A Hough transform approach to safety-aware scalar field mapping using Gaussian Processes

This paper presents a framework for mapping unknown scalar fields using a sensor-equipped autonomous robot operating in unsafe environments. The unsafe regions are defined as regions of high-intensity, where the field value exceeds a predefined safety threshold. For safe and efficient mapping of the scalar field, the sensor-equipped robot must avoid high-intensity regions during the measurement process. In this paper, the scalar field is modeled as a sample from a Gaussian process (GP), which enables Bayesian inference and provides closed-form expressions for both the predictive mean and the uncertainty. Concurrently, the spatial structure of the high-intensity regions is estimated in real-time using the Hough transform (HT), leveraging the evolving GP posterior. A safe sampling strategy is then employed to guide the robot towards safe measurement locations, using probabilistic safety guarantees on the evolving GP posterior. The estimated high-intensity regions also facilitate the design of safe motion plans for the robot. The effectiveness of the approach is verified through two numerical simulation studies and an indoor experiment for mapping a light-intensity field using a wheeled mobile robot.