Very little in terms of what you would consider AI or ML. It's a lot of trig and control theory. You do a lot of the math beforehand to figure out the script the craft will follow to reach the ISS. Once it gets close, you either use manual controls or let autopilot do the docking. The autopilot is basically looking some dots on a camera and firing the thrusters to make the dots line up right. It's more like a dumb PID controller than an AI. The autopilot isn't learning anything or somehow making connections that weren't already programmed. This is all stuff NASA figured out how to do in the 60s so it's nothing novel except for the mission and the hardware the math is done on.