I. Introduction
Staircases, an ubiquitous feature of human-built environments throughout history, have enabled access to different levels within structures. With the increasing availability of legged robot platforms, significant strides have been made in enabling agile locomotion across diverse terrain, including staircases. However, ensuring safe navigation in complex real-world scenarios, such as cluttered or damaged staircases, remains a formidable challenge. This necessitates robots that can not only perceive their environment but also continuously update their knowledge about the environment by inferring the underlying structure.