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Verifiable Obstacle Detection

Ayoosh Bansal, Hunmin Kim, Simon Yu, Bo Li, Naira Hovakimyan, Marco Caccamo, Lui Sha

TL;DR

Safety-critical obstacle existence detection is essential for autonomous vehicles, yet neural perception components remain largely unverifiable. The authors decouple safety from mission and demonstrate how a verifiable LiDAR-based Depth Clustering obstacle detector can be bounded using a Detectability Model framed around a reach-avoid index $r$. They derive minimal safety requirements, translate safety standards into sensor and algorithm parameter bounds, and validate the approach on real Waymo data, quantifying under- and overestimation errors and coverage bounds. The results show that verifiable, classical algorithms can deliver deterministic safety guarantees and serve as a robust backbone that can complement DNN-based perception in safety-critical AV pipelines.

Abstract

Perception of obstacles remains a critical safety concern for autonomous vehicles. Real-world collisions have shown that the autonomy faults leading to fatal collisions originate from obstacle existence detection. Open source autonomous driving implementations show a perception pipeline with complex interdependent Deep Neural Networks. These networks are not fully verifiable, making them unsuitable for safety-critical tasks. In this work, we present a safety verification of an existing LiDAR based classical obstacle detection algorithm. We establish strict bounds on the capabilities of this obstacle detection algorithm. Given safety standards, such bounds allow for determining LiDAR sensor properties that would reliably satisfy the standards. Such analysis has as yet been unattainable for neural network based perception systems. We provide a rigorous analysis of the obstacle detection system with empirical results based on real-world sensor data.

Verifiable Obstacle Detection

TL;DR

Safety-critical obstacle existence detection is essential for autonomous vehicles, yet neural perception components remain largely unverifiable. The authors decouple safety from mission and demonstrate how a verifiable LiDAR-based Depth Clustering obstacle detector can be bounded using a Detectability Model framed around a reach-avoid index . They derive minimal safety requirements, translate safety standards into sensor and algorithm parameter bounds, and validate the approach on real Waymo data, quantifying under- and overestimation errors and coverage bounds. The results show that verifiable, classical algorithms can deliver deterministic safety guarantees and serve as a robust backbone that can complement DNN-based perception in safety-critical AV pipelines.

Abstract

Perception of obstacles remains a critical safety concern for autonomous vehicles. Real-world collisions have shown that the autonomy faults leading to fatal collisions originate from obstacle existence detection. Open source autonomous driving implementations show a perception pipeline with complex interdependent Deep Neural Networks. These networks are not fully verifiable, making them unsuitable for safety-critical tasks. In this work, we present a safety verification of an existing LiDAR based classical obstacle detection algorithm. We establish strict bounds on the capabilities of this obstacle detection algorithm. Given safety standards, such bounds allow for determining LiDAR sensor properties that would reliably satisfy the standards. Such analysis has as yet been unattainable for neural network based perception systems. We provide a rigorous analysis of the obstacle detection system with empirical results based on real-world sensor data.
Paper Structure (32 sections, 6 theorems, 24 equations, 7 figures, 3 tables)

This paper contains 32 sections, 6 theorems, 24 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Motivation and Overview
  3. Related Work
  4. Minimal Requirements
  5. Classification
  6. Collision Risk
  7. Height
  8. Distance
  9. Underestimation Error
  10. Overestimation Error
  11. Projection
  12. Coverage
  13. Summary
  14. Parameters and Constraints
  15. LiDAR Parameters
  16. ...and 17 more sections

Key Result

Theorem 1

The obstacle is detected at distance $D$, if and only if one of the following conditions are true:

Figures (7)

  • Figure 1: Example scenes. (a) Role of obstacle height. (b) Distance and Occlusion of obstacles. (c) Projection of Obstacles.
  • Figure 2: A representation of point segmentation to ground vs. obstacle based on $\alpha$ thresholding when two points return from the obstacle.
  • Figure 3: Respresentation for $\alpha$ thresholding with only one point on obstacle.
  • Figure 4: Obstacle above ground plane.
  • Figure 5: Obstacle with ground inclination relative to the AV.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Theorem 1
  • proof
  • Corollary 1
  • Corollary 2
  • Corollary 3
  • Theorem 2
  • proof
  • Theorem 3
  • proof