Assuming that you have a spatially referenced blue marble image then you can use gdalwarp to do it.
I found these instructions on how to acquire the correct paramters for the Robinson projection
First, go back to spatialreference.org and search for Robinson. Its ID code is ESRI 54030 – not part of the EPSG library. Click on the link for the projection to open its window. You’ll be able to look at the projection data in a number of standard file formats. Select OGC_WKT from the list, and it will open the text in a new window, showing you the parameters of that projection. In your browser, go up to file, save as, and save the file as robinson_ogcwkt.txt in the same directory as the shapefile you want to reproject.
so something like
gdalwarp -t_srs robisnon_ogcwkt.txt bluemarble.tif robinsonBM.tif
should do it.
If you need to generate a spatially referenced Blue Marble image see my notes.