I designed and programmed my first 3x3 Rubik Cube Solver robot in the summer of 2007. The Robot used just 2 Light sensors to scan the cube's colours, then calculates a 50 move solution using only the NXT brick. It took almost 10 minutes to solve a well-mixed cube.
My Robot was one of the first Lego robots to solve a Rubik Cube automatically.
In 2013, I re-designed the robot using the same concept of having one motor to flip the cube over quarterly, and another motor to adjust/grip the cube.
An Android phone was used to capture each facelet's colour, and to compute a less than 20 move solution using the Two phase algorithm. It took less than 5 seconds to find a 20 move solution with a Google Nexus phone. The total solving time is often less than 2 minutes.