As I see it, the point of a robot is to do lots of simple things in programmable sequence. A self-replicating robot built of DNA is no exception.
"Sequential" and "self-assembly" don't usually go together, because self-assembly happens by itself (hence the name) which means that everything tends to happen at once. Also, self-assembly usually needs to be reversible, so that components can try various positions until they get it right; but that means that the things you've already done tend to come apart while you're doing more things.
Thus, to make things self-assemble in a lengthy sequence of operations requires re-thinking some assumptions. The assumption I've chosen to re-think is that self-assembly needs to be reversible.
A common problem with irreversible self-assembly is that things tend to stick together where you don't want, and then they can't come apart again to find the correct position. But what if the things were very unlikely to stick while bumping around in solution - but very likely to stick if held in close proximity?
A back-of-the-envelope calculation shows that using DNA strands to hold things near each other should be able to increase their effective concentration by a factor of a million or so. (The basic idea is not mine - I learned it from Eric Drexler - but the calculation is mine.)
This is the core of my simple self-replicating robot idea. If things are a million-fold more likely to stick when you hold them where you want them, then you should be able to build structures out of hundreds of the things before something sticks where you don't want it. And my robot design only requires a few dozen building blocks.
The first thing to do is to demonstrate this million-fold speedup in sticking (binding). That's the focus of the current proposal.
My plan is to design some DNA strands to bind very strongly but react very slowly, then demonstrate that they will bind a lot more quickly when held in close proximity. I would do this with pairs of DNA strands, each with a "test" section that binds slowly but strongly to the "test" section on the other strand, and a "holder" section that binds quickly but reversibly to the corresponding "holder" section.
I'd put one FRET pair on the tips of the "holder" sections, and another pair on the "test" sections. This would allow me to tell when the various parts of the strands hooked up.
I'd mix the strands together at a temperature too high for the "holders" to bind, and show that neither FRET pair was close, even after waiting a long time.
Then I'd lower the temperature to where the "holders" would bind, holding the "test" pairs somewhat close to each other. I'd wait a short time, until the "test" pairs also bound.
Then I'd heat the mixture back up, letting the "holder" sections disconnect, and show that the "test" pairs were still together.Instead of temperature change, I could also use strand replacement to free the "holder" strands to bind to each other, and then another replacement to separate them again. That way, all the "test" activity would happen at the same temperature.
So, if all this works, I would be able to demonstrate irreversible self-assembly on command. Once that was established, I'd be ready to make irreversibly assembling building blocks, and eventually build a DNA-programmed DNA robot to hold them together, one at a time, in the correct sequence to make whatever I wanted.