Actually, sudden collisions and rapidly changing dynamic loads are exactly why you would want to use a CVT for an application like a FIRST robot.
Follow the load path for a typical FIRST robot with a traditional gear train providing power to the wheels (or treads or whatever). When the robot slams into a wall, or rapidly goes from forward to reverse at full speed, the shock load transmitted through the gear train will be significant and can be enough to cause failure of the drive train. Examination of a number of case histories has shown that the in the vast majority of cases (better than 95%), the weak point in the system is in one of two places. If the gear train is designed properly, the failure mode will be a loss of traction between the wheels and the ground, and the wheels will just spin in place. Annoying, but not fatal.
But the other frequently seen mode is when the wheels do not break free, and the entire shock load is transmitted through the gear train. All too frequently this results in broken gear teeth and a trashed transmission requiring extensive repair or replacement. This is because the gear teeth tend to be the weakest points along the load path. Unless specific precautions are put in place (ie. designing primary failure points with shear pins, properly calculating tooth face width to increase load tolerance, etc.), the result is that a gear is turned into a disk. This failure mode makes up the vast majority of transmission failures that are seen at FIRST events (other than the problem of having the silly wire clips fall out of the Bosch gearboxes and causing them to drift into neutral that was a big problem a few years ago, but fortunately we don’t have those any more, so the less said about that situation the better).
Alternately, the failure mode in a CVT is a non-fatal event. The load path between the input and output elements is across an intermediate friction drive (based on the design, either balls, rollers, disks, or splines are used as the intermediate elements). When the system is over-loaded, the friction in the drive system is overcome, and the elements slip in relation to each other. In the worse case, there will be surface wear on either the intermediate element or the torque plates which may shorten the overall lifetime of the drive. But it is not a catastrophic failure, and a properly designed CVT will have wear compensation adjustments built in that will enable the CVT to continue operating.
This is exactly the sort of capability that you want to have on a robot that is going to see repeated severe shock loads. In a situation where you have a choice between a traditional gear train and a CVT, and both have been properly designed to withstand the same loads, and you know/suspect you are going to have dynamic shock loading situations that exceed the load ratings of the transmission, then selecting the system with the non-fatal failure mode would be a prudent choice.
Yes, I have repaired one. I have also designed one from the ground up.
-dave