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 letter 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 validate its practicality. By making MI computation tractable for online planning, Schur-MI helps bridge the gap between information-theoretic objectives and real-time robotic exploration.

翻译：互信息（MI）是机器人信息采集（RIG）中一种基于原理且广泛使用的目标函数，为传感器部署（SP）和信息路径规划（IPP）提供了强有力的理论保证。然而，其高昂的计算成本（主要由重复的对数行列式计算主导）限制了其在实时规划中的应用。本文提出Schur-MI，一种高斯过程（GP）互信息公式，它（i）利用RIG的迭代结构，在规划步骤间预计算并重用昂贵的中间量；（ii）采用舒尔补分解来避免大规模行列式计算。这些方法共同将每次MI评估的计算成本从$\mathcal{O}(|\mathcal{V}|^3)$降低到$\mathcal{O}(|\mathcal{A}|^3)$，其中$\mathcal{V}$和$\mathcal{A}$分别表示候选和已选定的传感位置。在真实世界海底地形数据集上的实验表明，Schur-MI相比标准MI公式实现了高达$12.7\times$的加速。利用自主水面航行器（ASV）进行自适应IPP的现场试验进一步验证了其实用性。通过使MI计算适用于在线规划，Schur-MI有助于弥合信息论目标与实时机器人探索之间的差距。