Adaptive Robotic Information Gathering via Non-Stationary Gaussian Processes

TL;DR

The proposed family of non-stationary kernels named Attentive Kernel (AK), which is simple and robust and can extend any existing kernel to a non- stationary one, is proposed, which can guide an Autonomous Surface Vehicle to prioritize data collection in locations with significant spatial variations, enabling the model to characterize salient environmental features.

Abstract

Robotic Information Gathering (RIG) is a foundational research topic that answers how a robot (team) collects informative data to efficiently build an accurate model of an unknown target function under robot embodiment constraints. RIG has many applications, including but not limited to autonomous exploration and mapping, 3D reconstruction or inspection, search and rescue, and environmental monitoring. A RIG system relies on a probabilistic model's prediction uncertainty to identify critical areas for informative data collection. Gaussian Processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data is typically non-stationary -- different locations do not have the same degree of variability. As a result, the prediction uncertainty does not accurately reveal prediction error, limiting the success of RIG algorithms. We propose a family of non-stationary kernels named Attentive Kernel (AK), which is simple, robust, and can extend any existing kernel to a non-stationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used stationary kernels and the leading non-stationary kernels. The improved uncertainty quantification guides the downstream informative planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with significant spatial variations, enabling the model to characterize salient environmental features.

Figures (24)

• Figure 1: Diagram of A Robotic Information Gathering System. The goal is to autonomously gather informative elevation measurements of Mount St. Helens to efficiently build a terrain map unknown a priori. The color indicates elevation, and black dots are collected samples.
• Figure 2: Comparison of Gaussian Process Regression with Radial Basis Function Kernel and Attentive Kernel.
• Figure 3: Research Topics Related to RIG.
• Figure 4: Learning A Non-Stationary Function using GPR with RBF Kernel. The target function in red color consists of five partitions separated by vertical dashed lines. The black dots around the function are data points. The function changes drastically in partition#3 and smoothly in the remaining partitions. The transitions between neighboring partitions are sharp. This simple function is challenging for a stationary kernel with a single length-scale. GPR with a stationary RBF kernel produces either the wiggly prediction shown in (a) or the over-smoothed prediction in (b). Note that, in (a), the prediction in the smooth regions is rugged, and the uncertainty is over-conservative when the training data is sparse. The prediction in (b) only captures the general trend, and every input location seems equally uncertain.
• Figure 5: Learning $f(x)=x\sin(40x^{4})$ with Soft Length-Scale Selection. The $\mathbf{w}$-plot visualizes the associated weighting vector $\mathbf{w}_{\bm{\theta}}(\mathbf{x})$ of each input location. The more vertical length a color occupies, the higher weight we assign to the GP with the corresponding length-scale. The set of predefined length-scales is color-labeled at the bottom. The learned weighting function gradually shifts its weight from smooth GPs to bumpy ones.

Theorems & Definitions (2)

• Definition 1: Attentive Kernel (AK)
• Proposition 1