I lead a four-person team that designed a gymnastics robot to compete on a set of rings to mimic human athletes. An IMU (inertial measurement unit: accelerometer and gyro) was used to provide feedback control.
Our robot, affectionately named Harry after the course professor, possessed a number of interesting characteristics. Our design approach for the mechanical design of the robot was "keep it simple" so we could focus on the controls and programming. The approach paid off - our robot was one of the few that actually worked during the presentation, and we won 1st place for the rings competition and 1st place overall for controls.
Open loop feedback (mechanical)
The mechanical design of the robot was an interesting challenge. When the robot is curled up, the center of gravity lies offset from the (axis of the) rings, causing the robot to perform crazy flips. This did not involve any additional coding and was the simplest way to accomplish the mission.
Closed loop feedback (software)
The robot uses an inertial measurement unit to calculate acceleration, velocity, and position of the robot. This information was used in a damping algorithm to quickly stop the robot's motion after a flip.