I would have gone for an (laser/thermal) ablation approach. It's slower, but you have no parts in contact with the surface you are mining - so you have no chance of your robot either getting stuck or the tools wearing out.

I doubt a rasping/digging robot can keep going for years on an asteroid. Especially since you never know what kind of hard substance you're going to hit. Find a small pocket of diamond hardness and your robot is broken.

Here on earth, construction and mining will become automated. Robots will soon begin mining and sorting through the garbage mountains surrounding our cities, sorting, reclaiming, and reaping great profits.

It should be far more economical to reclaim than to start from scratch, especially when it can be done by robots.

I doubt a rasping/digging robot can keep going for years on an asteroid. Especially since you never know what kind of hard substance you're going to hit. Find a small pocket of diamond hardness and your robot is broken.

Robots can be designed to deal with things like this. Mark II.

At last, NASA shows something actually useful and functioning piece of a new kind of mission.

@antialias: How would your ablation approach collect material for resource extraction?

How would your ablation approach collect material for resource extraction?

Vaporize, and centrifuge to separate.

Alternatively collect the melted runoff (which would need less energy but would necessitate contact to the object being mined. Still it would be a method that isn't prone to damage).

In general mechanical devices are faster and more energy efficient than the use of chemicals or raw energy for comminutions, which is the first step in separating the components of a massive object for further processing.

Here on earth, construction and mining will become automated. Robots will soon begin mining...

Its about 10 years already we use robots in mining. Seriously this is nothing new. Its even funny that NASA wants to develop something that is already there. But mining companies are simply not willing to share technologies.

The engineerig solutions on Earth aren't very applicable because they require lubricants and hydraulics (something you want to avoid in space because there are no service stations for refills and they also tend to freeze a lot)

Also on Eath you have (significant) gravity which is used implicitly to keep the mining machines steady and the flow of mined material controlled.
In space you have to look to different solutions. It's not much use using fast, rotary scoops when the tangential velocity of the scoops already exceeds the velocity needed to achieve (or leave) orbit.