LIDS Tea Talk: Lorenzo Shaikewitz

“High-Probability Ellipsoid Bounds on Object Pose Uncertainty via SDP Relaxation”

Quantifying the uncertainty of an object’s pose estimate is essential for robust control and planning. We propose estimator-agnostic uncertainty bounds which are guaranteed to cover the ground truth object pose with high probability under minimal assumptions. Using conformal prediction, we can obtain high-probability bounds on the locations of specific object keypoints. Collectively, these bounds induce an implicit, non-convex set of pose uncertainty constraints. In this talk, we reduce this set to explicit ellipsoidal outer bounds on object translation and orientation uncertainty. Our approach consists of a hierarchy of outer semidefinite approximations inspired by the classical S-lemma which is guaranteed to converge to the true minimum volume bounding ellipsoid. This requires no initial guess of the bound's shape or size and retains high-probability coverage guarantees. We test our approach on three real-world datasets and show it consistently returns useful uncertainty bounds.