jkuebbing

Hardware will be highly dependent on the tasks that must be completed. Some pieces will need to be able to perform highly parallel calculations. Others may only need to be able to do memory manipulation - network/tree searches and the like. Still others will only be interested in communicating with or to the robotic device.
 
Communications is always the difficult part of this type of system. What occurs to me initially is to use something like tcp/ip sockets for interprocess communications. This allows for easy movement of processing nodes to various pieces of hardware. One might start with everything running on a single piece of hardware. As more functionality is added and knowledge gained, nodes can be spun off to specialist hardware without rewriting. Separate pieces would be in a dedicated high-speed network.

Presumably you have a rough outline of the software system. Break the "big one" into different parts. One part builds the environment models. Another part does the analysis. And yet another part takes the analysis and determines what, if any direction needs to be passed back to the robot. One might even break up the model building into various parts, depending on what is actually being done. The tricky part with this approach is the communications between sub-systems.
 
While we always think that speed is measured in bps. That is not the case in a complex system. Transmitting information instead of raw data is much faster and requires much less bandwidth. So, for example, the robot sends IR data to the IR processing sub-system. That unit can simply compare the new data to what came before and pass on only key differences/changes. The model builder can adjust the model, etc. (Don't get hung up on how inaccurate my characterization is. The principal is the important part.)
 
These sub-systems can easily be individual pieces of software running on the same hardware. (Hopefully not simply parts of the same monolithic program.) Since the amount of actual data passing between the sub-systems is reasonably small, they could instead run on separate computers (or several sub-systems could run on a separate computer). This model is analogous to the human brain.

You can buy single slot workstation cards. Water cooling a card won't actually save you that much space. PCI-E risers are probably a better option - they're what I use.
For PSU, I don't know my around workstation ones, though I'm sure you can find ones that are dust proof.
 
You can do that, seems like a lot of effort though, get a good SSD and you can write as much as you like to them. The ones I mentioned are high end consumer products and are warrantied for 10 years. SSDs, particularly good ones, can have huge amounts written to them.