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Inspection planning under execution uncertainty

Shmuel David Alpert, Kiril Solovey, Itzik Klein, Oren Salzman

TL;DR

IRIS-U^2 addresses offline inspection planning under execution uncertainty by integrating Monte Carlo estimation of POI-coverage probabilities with the IRIS planning framework. It introduces IPV (inspection probability vectors), $(\varepsilon,\kappa)$-bounded nodes, and subsumption to efficiently propagate uncertainty through an A*-like search, yielding statistical guarantees on coverage, collision probability, and path length. The method demonstrates improved POI coverage and reduced collision in bridge inspection scenarios, with CI bounds tightening as the number of MC samples grows. The work also discusses bounded-suboptimal strategies to trade computation time for guarantees and analyzes planning-execution model mismatches, showing practical applicability for UAV structural inspections. The approach provides actionable guidelines for parameter choices to meet desired confidence levels while maintaining tractable planning times.

Abstract

Autonomous inspection tasks necessitate path-planning algorithms to efficiently gather observations from points of interest (POI). However, localization errors commonly encountered in urban environments can introduce execution uncertainty, posing challenges to successfully completing such tasks. Unfortunately, existing algorithms for inspection planning do not explicitly account for execution uncertainty, which can hinder their performance. To bridge this gap, we present IRIS-under uncertainty (IRIS-U^2), the first inspection-planning algorithm that offers statistical guarantees regarding coverage, path length, and collision probability. Our approach builds upon IRIS -- our framework for deterministic inspection planning, which is highly efficient and provably asymptotically-optimal. The extension to the much more involved uncertain setting is achieved by a refined search procedure that estimates POI coverage probabilities using Monte Carlo (MC) sampling. The efficacy of IRIS-U^2 is demonstrated through a case study focusing on structural inspections of bridges. Our approach exhibits improved expected coverage, reduced collision probability, and yields increasingly precise statistical guarantees as the number of MC samples grows. Furthermore, we demonstrate the potential advantages of computing bounded sub-optimal solutions to reduce computation time while maintaining statistical guarantees.

Inspection planning under execution uncertainty

TL;DR

IRIS-U^2 addresses offline inspection planning under execution uncertainty by integrating Monte Carlo estimation of POI-coverage probabilities with the IRIS planning framework. It introduces IPV (inspection probability vectors), -bounded nodes, and subsumption to efficiently propagate uncertainty through an A*-like search, yielding statistical guarantees on coverage, collision probability, and path length. The method demonstrates improved POI coverage and reduced collision in bridge inspection scenarios, with CI bounds tightening as the number of MC samples grows. The work also discusses bounded-suboptimal strategies to trade computation time for guarantees and analyzes planning-execution model mismatches, showing practical applicability for UAV structural inspections. The approach provides actionable guidelines for parameter choices to meet desired confidence levels while maintaining tractable planning times.

Abstract

Autonomous inspection tasks necessitate path-planning algorithms to efficiently gather observations from points of interest (POI). However, localization errors commonly encountered in urban environments can introduce execution uncertainty, posing challenges to successfully completing such tasks. Unfortunately, existing algorithms for inspection planning do not explicitly account for execution uncertainty, which can hinder their performance. To bridge this gap, we present IRIS-under uncertainty (IRIS-U^2), the first inspection-planning algorithm that offers statistical guarantees regarding coverage, path length, and collision probability. Our approach builds upon IRIS -- our framework for deterministic inspection planning, which is highly efficient and provably asymptotically-optimal. The extension to the much more involved uncertain setting is achieved by a refined search procedure that estimates POI coverage probabilities using Monte Carlo (MC) sampling. The efficacy of IRIS-U^2 is demonstrated through a case study focusing on structural inspections of bridges. Our approach exhibits improved expected coverage, reduced collision probability, and yields increasingly precise statistical guarantees as the number of MC samples grows. Furthermore, we demonstrate the potential advantages of computing bounded sub-optimal solutions to reduce computation time while maintaining statistical guarantees.
Paper Structure (50 sections, 4 theorems, 51 equations, 10 figures, 1 algorithm)

This paper contains 50 sections, 4 theorems, 51 equations, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Motion planning under uncertainty
  4. Inspection planning
  5. Problem Definition
  6. Basic definitions and notations
  7. Inspection planning (without execution uncertainty)
  8. Inspection-planning problem under execution uncertainty
  9. Algorithmic background
  10. Incremental Random Inspection-roadmap Search (IRIS)
  11. Monte-Carlo methods & confidence intervals
  12. Method
  13. IRIS-U$^2$---Algorithmic approach
  14. IRIS-U$^2$---Modified search operations
  15. Node definition
  16. ...and 35 more sections

Key Result

Lemma 6.1

For any desired CL of $1 - \alpha\in [0,1]$, the expected coverage of an executed path following $\pi$, denoted by $\vert \bar{\S}(\pi) \vert$, is at least: Here, the function $\hat{p}^-$ is obtained from the Clopper-Pearson method habtzghi2014modified and is defined in Eq. eq:Clopper-Pearson method in Appendix app:stat.

Figures (10)

  • Figure 1: A UAV executing a bridge-inspection task, following a command path pre-computed offline (dark blue). The UAV relies on GNSS satellite signals for navigation but the bridge obstructs one satellite signal during a particular segment of its path (light blue). This leads to a substantial deviation from the command path, which hinders the UAV's ability to inspect the POIs and may result in a collision with the bridge.
  • Figure 2: Planning a command path $\pi$ to inspect set of POI $\mathcal{I}$ given the input of IRIS--- $\mathcal{G}$, $\kappa$ and $\varepsilon$, and the additional parameters of IRIS-U$^2$--- $m$ the $\rho_{\text{coll}}$.
  • Figure 3: Toy scenario for running example with one POI (red dot), two obstacles (red rectangles), and four vertices (black dots) connected with six edges (black dashed lines).
  • Figure 4: (\ref{['subfig:CI lower bound of the POI coverage']}), (\ref{['subfig:paretoCICollision']}) Values (in percentage) of $\hat{p}^-(\kappa,m,\alpha)$ and $\hat{p}^+(\rho_\text{coll},m,\alpha)$ for $\alpha = 0.05$ as a function of the number of MC samples $m$ ($x$-axis) and the coverage approximation factors $\kappa$ and $\rho_\text{coll}$ ($y$-axis), respectively.
  • Figure 5: (\ref{['subfig:simpleScenario_illustration']}) Illustrative scenario for empirical evaluation depicting a roadmap, (black points being vertices and dashed lines being edges), POIs (red points), obstacles (red rectangles) and regions with high and low uncertainty. (\ref{['subfig:toy scenario path compared methods']}) Command paths computed by IRIS (blue), UP-IRIS (yellow), and IRIS-U$^2$ (orange) with $m=100$.
  • ...and 5 more figures

Theorems & Definitions (5)

  • Definition 1
  • Lemma 6.1: Executed path's expected coverage
  • Lemma 6.2: Executed path's collision probability
  • Lemma 6.3: Executed path's expected length
  • Lemma 6.4: Bounding executed path's sub-optimal coverage