Since self-replicating automata entered the fictional literature in Samuel Butler’s Erehwon, humans have been concerned that their uncontrolled replication could be dangerous; notable examples include Karel Čapek’s “R. U. R.”, Lem’s “Invincible”, Dick’s “Second Variety”, Drexler’s “gray goo”, Star Control 2’s “Slylandro Probe”, and, in a way, Goethe’s sorcerer’s apprentice’s broom. And, of course, our experience with biological self-replicating systems includes numerous troublesome examples of exponential self-replication, including locust plagues, cancer, all kinds of infectious diseases, toxic algal blooms, mold infestations, ant and other insect infestations, rats in cities, and cane toads in Australia. In computers, self-replicating code and related phenomena have caused many problems, from the TFTP “Sorcerer’s Apprentice Syndrome” and the accidental fork bomb to the helminthiasis of the internet (the “Morris worm”); nowadays, self-replicating code is a mainstay both of computer security attacks (where it is often called a worm) and defense (where it is often called a security patch or security update).
Our experience with biological systems, however, is misleading when it comes to mechanical systems. If you want to design a self-replicating mechanical system to have a high degree of assurance that it won’t continue running on its own, consuming more resources than anyone wanted to produce more replicas of the system than anyone wanted, there are a variety of strategies you can employ without unduly limiting the system's intentional uses.
Large size.
One reason that cancer is such a problem in animals is that we are made from trillions of essentially autonomous units, each capable of self-replication, most of which (except for red blood cells) do in fact self-replicate in the regular course of events. This provides hundreds of trillions of opportunities for exponential self-replication to arise during the lifetime of a single organism.
By contrast, we can design the self-replication process of a robot to use convergent assembly, in which the minimal self-replicating unit is very large — rather than the tens of microns of a typical eukaryotic cell, it could be hundreds of millimeters, or even more than a meter, in diameter. This lowers whatever risk of exponential replication may exist by a factor of about a quadrillion.
By using convergent assembly, in which the robot contains many small manipulators producing parts to be assembled by asmaller number of larger manipulators, it is possible to obtain this desirable large size without paying an excessive cost in replication time, though this is not intuitive from examining biological models such as elephants, humans, or whales, with their perilously low fertility rates.
Broadcast architecture.
Rather than keeping a copy of the full program to build a new robot inside of each robot, as cells do, it has been suggested (originally by Laing, I think, as a way to reduce the size of the robot) to store the program in a centralized transmitter, broadcasting the subprogram for each stage in the process to all of the robots at once. In this way, no robot ever contains the full construction program at once; if the central transmitter ceases to transmit, perhaps because a human has hit the red EMERGENCY STOP button, the entire replication process will cease.
Concern about the space used for the program might seem quaint today when the system-on-a-chip the Raspberry Pi is built around has a gigabyte of RAM. However, this may be purely an artifact of our primitive macroscopic fabrication technology — semiconductor fabs are optimized for efficiently producing consumer products, so the wire-sawing process used to dice wafers has unacceptable waste below a scale of a millimeter or so. With self-replication, we may be able to usefully reduce robot size below the level where each autonomous unit contains space for hundreds of thousands of memory bits.
From a certain point of view, a convergent-assembly desktop factory is a broadcast-architecture machine — after all, what distinguishes the smallest manipulators from autonomous replicators is precisely that they are fixed in place in a larger assembly governed by a larger program they do not have access to.
Manual process steps.
If the replication process turns a bucket of dirt and rocks into a bunch of robots, a simple way to prevent the process from running amok is to only fill the bucket through human intervention. For example, if the bucket is mounted on top of the replicator, a person could shovel dirt and rocks into it with a shovel. At a larger scale, the person could use a backhoe or a manually operated hydraulic excavator or power shovel capable of depositing hundreds of tons of material in a single operation.
The manual process step need not be the initial raw-material handling step; having a person manually pick up a bucket of finished parts from an autonomous digging part-fabricating robot and dump them into the parts hopper of an assembly robot would work too. If the human stopped carrying parts buckets, no further replicas would be produced. At the extreme, you could require a single human-executed final assembly step, such as installing a fuse or a magic word behind the robot's teeth, in order to bring the fully-assembled robot to life.
However, the raw-material extraction step of the process is the step most likely to cause damage to nearby objects such as buildings, other machinery, or humans, so it is the step most desirable to automate.
Alternation of generations.
If robot type A is well-suited to producing robot type B, and vice versa, but neither is well-suited to produce others of its own type, then it is possible to employ either type of robots to produce an arbitrary quantity of the other type of robot, or other articles, without ever enabling exponential growth. Exponential growth is only possible if replication of both robots is possible at once — both construction programs and all the necessary raw materials must be present.
Alternation of generations may be desirable for material-processing reasons as well. RepRaps and similar FDM machines cannot replicate themselves from raw materials because, among other things, they cannot manufacture their hotends (extrusion nozzles), because the hotends necessarily remain solid at temperatures that melt the thermoplastic extruded through them.
Moses, Yamaguchi, and Chirikjian refer to this kind of alternation of generations as a “cyclic fabrication system”, saying, “It is cyclic in the way the game ‘rock-paper-scissors’ is cyclic: tools, materials, and fabrication processes are chosen such that one process creates tools used in the next process…” They suggest prototyping using a hard two-part polyurethane resin which can be cast in wax molds, which in turn can easily be machined by fully-hardened polyurethane; or using a low-melting metal alloy to make mandrels on which to electrodeposit softer but higher-melting metals such as copper and nickel.