Can you move main-belt asteroids to the Earth sphere?

[Erisie]

One of the most important points of the Gundam franchise in general is its use of asteroids for raw materials and military bases. However, most of the asteroids seen are pretty large objects, apparently brought from the main asteroid belt. 3 Juno (Luna II) is 233 km wide and has a mass of 267 quadrillion metric tons.
Near-Earth objects tend to be pretty small: the largest is about 33 km wide. You'd require a lot of these to build even a single O'Neill cylinder.

How much energy would you require to move such an enormous object from the main belt to Earth's system? From the look of it, and despite the use of shortcuts (unstable orbits for many main belt objects, slingshot gravity assists, Oberth maneuvers), it would still require an insane amount of energy. I've looked for the subject in both English and Japanese websites, but nothing comes out. Has anyone done the math for, say, the thrust that Axis needed to move from the belt to the Earth sphere in 20 months?

[Dendrobium Stamen]

It's worth remembering, when it comes to objects such as Axis, that the wonders of Newtonian physics mean you don't need a lot of thrust - the way one does when, say, blasting a rocket from Florida to space - but can instead apply smaller amounts over a longer period of time, for a cumulative effect.

From what I gather of the background material, when moving objects from the Belt to the Earth Sphere, the objective is to apply as little energy as possible to "nudge" the rock out of its Solar orbit toward Earth, and then correct it into a stable orbit at a LaGrange point when it gets close enough. Still a fair amount of thrust, but not colossal, especially in a world where atomic fusion is a day-to-day energy source.

So, in short - a lot, but in multiple smaller bursts, rather than one big bang.

[latenlazy]

A further benefit in the UC-Verse is that they can find ample fuel for the kind of fusion they use on the asteroids, so they don't have to bring enough fuel for the journey back with them.

[Erisie]

the objective is to apply as little energy as possible to "nudge" the rock out of its Solar orbit toward Earth, and then correct it into a stable orbit at a LaGrange point when it gets close enough.

It would actually require at least two maneuvers/burns (Hohmann transfer): one to take the asteroid out of its stable solar orbit, and another one to put it on the Earth system. If you wanted to make a slingshot using Mars' gravity, you'll need at least three burns, plus making minute calculations in your trajectory to perform the assist properly and not crash in the process.

As a thought experiment, let's say that this isn't done using fusion engines, but with nuclear pulse propulsion: pushing a spacecraft with subsequent nuclear explosions.
If you had all the world's current nuclear stockpile (calculated at 6,400 megatons of TNT) available for this project, is it possible to move an asteroid the size of 3 Juno to the Earth sphere within a reasonable timeframe? I know that I'm asking for a lot of advanced physics here, and I haven't found anyone who has done the calculations for a "medium-sized" object like this one. All the information available online is either on tiny NEO rocks or gargantuan projects of cosmic engineering like moving the whole Earth.

The difficulties are not only the asteroid's mass (see OP), but also its orbital speed: 18 m/s in average.