Global Uncertainty-Aware Planning for Magnetic Anomaly-Based Navigation

TL;DR

The paper tackles navigation and localization in GPS-denied environments using magnetic anomalies by introducing MagNav, a global, multi-objective planner that uses entropy maps derived from magnetic field gradients to steer paths toward high-information regions while pursuing mission goals. It introduces a concrete entropy-map construction from magnetic data and a potential-field formulation that combines goal progress with information gain, implemented with a Stanley controller for path tracking. Hardware experiments validate improved localization stability and accuracy, demonstrating that entropy-map–guided paths reduce localization uncertainty and are robust to initial conditions, with adaptability to other gradient-based maps such as topography or underwater depth. The work advances active localization by providing a globally informed planning framework that complements existing local planners and offers a practical, gradient-based approach for GPS-denied navigation in diverse environments.

Abstract

Navigating and localizing in partially observable, stochastic environments with magnetic anomalies presents significant challenges, especially when balancing the accuracy of state estimation and the stability of localization. Traditional approaches often struggle to maintain performance due to limited localization updates and dynamic conditions. This paper introduces a multi-objective global path planner for magnetic anomaly navigation (MagNav), which leverages entropy maps to assess spatial frequency variations in magnetic fields and identify high-information areas. The system generates paths toward these regions by employing a potential field planner, enhancing active localization. Hardware experiments demonstrate that the proposed method significantly improves localization stability and accuracy compared to existing active localization techniques. The results underscore the effectiveness of this method in reducing localization uncertainty and highlight its adaptability to various gradient-based navigation maps, including topographical and underwater depth-based environments.

Figures (8)

• Figure 1: Pipeline for the Informative Potential Field Global Planner. The magnetic anomaly map, characterized by rich gradients, is used to compute an entropy map. This entropy map enables the application of a multi-objective potential function that balances both information gain and progress toward a specified goal. The resulting multi-objective path is depicted in the 3D plot, where the planned path is shown over the potential field, along with its projection onto a 2D plane as a dotted line.
• Figure 2: (a) Simulated paths with localization uncertainty ellipses over a magnetic anomaly map. Paths through high-intensity variation reduce uncertainty, while low-variation paths show growing covariance. White regions correspond to areas where uncertainty is reduced. (b) Determinant of localization uncertainty for the paths in (a), with highlighted areas corresponding to the white regions of reduced uncertainty in (a).
• Figure 3: TurtleBot4 with a total field magnetometer with vector add-on and motion capture markers.
• Figure 4: Entropy map generated from the magnetic anomaly map.
• Figure 5: (a) The planned path through the entropy map. (b) The planned path through the magnetic anomaly intensity map.