I am researching for a student nano-cubesat program, and came across the use of flywheels for attitude control. I looked up some successful projects and found that one university had used 4 reaction wheels in place of 3. Why would that be? Wouldn't using 3 be simpler? Is it just because of the redundancy? If so, isn't this a heavy price to pay in terms of operating complexity for the safety gained?
Three is indeed simpler. However, reaction wheels, being moving parts, are more prone to failure than purely electrical systems, especially for missions lasting many years where bearings may eventually wear out, especially if lubrication retention is not adequately addressed. Adding a 4th wheel makes some of the math more complex for the ADCS software, but it's typically a trivial issue compared to the rest of the problem and it's a nice way to add just one part that backs up three potential failure points, so it can be a good trade for missions needing a little more reliability. For most cubesats, the short lifetimes and limited volume mean that 3 wheels is the best choice, especially if the wheels come from a commercial provider who has a good heritage of success on orbit. If the wheels are student built or experimental, you might still want a 4th just in case, even for a cubesat.