Robot Design and Challenge Competitions
These are just a few, there are a lot more if you google “robot competition”
RobotChallenge is an international championship for self-made, autonomous, and mobile robots. Each year robots compete in different competitions – Robot Sumo, Line Follower, Air Race, Humanoid Sprint, Puck Collect and Freestyle.
Rules and entry fees listed on website.
Robofest - Robofest is a festival of competitions and events with autonomous robots that encourages students to have fun while learning principles of physical science, computer science, technology, engineering, and math (STEM), and Information and Communication Technologies (ICT). Students design, construct, and program the robots. Any robotics kits are allowed in the construction of robots.
http://www.theroboticschallenge.org/ - Darpa Robotics Challenge