Artificial intelligence and machine learning involves software programs classifying data and making decisions about things in the real world. Robotics involves manipulating objects in the real world. This creates the ability to manipulate the real world using a combination of machine learning and robotics.
At the same time, artificial intelligence programs can use data from the real world acquired through robotics to improve their performance. AI/machine learning have a symbiotic relationship.
One obvious application of AI to robotics is in computer vision. Computer vision allows robots and drones to navigate the real world more accurately. This has other applications for people: One experimental robot could remind people about ordinary things such as leaving milk outside of the refrigerator.