I am helping mentor with FIRST Robotics Team 830 this year. Here are the rules for the  2013 FIRST Robotics Competition.  The TL;DR is that the robot basically needs to collect and shoot frisbees and climbing a really tall tower. The video below describes things very succinctly.

We need to get this done in the mater of just a few weeks. I started looking for a few inspiration ideas.

A personal favorite, the RiSE robot from the KodLab. A little too complex for our timeframe.

I really like this mechanism but I am not sure it will work on the pyramid.

Here is a slightly simpler version of the same mechanism.

This is a similar approach. Not quite applicable to our situation.

Here is a FIRST team actually meeting the challenge.

This design looks like it could be used for our applications with some modifications.

On the subject the frisbee launching this mechanism rules.

Finally, a nice primer on the physics of frisbee launching.