What I previously did in ArcGIS 10.1 is to convert the polylines to points in a cell size (25 km) that is quite larger than the study area (10). This way, I could "average" the points. Then I converted the raster cells back into lines. In a way they were "averaged" but the lines are very straight and formed small box-like in the intersection following the cell size.
I have read some solutions using R. I am interested to be provided with suggestions to do this in R.