Robust Safe Control with Multi-Modal Uncertainty

TL;DR

This paper presents a new robust safe control framework that effectively manages multi-modal uncertainties in dynamic systems, improving safety and reducing conservatism compared to traditional uni-modal approaches.

Contribution

The paper introduces novel methods for deriving least conservative robust safe controls under multi-modal Gaussian uncertainties and control limits, along with a safety index synthesis technique.

Findings

Validated on a simulated Segway with consistent realizability

Demonstrated less conservatism than uni-modal uncertainty controllers

Enhanced safety and performance in robotic applications

Abstract

Safety in dynamic systems with prevalent uncertainties is crucial. Current robust safe controllers, designed primarily for uni-modal uncertainties, may be either overly conservative or unsafe when handling multi-modal uncertainties. To address the problem, we introduce a novel framework for robust safe control, tailored to accommodate multi-modal Gaussian dynamics uncertainties and control limits. We first present an innovative method for deriving the least conservative robust safe control under additive multi-modal uncertainties. Next, we propose a strategy to identify a locally least-conservative robust safe control under multiplicative uncertainties. Following these, we introduce a unique safety index synthesis method. This provides the foundation for a robust safe controller that ensures a high probability of realizability under control limits and multi-modal uncertainties. Experiments on a simulated Segway validate our approach, showing consistent realizability and less conservatism than controllers designed using uni-modal uncertainty methods. The framework offers significant potential for enhancing safety and performance in robotic applications.