The robot can replicate recorded movements - brush angle, pressure, timing etc.
An photoshop filter can shift pixels around to make a photo look like an oil painting.
What nobody has come up with yet (and would likely be hard to develop, or at least costly) is a way to translate a photograph, or a photoshop filter into the set of movements required to render it in physical oil paint.
Getting a robot to actally lay down each stroke with paint is left as an exercise for the reader. ;-)
Photoshop filters and more advanced converters like DeepArt produce something which look like strokes, but have no concept of strokes. Illustrator convert to vector/stroke/outline uses a concept of stroke which makes no accounting for the drag and physics of a brush, and may not even by physically possible to produce.
There are, of course, some conversions which we can achieve already. We have pen-based plotters and could write simple contrast/cross hatching converters etc. But these are qualitatively different from scanning an image and converting it into the strokes for a robot arm.
http://jivp.eurasipjournals.springeropen.com/articles/10.118...
And there is a lot of work available on brushstroke analysis for authentication purposes. Here is a pop-sci example from about 8 years ago:
http://www.pbs.org/wgbh/nova/tech/art-authentication.html
Additionally, in terms of desktop graphics editors such as Photoshop and Illustrator, rest assured that Fractal Design Painter definitely had a model that incorporated (well, approximated anyway) medium, angle, brush size, pressure, direction changes, the color you were painting over, etc. 20 years ago, and the latest version of Corel Painter has added features such as particle systems and modeling individual bristles (and other features have been added in the interim).
The intent in Painter is to enable the creation of new works in a way that feels natural to artists used to traditional media (not to mention reproducing the appearance of those media), which isn't quite what we're talking about here, but hopefully this demonstrates that such models do actually exist.