CLOSURE: Fast Quantification of Pose Uncertainty Sets
arxiv(2024)
摘要
We investigate uncertainty quantification of 6D pose estimation from keypoint
measurements. Assuming unknown-but-bounded measurement noises, a pose
uncertainty set (PURSE) is a subset of SE(3) that contains all possible 6D
poses compatible with the measurements. Despite being simple to formulate and
its ability to embed uncertainty, the PURSE is difficult to manipulate and
interpret due to the many abstract nonconvex polynomial constraints. An
appealing simplification of PURSE is to find its minimum enclosing geodesic
ball (MEGB), i.e., a point pose estimation with minimum worst-case error bound.
We contribute (i) a dynamical system perspective, and (ii) a fast algorithm to
inner approximate the MEGB. Particularly, we show the PURSE corresponds to the
feasible set of a constrained dynamical system, and this perspective allows us
to design an algorithm to densely sample the boundary of the PURSE through
strategic random walks. We then use the miniball algorithm to compute the MEGB
of PURSE samples, leading to an inner approximation. Our algorithm is named
CLOSURE (enClosing baLl frOm purSe boUndaRy samplEs) and it enables computing a
certificate of approximation tightness by calculating the relative size ratio
between the inner approximation and the outer approximation. Running on a
single RTX 3090 GPU, CLOSURE achieves the relative ratio of 92.8
object pose estimation dataset and 91.4
registration dataset with the average runtime less than 0.2 second. Obtaining
comparable worst-case error bound but 398x and 833x faster than the outer
approximation GRCC, CLOSURE enables uncertainty quantification of 6D pose
estimation to be implemented in real-time robot perception applications.
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