I post this solution that could potentially help anyone who need it in the future
On the principle, you must create an addon, to have a new joystick profile
I based myself on the SNES controller (/usr/share/kodi/addons/game.controller.snes)
And controller MSX keyboard (/storage/.kodi/addons/game.controller.msx.keyboard/)
So I created the corresponding files
└── storage
└── .kodi
└── addons
└── game.controller.acgam-r1
├── addon.xml
└── resources
├── icon.png
├── language
│ └── resource.language.fr_fr
│ └── strings.po
├── layout.png
└── layout.xml
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You then need to create a file to assign the buttons to the Kodi functions (the predefined functions did not satisfy me in : /usr/share/kodi/system/keymaps/)
The path for this file
/storage/.kodi/userdata/keymaps/customcontroller.ACGAM-R1.xml
This allows complete customization for commands
/! Pay attention to the syntax into the files, it’s very important (especially for the file in the /keymaps folder)
Once all this is done, you have to enable the extension (addon) in Kodi, I have also disabled the updates for this extension
A screenshot of my addon
helpful links
HOW-TO:Modify joystick.xml - Official Kodi Wiki
List of built-in functions - Official Kodi Wiki