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Uncertainty-aware Risk Assessment of Robotic Systems via Importance Sampling

Woo-Jeong Baek, Tom P. Huck, Joschka Haas, Jonas Lewandrowski, Tamim Asfour, Torsten Kröger

TL;DR

This work studies the impact of temporal and spatial uncertainties on the occurrence probability of dangerous failures, thereby deriving an approach for an uncertainty-aware risk assessment and shows how the results can be used to evaluate arbitrary safety limits of robot systems.

Abstract

In this paper, we introduce a probabilistic approach to risk assessment of robot systems by focusing on the impact of uncertainties. While various approaches to identifying systematic hazards (e.g., bugs, design flaws, etc.) can be found in current literature, little attention has been devoted to evaluating risks in robot systems in a probabilistic manner. Existing methods rely on discrete notions for dangerous events and assume that the consequences of these can be described by simple logical operations. In this work, we consider measurement uncertainties as one main contributor to the evolvement of risks. Specifically, we study the impact of temporal and spatial uncertainties on the occurrence probability of dangerous failures, thereby deriving an approach for an uncertainty-aware risk assessment. Secondly, we introduce a method to improve the statistical significance of our results: While the rare occurrence of hazardous events makes it challenging to draw conclusions with reliable accuracy, we show that importance sampling -- a technique that successively generates samples in regions with sparse probability densities -- allows for overcoming this issue. We demonstrate the validity of our novel uncertainty-aware risk assessment method in three simulation scenarios from the domain of human-robot collaboration. Finally, we show how the results can be used to evaluate arbitrary safety limits of robot systems.

Uncertainty-aware Risk Assessment of Robotic Systems via Importance Sampling

TL;DR

This work studies the impact of temporal and spatial uncertainties on the occurrence probability of dangerous failures, thereby deriving an approach for an uncertainty-aware risk assessment and shows how the results can be used to evaluate arbitrary safety limits of robot systems.

Abstract

In this paper, we introduce a probabilistic approach to risk assessment of robot systems by focusing on the impact of uncertainties. While various approaches to identifying systematic hazards (e.g., bugs, design flaws, etc.) can be found in current literature, little attention has been devoted to evaluating risks in robot systems in a probabilistic manner. Existing methods rely on discrete notions for dangerous events and assume that the consequences of these can be described by simple logical operations. In this work, we consider measurement uncertainties as one main contributor to the evolvement of risks. Specifically, we study the impact of temporal and spatial uncertainties on the occurrence probability of dangerous failures, thereby deriving an approach for an uncertainty-aware risk assessment. Secondly, we introduce a method to improve the statistical significance of our results: While the rare occurrence of hazardous events makes it challenging to draw conclusions with reliable accuracy, we show that importance sampling -- a technique that successively generates samples in regions with sparse probability densities -- allows for overcoming this issue. We demonstrate the validity of our novel uncertainty-aware risk assessment method in three simulation scenarios from the domain of human-robot collaboration. Finally, we show how the results can be used to evaluate arbitrary safety limits of robot systems.
Paper Structure (28 sections, 11 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 28 sections, 11 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Probabilistic Risk Assessment Methods
  4. Uncertainty Propagation in Robotics
  5. Importance Sampling in Robot Systems
  6. Preliminaries
  7. Measurement Uncertainties
  8. Importance Sampling
  9. Problem Statement and Motivation
  10. Approach
  11. Specification of Components and Uncertainties (Step 1)
  12. Experiments with Uncertainty Models (Step 2)
  13. Grid-based Importance Sampling (Step 3)
  14. Risk Reduction and Safe System Design (Step 4)
  15. Experiments and Results
  16. ...and 13 more sections

Figures (5)

  • Figure 1: We develop an uncertainty-aware risk assessment method for robotic systems.
  • Figure 2: We present an uncertainty-aware risk assessment method by feeding samples from different uncertainty models into the simulator. The obtained results are analyzed with respect to the probability of the occurrence of dangerous events. In addition, we introduce grid-based importance sampling to draw conclusions with sufficient statistical significance.
  • Figure 3: Grid densities obtained for the standard normal density distribution for the area of grild cells ($e=10$).
  • Figure 4: We validate and evaluate our techniques by means of three HRC scenarios. In all scenarios, the robot performs evasive movements once the human-robot distance falls under a specified limit.
  • Figure 5: After studying how the collisions depend on the spatial and temporal uncertainties, we perform the risk evaluation by accounting for the collision forces.