Informative Path Planning in Random Fields via Mixed Integer Programming

TL;DR

This paper introduces a mixed integer programming approach for optimal path planning in random fields, aiming to minimize estimation error within a given budget, and demonstrates its effectiveness over existing methods.

Contribution

It develops a novel mixed integer quadratic programming formulation that optimizes over measurement subsets and estimators, enabling optimal solutions for the NP-hard problem.

Findings

Outperforms previous branch and bound algorithms in simulations

Provides a convex formulation applicable to various covariance structures

Achieves near-optimal solutions efficiently

Abstract

We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum error over a finite set of prediction locations. The problem is known to be NP-hard. However, we strive to compute optimal solutions by leveraging advances in mixed integer optimization. Our approach is based on expanding the search space so we optimize not only over the collected measurement subset, but also over the class of all linear estimators. This allows us to formulate a mixed integer quadratic program that is convex in the continuous variables. The formulations are general and are not restricted to any covariance structure of the field. In simulations, we demonstrate the effectiveness of our approach over previous branch and bound algorithms.