提出快速互信息计算方法，让机器人实时规划更高效。
Schur-MI: Fast Mutual Information for Robotic Information Gathering
- 利用高斯过程的迭代结构复用中间计算结果
- 通过舒尔补避免大规模行列式计算，提速12.7倍
- 适合需要在线决策的自主机器人探索任务
互信息（MI）是机器人信息采集（RIG）中广泛使用且理论严谨的目标函数，适用于传感器部署和信息导向路径规划。但其高计算成本——主要源于重复的对数行列式计算——限制了在实时规划中的应用。本文提出Schur-MI，一种基于高斯过程的MI新公式：(i) 利用RIG的迭代特性，在规划步骤间预计算并复用昂贵的中间量；(ii) 采用舒尔补分解避免大规模行列式运算。两者结合使每次MI评估的复杂度从 $\mathcal{O}(|\mathcal{V}|^3)$ 降至 $\mathcal{O}(|\mathcal{A}|^3)$，其中 $\mathcal{V}$ 和 $\mathcal{A}$ 分别表示候选与已选传感位置。在真实海底地形数据集上的实验表明，Schur-MI相较标准方法最高提速12.7倍。与自主水面艇（ASV）进行自适应路径规划的实地测试进一步验证了该方法的实用性。Schur-MI使信息论目标在在线规划中变得可行，推动理论目标与实际机器人探索之间的融合。代码开源：www.sgp-tools.com
原文摘要 · Abstract (English)
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
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