Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data

TL;DR

This paper introduces a method to learn system disturbances online using risk measures, enabling risk-aware control with minimal data, demonstrated on drone control improvements.

Contribution

It proposes a novel Surface-at-Risk measure for stochastic processes and models disturbance norms with Gaussian Process Regression for risk-aware control.

Findings

Effective disturbance learning with less than a minute of data

Improved drone control performance using the proposed risk-aware method

Theoretical guarantees on the accuracy of the risk measure estimation

Abstract

Recent advances in safety-critical risk-aware control are predicated on apriori knowledge of the disturbances a system might face. This paper proposes a method to efficiently learn these disturbances online, in a risk-aware context. First, we introduce the concept of a Surface-at-Risk, a risk measure for stochastic processes that extends Value-at-Risk -- a commonly utilized risk measure in the risk-aware controls community. Second, we model the norm of the state discrepancy between the model and the true system evolution as a scalar-valued stochastic process and determine an upper bound to its Surface-at-Risk via Gaussian Process Regression. Third, we provide theoretical results on the accuracy of our fitted surface subject to mild assumptions that are verifiable with respect to the data sets collected during system operation. Finally, we experimentally verify our procedure by augmenting a drone's controller and highlight performance increases achieved via our risk-aware approach after collecting less than a minute of operating data.