.63 ppm	Hg	0.019 ppm	Rh	0.192 ppm	Zr	311 ppm

The closures calculated from these data are plotted against extraction ratio in figure 5.23. (Data for the human body are included for purposes of comparison.) Note that 100% closure (C = 1) is achieved for the "U.S. Industrial" estimate (84 elements of the space probe "seed") at R = 2984; for "Demandite" (28 elements) at R = 1631; and for the appendix 5E "LMF" (18 elements) at R = 45. This suggests that the fewer the number of different elements, and the more common and more efficiently extractable are the elements the factory system needs for replication to occur, the lower will be the total mass of raw materials which must be processed by the LMF.

Figure 5.23 - Quantitative materials closure data for various self-replicating systems.

Note also that in all three cases, virtually complete (>90%) closure is achieved for extraction ratios of 2 to 14. The incremental gains in closure after 90% are purchased only at great price - from 1 to 3 orders of magnitude more raw materials mass must be processed to achieve the last bit of full materials autonomy. Two conclusions may be drawn from this observation. First, for any given SRS design it may well be more economical to settle for 90-95% system closure and then import the remaining 5-10% as "vitamins" from Earth. Second, in those applications where 100% closure (full materials autonomy) is desirable or required, great care must be taken to engineer the self-replicating system to match the expected input substrate as closely as possible. This demands, in the case of quantitative materials closure, a design which minimizes the value of R, thus optimizing the use of abundantly available, easily extractable elements.

5.3.7 Conclusions

The team reached the following major conclusions regarding the feasibility of self-replicating machine systems:

• The basic concept of physical machine systems capable of self-replication appears credible both from a theoretical and a practical engineering standpoint.
• It is reasonable to begin designing replicating systems based on current knowledge and state-of-the-art technology, but final design definition will require significant further research.
• Complete systems closure is achievable in principle, though partial closure may be more feasible from an economic and pragmatic engineering standpoint in the near term.
• It is feasible to begin immediate work on the development of a simple demonstration SRS on a laboratory scale, with phased steps to more sophisticated levels as the technology is proven and matures.