Schur-MI: Fast Mutual Information for Robotic Information Gathering

TL;DR

Schur-MI introduces a computationally efficient method for mutual information in robotic planning, enabling real-time adaptive exploration by reducing calculation costs through innovative matrix factorization and reuse strategies.

Contribution

It presents Schur-MI, a novel Gaussian process-based MI formulation that significantly accelerates computation for real-time robotic information gathering.

Findings

Achieves up to 12.7x speedup over standard MI methods.

Reduces MI evaluation complexity from O(|V|^3) to O(|A|^3).

Validated through real-world bathymetry data and autonomous surface vehicle trials.

Abstract

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.