Schur-MI: Fast Mutual Information for Robotic Information Gathering
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Mutual Information
Robotic Information Gathering
Real-time Planning
Computational Cost
Gaussian Process
Innovation
Methods, ideas, or system contributions that make the work stand out.
Schur complement
mutual information
Gaussian process
information gathering
real-time planning
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