Yes there is research. But it's not as easy as nuking Mars. Nuclear bombs wouldn't release anything like enough energy to start with.
Most of the proposals focus mainly on the first stage of creating a dense CO2 atmosphere. This would not be breathable by humans, and indeed CO2 is poisonous to humans in concentrations above 1% of the atmosphere. So even if you had plenty of oxygen, we couldn't survive in a CO2 dominated atmosphere. We need a buffer gas like nitrogen - which if it exists on Mars is only present in rock. And huge quantities of it are needed also. It is the main part of our atmosphere.
The oxygen is problematical also. If there is enough CO2 on Mars to make an atmosphere as dense as Earth's - which is not known, it might only have enough for a few percent of the Earth's pressure - you then have to convert all that CO2 to oxygen and organics, all except a fraction of a percent of the atmosphere. To do that on Earth took hundreds of millions of years. On Mars they hope to speed it up to perhaps 100,000 years. The most optimistic say it could be done in a few thousand years.
Bear in mind, this means that your plants have to take enough carbon out of the atmosphere to create a layer of organics covering the entire surface - peat say - to a depth of several meters. It is no use them creating oxygen, and then using it up again, as trees do if you grow them, fell them and then burn them or they decay. They have to be continually buried, to increase the levels of oxygen - the amount of oxygen generated by photosynthesis is directly linked to the amount of carbon captured as organics.
Anyway so back to the CO2 release which is their first stage. Mars does have a fair bit of dry ice. Enough to nearly double its atmospheric pressure at least. The problem is, this takes you only to 2% of Earth's atmosphere.
And - what's more, the atmosphere there is in an optimum state, with the dry ice at the poles exactly in equilibrium with the atmosphere, which means, if you manage to temporarily liberate, say, all 10,000 cubic kilometers of dry ice to double the atmospheric pressure - well within a short time, it will all condense back again as dry ice.
You need to increase it to 10% of Earth's atmospheric pressure to get it into a runaway greenhouse effect, which means, to liberate about 140,000 cubic kilometers of dry ice - if that much dry ice exists on Mars in the first place, which we don't know.
These numbers are way beyond what you could achieve by dropping a few nukes on the poles.
So - we need mega-engineering. That's not going to happen naturally.l
There are several suggestions. You can use orbiting mirrors. But you need to double the amount of sun that hits Mars to get it as warm as Earth - so that means a mirror about the size of a planet, of order thousands of kilometers in diameter. Even with thin film mirrors, that's a huge project.
Greenhouse gases are more feasible. But by "easy solution" here - this still means finding and mining the same amount of fluorine on Mars that you find in 11 cubic kilometers of fluorite ore.
It's still a mega-engineering project in anyone's book. And producing the greenhouse gases uses a lot of power. The author estimates that you might be able to do it by building 245 nuclear power stations on Mars, each generating half a gigawatt. Which then have to run 24/7 for a century to produce enough greenhouse gases to tip Mars over into a runaway greenhouse effect.
Then - a thick CO2 atmosphere on Mars still isn't enough to keep it warm enough for trees at the equator. So you need to continue production of the greenhouse gases in order to keep it warm enough for trees.
Then - if you do ever manage an atmosphere breathable by humans - over that hundred thousand year period or the optimists think, perhaps less, pessimists would doubtless say longer - anyway if you succeed - then you remove all the CO2 from the atmosphere. So then you need to step up your production of greenhouse gases to compensate. Or build your orbital mirrors.
In short, it is not a "fixer upper of a planet" in the sense of a quick fix. It is rather, like a house that has problems with its foundations, power supply, air conditioning, roof, walls and just about everything else, and has to be continually maintained at great expense for the foreseeable future.
There may be ways we could do it, that don't involve megatechnology, but if so, nobody has described them convincingly yet.
The greenhouse gases idea is undoubtedly very ingenious, 11 cubic kilometers of fluorite ore is a major improvement on 140,000 cubic kilometers of dry ice, and 245 power stations seem a lot more manageable than a planet sized mirror. But still, it is only "easy" compared to what came before.
You have to ask, is it worth it? For this level of technology we could probably build solar mirrors and power stations to provide free energy for the entire Earth. Or any number of other global projects to improve conditions on Earth.
And if you are worried about asteroids - well we have nearly mapped all the big ones anyway - done all the 10 km or larger ones closer to the sun than Jupiter. We have nearly finished mapping out all the one kilometer ones also, at around one a month, expect to get to 99% of them mapped by the 2020s.
Surely it's a more worthwhile way to protect Earth to complete that survey as fast as possible, and then if we continued to give this our priority, then within a few decades, we can probably know the position of all the asteroids of any size throughout the entire solar system right out to Pluto. I don't see why not, as we already can detect tiny objects of a few hundred kilometers way beyond Pluto. What will we be able to do, say, by the 2050s?
It's fascinating sci. fi. and a great thing to think about. But we are so far from being able to actually do such things - that we can't even micro-adjust the amount of CO2 in the Earth's atmosphere by the tiniest fraction of a percent. And with Biosphere 2, the whole thing failed because they failed to take account of some interaction with the concrete. What kind of interactions are we failing to take account of when planning ways to terraform a planet?
There are many other issues though, things that could go wrong, along the way. And in any case, I'm not at all sure that they are going to get approval from the astrobiologists that it is okay to send humans to Mars and that it won't interfere with the search for life or get in the way of planetary protection. And - do you want to totally ruin the main science value of Mars? So that if we ever find life there, our first assumption is that it is from the human colonists?
We need to be very very sure that humans won't get in the way of planetary protection of Mars before any project like this could get the green light from the international scientific community, seems to me.