The Egg-Bot is designed to draw vector art, that is, the kinds of drawings that you can make with a single pen on paper, where you try to make your drawing out of long continuous strokes. It is not designed for bitmap or "raster" graphics, where you represent an image by dots that are either present or not. You can make it draw arrays of dots, one at a time, but this is slow and inefficient work for a machine that can draw lines quickly.
The fundamental problem is one of art, not of science: There are infinitely many ways to represent an image with a set of lines, and there is no one "right" way to do it. There are all kinds of methods to approximate a drawing with an automatically generated sketch, including TSP art and stipple plots.
Another approach is to use the fact that Inkscape is capable of tracing bitmap images to produce vector approximations of the images. On this page, we have links to various tutorials about tracing images within Inkscape.
Here are links to some tutorials about how to use Inkscape's tracing tools:
- Multi-part tuturial at the unofficial Inkscape manual
- Official tutorial on tracing
- tutorial by Darth_Gim (aka LDS-Jedi) at Deviantart
Additional relevant tutorial links are welcome, of course!
After using Inkscape's "Trace Bitmap" tool, you may wish to try the experimental Eggbot extension Post process trace bitmap.