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Modern nonlinear control theory seeks to develop feedback controllers thatendow systems with properties such as safety and stability. The guaranteesensured by these controllers often rely on accurate estimates of the systemstate for determining control actions. In practice, measurement modeluncertainty can lead to error in state estimates that degrades theseguarantees. In this paper, we seek to unify techniques from control theory andmachine learning to synthesize controllers that achieve safety in the presenceof measurement model uncertainty. We define the notion of a Measurement-RobustControl Barrier Function (MR-CBF) as a tool for determining safe control inputswhen facing measurement model uncertainty. Furthermore, MR-CBFs are used toinform sampling methodologies for learning-based perception systems andquantify tolerable error in the resulting learned models. We demonstrate theefficacy of MR-CBFs in achieving safety with measurement model uncertainty on asimulated Segway system.

Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions