I'd like to be able to let users resequence the images they've uploaded to a site.

Currently, my site's users use the File Manager UI for uploading files via a simple form control, but this doesn't seem to allow resequencing. From the dashboard, a site admin can resequence files that have been added to a file set, but I can't see how to allow non-admins to do this: the File Manager UI made available to them seems to be unaware of File Sets (hence resequencing).

I've tried finding API doco, but failed.

Is there any straightforward way to allow users to resequence images?