  Rapid advances in perception have enabled large pre-trained models to be used
out of the box for transforming high-dimensional, noisy, and partial
observations of the world into rich occupancy representations. However, the
reliability of these models and consequently their safe integration onto robots
remains unknown when deployed in environments unseen during training. In this
work, we address this challenge by rigorously quantifying the uncertainty of
pre-trained perception systems for object detection via a novel calibration
technique based on conformal prediction. Crucially, this procedure guarantees
robustness to distribution shifts in states when perceptual outputs are used in
conjunction with a planner. As a result, the calibrated perception system can
be used in combination with any safe planner to provide an end-to-end
statistical assurance on safety in unseen environments. We evaluate the
resulting approach, Perceive with Confidence (PwC), in simulation and on
hardware where a quadruped robot navigates through previously unseen indoor,
static environments. These experiments validate the safety assurances for
obstacle avoidance provided by PwC and demonstrate up to $40\%$ improvements in
empirical safety compared to baselines.
