Do my stepper motors provide enough torque to move a small cart?

I'm not sure how to do it with external indicators. It's because I need to make it move to discrete positions across a library like setting (see picture).

It would be hard to control its position by calculating speed and distances and setting the speed for an X amount of time such that it reaches that point and taking acceleration and deceleration into account would be a headache.

In the picture (basic d, I have a home position for my cart and each node on the map is where I want it to be able to get to. Then it should basically face the shelf and grab a book (very light weighted) and bring it back to home position.