I came up with a design that can pick up balls from the ground, shoot (possibly full-court), pass and catch. However, it would be a hassle to get it within the dimensions because it involves completely enclosing the ball!
Check out the design
here.
I haven't drawn the catching feature on it. However, just cut out a door at the top of the cage, move the conveyor belts to the side and build a hopper on top of the opening! Also, it is linear so it will also look kinda cool!
By the way, are we allowed to extend pass the chassey of the robot by, I believe 20 inches on each side, or is it just one side? If so, this is a perfectly feasible idea!!!