Resolume has no support for external device control natively.
However there are ways you can work around this, for example you can create your own FreeframeGL plugin which passed the video through without effects and has parameters which control external devices via whatever interfaces you like. This is quite involved though and you'll need to understand some C to go down this route. (the openframeworks plugin used to be a good and easy introduction to FFGL plugins, I used it to make an OSC end actions plugin for resolume 3, though you may have difficulty getting them running on recent versions of OF)
You may be able to do something in Flash too - though the stability of flash in resolume is somewhat less than perfect. Recently I've used QuartzComposer to control external devices - you can load in a quartz patch as though its a video clip and then have whatever parameters you need controllable from within resolume. It works really well, i've systems out on tours running kinect cameras operated through QC+Resolume controlled by the lighting guy over artnet from FOH. The quartz patch when loaded into resolume allows for tilt and depth control of the kinect camera with realtime tweaking possible from the lighting desk.
I'd like to see more support for external devices in reolume, it would be great to have a generic comms system where you could send strings out via UDP /TCP / RS232 / whatever. Being able to do things like shutter projectors and control matrix switchers directly from resolume would be fantastic and would bring the application inline with other media servers such as Catalyst.
In the meantime you can create your own workarounds, though its much harder and more time consuming than it should be really.