Similar to the above posts we read the rules and start discussing the aspects of the game that we see are going to be played. Over the next week we brake off into smaller groups that prototyped shooters, brainstormed how to climb the tower, and continued to brainstorm robot concepts. Everyday during week 1 we typically begin with a meeting, break for projects, and then return to a meeting as mentors come in from work and we break for dinner.
We worked through some basic Lego robots this past year on a tabletop version of the pyramid to visualize how to climb the pryamid. Through it we learned a lot about the geometry and involved and where the best route of attack was.
For some robot concepts like this past year's shooter and some mechanisms in 2012 we worked on them until we had the proof of concept down/the numbers we needed to design it. Our climber this year was brainstormed until a student came up with an idea of which he CADed out and designed until we had what we needed around the end of week 3 to build it. We tested it some more, kept iterating some aspects of it until we had what we needed in week 5 to build the competition climber which at that point was a nearly identical system except the parts were re-cut and less cheese holed from moving components around. Our shooter in 2012 took a similar road in that our prototype was tweaked and modified until eventually we took it apart, painted it, and built a mounting system to the robot. The same shooter we started with in week 2/3 stayed to be the one on the competition robot.
Here is a photo from 2012 where in the course of a few evenings in week 1 we prototyped skid plates for the bottom of our robot to cross the bump as well as our ball pickup system. Very basic systems but we learned what we needed from them before making the models in CAD.