Brain of the beast
I think the path calculations should be done locally (i.e. hardwired, not on a remote server as suggested somewhere in the article). Remote control is just asking for problems. What if you lose the link? There can be a remote oversight, but the core of the control should be local. Also, for safety reasons, if contact with the remote control channel is lost the mower needs a local system so that it can park itself safely, say, on the nearest Iranian desert*.
I suggest using a Ben Nanonote as the local brain. It's cheap, relatively inexpensive (100 bucks), resilient (I dropped mine a few times while in the tube; it takes 1.5 m falls on concrete -with forward momentum, even- without a complaint), fully copyleft, flashable at will, it has ethernet over usb or can be fitted with a WiFi microSD card (if you can find one). 336 MHz MIPS-compatible chip, 2GB NAND, 32 MB RAM, with a small colour monitor and a full-featured keyboard for in-situ interaction if needed; what's not to like?
There's plenty of space to put your -legally obtained- music tracks, so attach a 50 quids sound system from Costco -with a massive subwoofer- to the lawn-mowing core and presto!, you got yourself an efficient neighbour-angerer.
The current shipped image is an OpenWRT with Python2.6, Lisp, 4th, gforth, perl I think, etc (and of course C). Even Octave, the open-source MatLab clone! so it could be used out of the box; of course it's all open source, so the sky (and your cross-compile toolchain) is the limit.
If you keep the microSD slot for wireless comm, the only possible channel to control the mowbot would be the USB port of the Ben (I'm guessing ethernet over usb would be the most convenient way to talk to whatever board is talking to the microcontrollers - and encoders, but what do I know? see disclaimer below). I can submit a tentative circuit board design if needed**. I do know my way around optical encoders, microcontrollers and such, and high-level languages are not a problem, but I have litterally zero experience in linking both through USB, so YMMV, as the cool kids say. The datastream needed is really more a datatrickle, so the Ben's USB 2.0 will be plenty fast. That's a good start, right? RIGHT?
*Nah, just kidding
** Caveat lector: all circuit board designs I might submit will be heavily inspired by pre-existing, proprietary designs belonging to various companies, all of which are long dead -but some might have been bought by Oracle, some of the angles might be rounded, which I hear is patented by Apple, and component colour might involve brown, so beware the Zune patent pool; your status = warned. The designs predate the "patent the obvious" goldrush, which is good, but almost always involve a 386 chip, which is bad. Well, for some values of "bad".