  We consider perception-based control using state estimates that are obtained
from high-dimensional sensor measurements via learning-enabled perception maps.
However, these perception maps are not perfect and result in state estimation
errors that can lead to unsafe system behavior. Stochastic sensor noise can
make matters worse and result in estimation errors that follow unknown
distributions. We propose a perception-based control framework that i)
quantifies estimation uncertainty of perception maps, and ii) integrates these
uncertainty representations into the control design. To do so, we use conformal
prediction to compute valid state estimation regions, which are sets that
contain the unknown state with high probability. We then devise a sampled-data
controller for continuous-time systems based on the notion of measurement
robust control barrier functions. Our controller uses idea from self-triggered
control and enables us to avoid using stochastic calculus. Our framework is
agnostic to the choice of the perception map, independent of the noise
distribution, and to the best of our knowledge the first to provide
probabilistic safety guarantees in such a setting. We demonstrate the
effectiveness of our proposed perception-based controller for a LiDAR-enabled
F1/10th car.
