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DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety

Masoud Ataei, Vikas Dhiman

TL;DR

This work addresses safety-critical robot control under uncertainty by evaluating a broad set of uncertainty quantification methods within Control Barrier Function (CBF) frameworks. It identifies complementary strengths: model-variance-based approaches excel at estimating out-of-domain uncertainty, while direct estimation methods excel in-domain. To leverage both, the authors introduce DADEE, a hybrid estimator that combines Anchored Ensembles with a direct in-domain uncertainty predictor, achieving superior calibration and safer CBF-based control in simulation. The approach improves safety performance in a robot navigation scenario and is released with open-source code to enable replication and extension.

Abstract

Uncertainty-aware controllers that guarantee safety are critical for safety critical applications. Among such controllers, Control Barrier Functions (CBFs) based approaches are popular because they are fast, yet safe. However, most such works depend on Gaussian Processes (GPs) or MC-Dropout for learning and uncertainty estimation, and both approaches come with drawbacks: GPs are non-parametric methods that are slow, while MC-Dropout does not capture aleatoric uncertainty. On the other hand, modern Bayesian learning algorithms have shown promise in uncertainty quantification. The application of modern Bayesian learning methods to CBF-based controllers has not yet been studied. We aim to fill this gap by surveying uncertainty quantification algorithms and evaluating them on CBF-based safe controllers. We find that model variance-based algorithms (for example, Deep ensembles, MC-dropout, etc.) and direct estimation-based algorithms (such as DEUP) have complementary strengths. Algorithms in the former category can only estimate uncertainty accurately out-of-domain, while those in the latter category can only do so in-domain. We combine the two approaches to obtain more accurate uncertainty estimates both in- and out-of-domain. As measured by the failure rate of a simulated robot, this results in a safer CBF-based robot controller.

DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety

TL;DR

This work addresses safety-critical robot control under uncertainty by evaluating a broad set of uncertainty quantification methods within Control Barrier Function (CBF) frameworks. It identifies complementary strengths: model-variance-based approaches excel at estimating out-of-domain uncertainty, while direct estimation methods excel in-domain. To leverage both, the authors introduce DADEE, a hybrid estimator that combines Anchored Ensembles with a direct in-domain uncertainty predictor, achieving superior calibration and safer CBF-based control in simulation. The approach improves safety performance in a robot navigation scenario and is released with open-source code to enable replication and extension.

Abstract

Uncertainty-aware controllers that guarantee safety are critical for safety critical applications. Among such controllers, Control Barrier Functions (CBFs) based approaches are popular because they are fast, yet safe. However, most such works depend on Gaussian Processes (GPs) or MC-Dropout for learning and uncertainty estimation, and both approaches come with drawbacks: GPs are non-parametric methods that are slow, while MC-Dropout does not capture aleatoric uncertainty. On the other hand, modern Bayesian learning algorithms have shown promise in uncertainty quantification. The application of modern Bayesian learning methods to CBF-based controllers has not yet been studied. We aim to fill this gap by surveying uncertainty quantification algorithms and evaluating them on CBF-based safe controllers. We find that model variance-based algorithms (for example, Deep ensembles, MC-dropout, etc.) and direct estimation-based algorithms (such as DEUP) have complementary strengths. Algorithms in the former category can only estimate uncertainty accurately out-of-domain, while those in the latter category can only do so in-domain. We combine the two approaches to obtain more accurate uncertainty estimates both in- and out-of-domain. As measured by the failure rate of a simulated robot, this results in a safer CBF-based robot controller.
Paper Structure (17 sections, 2 theorems, 17 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 2 theorems, 17 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Uncertainty estimation in deep learning
  4. Approximate Bayesian learning
  5. Variational inference (VI)
  6. Direct estimation of uncertainty
  7. Monte-Carlo approaches
  8. Point estimators
  9. Laplace Approximation
  10. Control Barrier Funcitons (CBFs)
  11. Methodology
  12. Experiments and results
  13. 1-D regression experiment
  14. Evaluation metrics
  15. Sensitivity to perturbations
  16. ...and 2 more sections

Key Result

Theorem 1

Consider a control barrier function $h \in \mathbb{C}^1({\@fontswitch\mathcal{X}}, \mathbb{R})$ whose zero superlevel set is the safety set, ${\@fontswitch\mathcal{C}}_{\text{safe}} = \{\mathbf{x} \in {\@fontswitch\mathcal{X}} | h(\mathbf{x}) \ge 0 \}$. Additionally, assume that $\nabla h(\mathbf{x} and $\alpha$ is an extended class ${\@fontswitch\mathcal{K}}_\infty$ function. We call the constrai

Figures (3)

  • Figure 1: The posterior distribution prediction for GP, Anchored Ensemble, DEUP, and DADEE. Anchored ensemble estimates uncertainty accurately out-of-domain, increasing the number of models results in more accurate estimation, while DEUP does so in-domain. GP and DADEE recover the true distribution correctly in both out-of-domain and in-domain.
  • Figure 2: (Left) The variance estimated by Model-variance-based methods (MC-Dropout, SWAG, Anchor, Ensemble, and LA) approaches zero as the volume of training data increases. Meanwhile, the variance estimates produced by the direct estimation-based approaches (DEUP, MLLV) instead approach the true irreducible in-domain noise. (Right) Sensitivity in variance predictions: Sensitivity measures the change in variance as it responds to small changes in input (Defined in \ref{['eq:RelativeVariance']}). MC-Dropout is unstable because a new set of activations is masked every time the network is reevaluated.
  • Figure 3: (Left) The trajectory of the simulated uncertainty-aware safe control-guided robot using Ensemble, DADEE, and MLP. (Right) 3D visualization of data shown left.

Theorems & Definitions (2)

  • Theorem 1: Control barrier condition ames2019CBFdhiman2023controlbarriers
  • Theorem 2: Prop 4,5dhiman2023controlbarriers