Learning-Based Adaptive Navigation for Scalar Field Mapping and Feature Tracking

Scalar field features such as extrema, contours, and saddle points are essential for applications in environmental monitoring, search and rescue, and resource exploration. Traditional navigation methods often rely on predefined trajectories, leading to inefficient and resource-intensive mapping. This paper introduces a new adaptive navigation framework that leverages learning techniques to enhance exploration efficiency and effectiveness in scalar fields, even under noisy data and obstacles. The framework employs Partial Differential Equations to model scalar fields and a Gaussian Process Regressor to estimate the fields and their gradients, enabling real-time path adjustments and obstacle avoidance. We provide a theoretical foundation for the approach and address several limitations found in existing methods. The effectiveness of our framework is demonstrated through simulation benchmarks and field experiments with an Autonomous Surface Vehicle, showing improved efficiency and adaptability compared to traditional methods and offering a robust solution for real-time environmental monitoring.