It's possible.
I would suggest breaking the problem up into some distinct pieces.
Simulation - this is purely simulating the position of the robot and the environment around it. Completely ignore anything related to graphics with this task. Focus in on just the maths involved. e.g. If my robot is here and a rock is over there, is my robot touching the rock? As it's a 2D app, you might be able to get away with a lot assumptions and simplifications. e.g. the robot and the rocks can all be simulated via squares or circles.
(Circles are especially easy to deal with as it basically just involves checking that the distance between the centre of the robot and the centre of the rock is sufficiently large.)
Networking - Create two simple console apps and get them to communicate via the sockets API. Once you've got this working then integrating it into an XNA game will be more obvious.
UI - this is where you can (finally) concentrate on graphics and user input. This sounds like it can be achieved with the regular Spritebatch draw calls and input reading methods (such as Keyboard, Mouse or GamePad).