Schur-MI：ロボット情報収集のための高速相互情報量計算
Schur-MI: Fast Mutual Information for Robotic Information Gathering
ガウス過程の相互情報量計算をSchur補分解と中間量の再利用で高速化し、リアルタイムの情報収集計画を可能にした。
詳しい要約
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著者: Kalvik Jakkala, Jason O'Kane, Srinivas Akella
分類: cs.RO
原文アブストラクト
Mutual information (MI) is a principled and widely used objective for robotic information gathering (RIG), providing strong theoretical guarantees for sensor placement (SP) and informative path planning (IPP). However, its high computational cost - dominated by repeated log-determinant evaluations - has limited its use in real-time planning. This paper presents Schur-MI, a Gaussian process (GP) MI formulation that (i) leverages the iterative structure of RIG to precompute and reuse expensive intermediate quantities across planning steps, and (ii) uses a Schur-complement factorization to avoid large determinant computations. Together, these methods reduce the per-evaluation cost of MI from $\mathcal{O}(|\mathcal{V}|^3)$ to $\mathcal{O}(|\mathcal{A}|^3)$, where $\mathcal{V}$ and $\mathcal{A}$ denote the candidate and selected sensing locations, respectively. Experiments on real-world bathymetry datasets show that Schur-MI achieves up to a $12.7\times$ speedup over the standard MI formulation. Field trials with an autonomous surface vehicle (ASV) performing adaptive IPP further demonstrate the method's practicality. By making MI computation tractable for online planning, Schur-MI helps bridge the gap between information-theoretic objectives and real-time robotic exploration. Our code is available at: www.sgp-tools.com
