HACKER’S SOLUTIONS: HACK THE REMOTE
The official Roomba remote is an infrared (IR) device like a TV remote, so not immediately compatible with SmartThings. There is a zigbee radio in some models, not all, but it uses a proprietary dialect, so not much joy there, either. There is a serial port inside the device and some people have made an arduino shield device that plugs into the serial port and then has a transmitter, but that’s some serious overkill,looks ugly, raises the footprint so it may run into stuff like when going under chairs, and voids the Roomba warranty, so probably not a first choice solution. 
There is a commercially available version similar to the arduino hack but it costs 100 euros and only works with older Roomba models. @sidjohn1 was able to get this (called thinking cleaner ) to work with his SmartThings, but it’s obviously an expensive way to go, especially since it only solves the Roomba issue.
Smartthings Roomba Control via Thinking Cleaner Version 1.5.1 Released
It’s pretty easy to control a Roomba via an iTach WiFi to IR bridge, but while a more elegant solution than the Arduino path, it requires some fairly serious DIY commitment. Cost is about $100 for a bridge but you can control multiple devices from that. @scottinpollock could say more about the iTachs, he uses them for other IR controllable devices like home entertainment systems.
Some people have been able to get one of the various Harmony remote models to work with one of the various Roomba models, but there’s not 100% compatability and you still need something to connect the Harmony to SmartThings, which isn’t easy right now.
https://www.youtube.com/watch?v=7_3GDmol58c
So those are all older model Roomba solutions.
For the newer models, there is a WiFi option with JSON files and a lot of third party developers have taken advantage of that to create Roomba controllers that work as smartphone apps or with other home automation systems.
RooWiFi , for example, has plug ins for Vera and Domotica. Those are NOT zwave protocols, they’re using a webservice interface.
http://www.roowifi.com/home-automation/
I would expect something like this could be built for SmartThings as well, it just doesn’t look like anyone has.
So for the technical audience, that’s three completely different ways of accessing the Roomba controls: via standard IR one way communication, like the official remote; via a new antenna plugged into the internal serial port; or as a WiFi connected web service.
ENGINEER’S SOLUTION: SMART PRESSURE MAT AT THE DOCKING STATION
From a completely different direction, if you park the Roomba under a shelf or sofa, someplace sheltered, you should be able to put a proximity sensor so you can tell when the Roomba has left or returned to the docking station.
You should also be able to do this easily and more cheaply than any other solution with a pressure mat that the Roomba drives over, but it would have to be high sensitivity as many cheap pressure mats don’t trigger until there’s 25 pounds of pressure to avoid false alarms. However, LondonMat does make some nice ones that trigger at a “nominal” 5 pounds of pressure. Some Roomba models are over 7 pounds, and I suspect these would successfully trigger. You would still have to attach a contact sensor to these to make them networkable, but that’s just the “smart door mat” project:
Roomba weights:
LondonMat manufacturer site, but these are available at other retailers as well. See their online shop for their pricing. The minimal force ones are called “switching mats” or “signal mats.”
http://www.londonmat.com/Mats/SignalMatProd.html
Oh, and here’s a guy who made his own roller switch pressure mat using LIttleBits, then used its WiFi connector to talk to IFTTT (there’s a LittleBits channel). I suspect the total cost would end up being more than buying a pressure mat, and you might run into a 15 minute IFTTT polling delay that wouldn’t fit the alarm code use case, but it looks like a fun project and at least demonstrates proof of concept for the pressure mat idea. 
http://littlebits.cc/projects/roomba-has-finished-cleaning
So if it was me, I’d start from a signal mat and work out from there. Roomba on mat = one mode, Roomba off mat = another.
But you could start from the controller side if you prefer. 