What's a good egg substitute in pizza dough? I'm trying to perfect my pizza dough recipe, and build a device that measures out and adds the ingredients to the mixer automatically.

I'm using an egg in the recipe, but making a machine that cracks an egg and puts it in a bowl is too complex for me. 

Is there an egg substitute that comes in either powder or liquid form that works well in pizza dough? Anyone had experiences using egg substitutes in pizza dough, and which ones worked/didn't work?

The future of pizza depends on it ;)

I thought the recipe would be helpful because the substitute might work better/worse depending on the other ingredients. The goal of the recipe is a fluffy, sort of sweet, soft pizza crust, and I usually do a Hungry Howie's style garlic herb seasoning on it.

1 cup milk

1/4 cup vegetable oil

1 tsp salt

1/4 cup sugar

1 egg

3 3/4 cup flour

2 tsp bread machine yeast
This doesn't look like a recipe for pizza dough, rather it looks more like a naan or flatbread recipe. I am not exactly sure what you are aiming for, but why not simply eliminate the egg and increase the milk (or add water) by a small amount to compensate for the lost moisture?