So as an engineer you are constrained mostly by the laws of physics and available cash (1).
I think what you asked for is
Code:
Browser/Javascript <---> Driver Station <---> Robot
and I'll posit that you could put an ActiveX control on the DS and have it fill the blanks in.
OTOH, I have to ask why? There will be pretty decent lag between the browser and the DS, so any real time control is going to be hard. And during a match, the DS/Robot are on a closed network, so you won't be able to get to it from the outside.
Thanks!
(1) I used to say "laws of physics, time and cash; but a roboteer pointed out that going back or stopping time would break the physics part, so I shortened it.