How to be more "natural" with my girlfriend?

Probably thinking about it too much isn't helping. Rather than going on formal "dates" to the movies, dinner, coffee or whatever it is you do, what about doing something a bit more adventurous? Talk to her about what she's always wanted to do, what she'd put on a list of "things to do before I die/reach 40/get married/whatever". See if there are any that are possible that you'd like too, and do them. You will be having fun together, getting to know each other better, and affection will happen more easily because you'll be sharing experiences and thinking about those, rather than sitting still worrying about how you should act. They dont have to be very wild or expensive, just something you have both never tried and have wondered about. Do a few things, not just one, and dont present it to her as a practical solution to your "robotic" behaviour, just get chatting and ask her about the things she'd really like to do, if she could, and suggest you try them. All of this is going to help you get to know each other, and relax with each other, and sharing experiences is one of the best bonding activities there is. Good luck, and have fun!