This paper develops rollover prevention guarantees for mobile robots using control barrier function (CBF) theory, and demonstrates these formal results experimentally. To this end, we consider a safety measure based on the zero moment point to provide conditions on the control input through the lens of CBFs. However, these conditions depend on time-varying and noisy parameters. To address this, we present a differentiator-based safety-critical controller that estimates these parameters and pairs Input-to-State Stable (ISS) differentiator dynamics with CBFs to achieve rigorous guarantees of safety. Additionally, to ensure safety in the presence of disturbance, we utilize a time-varying extension of Projection-to-State Safety (PSSf). The effectiveness of the proposed method is demonstrated through experiments on a tracked robot with a rollover potential on steep slopes.

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