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Hierarchical Fault-Tolerant Coverage Control for an Autonomous Aerial Agent

Savvas Papaioannou, Christian Vitale, Panayiotis Kolios, Christos G. Panayiotou, Marios M. Polycarpou

TL;DR

This paper addresses fault-tolerant coverage control for autonomous UAVs operating under non-Gaussian disturbances. It introduces a two-stage hierarchical framework: Stage-1 uses a disturbance-free model-predictive control to generate mobility and camera-configuration plans that maximize coverage of surface POIs; Stage-2 performs exact uncertainty propagation of non-Gaussian disturbances through the nonlinear dynamics using mixed-trigonometric-polynomial moments and imposes moment-based constraints to guarantee coverage with probability at least $1-\epsilon$. A Vysochanskij-Petunin bound is employed to translate moment information into probabilistic safety guarantees, and the stages are solved with MIQP for Stage-1 (via Gurobi) and nonlinear optimization for Stage-2. Simulation results demonstrate robust coverage performance under non-Gaussian disturbances and varying risk levels, highlighting the method’s potential for reliable 3D POI coverage in realistic UAV scenarios, with future work pointing toward fault-tolerant camera control and multi-agent extensions.

Abstract

Fault-tolerant coverage control involves determining a trajectory that enables an autonomous agent to cover specific points of interest, even in the presence of actuation and/or sensing faults. In this work, the agent encounters control inputs that are erroneous; specifically, its nominal controls inputs are perturbed by stochastic disturbances, potentially disrupting its intended operation. Existing techniques have focused on deterministically bounded disturbances or relied on the assumption of Gaussian disturbances, whereas non-Gaussian disturbances have been primarily been tackled via scenario-based stochastic control methods. However, the assumption of Gaussian disturbances is generally limited to linear systems, and scenario-based methods can become computationally prohibitive. To address these limitations, we propose a hierarchical coverage controller that integrates mixed-trigonometric-polynomial moment propagation to propagate non-Gaussian disturbances through the agent's nonlinear dynamics. Specifically, the first stage generates an ideal reference plan by optimising the agent's mobility and camera control inputs. The second-stage fault-tolerant controller then aims to follow this reference plan, even in the presence of erroneous control inputs caused by non-Gaussian disturbances. This is achieved by imposing a set of deterministic constraints on the moments of the system's uncertain states.

Hierarchical Fault-Tolerant Coverage Control for an Autonomous Aerial Agent

TL;DR

This paper addresses fault-tolerant coverage control for autonomous UAVs operating under non-Gaussian disturbances. It introduces a two-stage hierarchical framework: Stage-1 uses a disturbance-free model-predictive control to generate mobility and camera-configuration plans that maximize coverage of surface POIs; Stage-2 performs exact uncertainty propagation of non-Gaussian disturbances through the nonlinear dynamics using mixed-trigonometric-polynomial moments and imposes moment-based constraints to guarantee coverage with probability at least . A Vysochanskij-Petunin bound is employed to translate moment information into probabilistic safety guarantees, and the stages are solved with MIQP for Stage-1 (via Gurobi) and nonlinear optimization for Stage-2. Simulation results demonstrate robust coverage performance under non-Gaussian disturbances and varying risk levels, highlighting the method’s potential for reliable 3D POI coverage in realistic UAV scenarios, with future work pointing toward fault-tolerant camera control and multi-agent extensions.

Abstract

Fault-tolerant coverage control involves determining a trajectory that enables an autonomous agent to cover specific points of interest, even in the presence of actuation and/or sensing faults. In this work, the agent encounters control inputs that are erroneous; specifically, its nominal controls inputs are perturbed by stochastic disturbances, potentially disrupting its intended operation. Existing techniques have focused on deterministically bounded disturbances or relied on the assumption of Gaussian disturbances, whereas non-Gaussian disturbances have been primarily been tackled via scenario-based stochastic control methods. However, the assumption of Gaussian disturbances is generally limited to linear systems, and scenario-based methods can become computationally prohibitive. To address these limitations, we propose a hierarchical coverage controller that integrates mixed-trigonometric-polynomial moment propagation to propagate non-Gaussian disturbances through the agent's nonlinear dynamics. Specifically, the first stage generates an ideal reference plan by optimising the agent's mobility and camera control inputs. The second-stage fault-tolerant controller then aims to follow this reference plan, even in the presence of erroneous control inputs caused by non-Gaussian disturbances. This is achieved by imposing a set of deterministic constraints on the moments of the system's uncertain states.
Paper Structure (14 sections, 1 theorem, 15 equations, 2 figures, 2 algorithms)

This paper contains 14 sections, 1 theorem, 15 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Preliminaries
  2. Agent Dynamical Model
  3. Assumption 1:
  4. Agent Sensing Model
  5. Points of Interest
  6. Robust Hierarchical Coverage Control
  7. Stage-1: Coverage Reference Plan
  8. Assumption 2:
  9. Stage-2: Fault-Tolerant non-Gaussian Control
  10. Lemma 1:
  11. Evaluation
  12. Simulation Setup
  13. Results
  14. Conclusion

Key Result

Theorem 1

Let $x$ be a real valued unimodal random variable with finite expectation $\mathbb{E}[x]$, variance $\mathbb{E}[(x-\mathbb{E}[x])^2]$, and $r \ge 0$, the one-sided Vysochanskij-Petunin inequality is given by: and holds when $r^2\geq\frac{5}{3}\mathbb{E}[(x-\mathbb{E}[x])^2]$. The proof can be found in VP.

Figures (2)

  • Figure 1: The figure shows an illustrative example of the stage-1 controller.
  • Figure 2: The figure illustrates a Monte-Carlo simulation of the agent's state (i.e., position) at the end of the horizon obtained by the stage-2 controller for different confidence levels $\epsilon$. (a) $\epsilon=0.005$, (b) $\epsilon=0.0250$, (c) $\epsilon=0.05$, and (d) $\epsilon=0.1$.

Theorems & Definitions (1)

  • Theorem 1