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Geometric Look-Angle Shaping Strategy for Enclosed Inspection

Amit Shivam, Manuel C. R. M. Fernandes, Sergio Vinha, Fernando A. C. C. Fontes

Abstract

This paper introduces inspection through GLASS, a Geometric Look-Angle Shaping Strategy for enclosed regions using unmanned aerial vehicles. In doing so, the vehicles guidance command is constructed through a bounded, geometry-consistent shaping of the look angle relative to a desired standoff path. By embedding a smooth, hyperbolic-tangent-type shaping function within a polar geometric framework, GLASS ensures global existence of the guidance dynamics. It avoids the far-field limitations inherent to conventional formulations. Lyapunov stability analysis establishes asymptotic convergence to a prescribed inspection standoff under explicit curvature feasibility conditions, along with analytical settling-time characteristics. The proposed strategy incorporates maximum turn-rate constraints without inducing singularities throughout the workspace. High-fidelity six-degree-of-freedom quadrotor simulations demonstrate the effectiveness of GLASS in representative enclosed inspection scenarios, highlighting a practically viable guidance framework for autonomous enclosed inspection missions.

Geometric Look-Angle Shaping Strategy for Enclosed Inspection

Abstract

This paper introduces inspection through GLASS, a Geometric Look-Angle Shaping Strategy for enclosed regions using unmanned aerial vehicles. In doing so, the vehicles guidance command is constructed through a bounded, geometry-consistent shaping of the look angle relative to a desired standoff path. By embedding a smooth, hyperbolic-tangent-type shaping function within a polar geometric framework, GLASS ensures global existence of the guidance dynamics. It avoids the far-field limitations inherent to conventional formulations. Lyapunov stability analysis establishes asymptotic convergence to a prescribed inspection standoff under explicit curvature feasibility conditions, along with analytical settling-time characteristics. The proposed strategy incorporates maximum turn-rate constraints without inducing singularities throughout the workspace. High-fidelity six-degree-of-freedom quadrotor simulations demonstrate the effectiveness of GLASS in representative enclosed inspection scenarios, highlighting a practically viable guidance framework for autonomous enclosed inspection missions.
Paper Structure (16 sections, 3 theorems, 40 equations, 8 figures, 3 tables)

This paper contains 16 sections, 3 theorems, 40 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Proposed Look-Angle Based Guidance Law
  4. Far-Field Limitation of Arcsine Shaping Function
  5. Proposed GLASS Shaping Law
  6. Geometric Feasibility and Regularity
  7. Closed-Loop Stability on General Standoff Curves
  8. Analytical Tube-Entry Time
  9. Simulation results
  10. Ideal dynamics
  11. Simulation with nonideal initial heading
  12. Comparative study
  13. 6DOF simulation results
  14. Course-to-acceleration mapping
  15. Acceleration-to-attitude mapping and yaw synchronization
  16. ...and 1 more sections

Key Result

Theorem 1

Define . For any $e\in\mathbb{R}$, the algebraic constraint admits a real solution $\lambda(e,\gamma,d)$ and the two solution branches Then the following hold: Moreover, each solution branch is continuous and continuously differentiable in $e$, with globally bounded slope.

Figures (8)

  • Figure 1: Problem scenario
  • Figure 2: Results for ideal dynamics for outside initial position
  • Figure 3: Results for ideal dynamics for inside initial position
  • Figure 4: Results for outside initial UAV position
  • Figure 5: Results for inside initial UAV position
  • ...and 3 more figures

Theorems & Definitions (6)

  • Theorem 1: Global feasibility
  • proof
  • Theorem 2: Global asymptotic convergence
  • proof
  • Theorem 3
  • proof