The PID Rug Bump Challenge is the ability for a small robot (with 35mm radius wheels) to confront the edge of the thick Kilim rug in my lounge (17mm thick) with one wheel — the other remaining on the wood floor — without being deterred from its path, i.e., recovering from that bump whilst maintaining its original heading.
The "ideal" behaviour would be follows, quoting David Anderson of the DPRG:
Tuning the PID Controllers so that they respond in kind is the challenge.
More on this as the story develops...