You could use the SAMBA protocol (or Apple's implementation of it), to connect to a Windows Share.
Either open Finder and choose "Go" -> "Connect to Server" in the menu bar.
Now connect to your share(s) using the SMB:// as protocol definition. If activated it will ask you for authentication afterwards. Then the share will be mounted like any other mount point.
Or you could use the terminal to mount the file system using the
After you've mounted the Windows Share you should be able to use any command line tool or GUI software do to your copying. Instead of robocopy you could use rsync for example (which is built in and pretty powerful).
One note: Just remember that saving files directly from within apps on a share could cause some troubles if they are using Apples's Versions feature, which is not supported by FAT or NTFS file systems.