If you're interested in a more structured approach to Lego robots, you should check out FIRST Lego League! [0]
It's a competition where kids learn not just how to program the robot, but important critical thinking skills, how to appropriately attack a problem, and how to make a measurable impact in their communities.
FIRST makes it easy for parents to start a team for a small group of kids in your neighborhood, and provides structure, mentorship, and the competition format at the end of the season.
Disclosure: I occasionally judge FLL events. These kids are some of the most amazing and inspiring children I've encountered, and I recommend it simply because I think it's a fantastic program.