This news story has the first public hint I've seen of a feature slated for the 2020 rover: autonomous navigation in hardware. So now I can talk about it. :-)
Generally speaking, the rover drives fastest for the first part of its traverse -- up to 160m on Opportunity, but more commonly around a third of that, and even less on Curiosity -- where we chart the whole course for it. We basically say, "just close your little rover eyes and trust me on this part."
Sometimes, though, you know your direction and you just want to make as much distance as possible -- maybe there's a nifty crater a week away, and the science team says to floor it. So the rover passes the point where we could see obstacles well enough to manually plan a path around them, and from there she's on her own.
For this part of the drive, we use a feature called "autonomous navigation," or "autonav" for short: the rover takes a stereo pair of images of the world in front of it, constructs a 3-D model, and scans it for any geometric hazards (large rocks, deep ditches, and so on). If the path toward the goal looks safe, the rover moves a little bit (up to maybe 1.5m in the best case) in the desired direction, and then repeats the process.
It's slow, though: Curiosity's CPU runs at a mere 200 MHz, and Opportunity's is a tenth of that. For perspective, your desktop likely has two or four cores each at least ten times as fast as Curiosity's -- heck, your phone can run rings around it. (But then, your phone would die fast in the high-radiation Martian environment.) So it's not much horsepower to do 3-D image processing. Autonav is great as far as it goes, in that it lets you do something slowly that otherwise you couldn't do at all -- but it is slow.
Which is where the hardware acceleration comes in. Last I heard, at least, the basic plan is to fly a piece of hardware called an FPGA -- a Field-Programmable Gate Array, essentially a reprogrammable piece of hardware -- and move the autonav logic into it. This advance will do for autonav processing what graphics hardware does for gaming. The 2020 rover's wheels will still turn slowly, but at least they'll turn continuously -- and slow and steady is all it takes to win this race.