I recently had a go at trying to get a LibGDX to run on a Raspberry Pi. Any project. Unfortunately I failed. (If you've succeeded, please let me know, but from what I could glean from googling, no-one has succeeded yet.).
So instead I tried to get some Java code working that could read PS4 controllers/gamepads on a Raspberry Pi. My aim is to use the Pi as a mini-gaming-console, so I can keep it near our big TV and create some simple co-op games that I could play with my kids, rather than drag them over to a small laptop with its small screen.
And I succeeded! By standing in the shoulders of giants (in this case, the JInput authors) and finding the native JInput modules compiled for AMD, it seems to work.
The repo is here: https://github.com/SteveSmith16384/jinputtest . Currently only tested with PS4 gamepads. Let me know if it works for you.