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Distributed Coverage Hole Prevention for Visual Environmental Monitoring with Quadcopters via Nonsmooth Control Barrier Functions

Riku Funada, María Santos, Ryuichi Maniwa, Junya Yamauchi, Masayuki Fujita, Mitsuji Sampei, Magnus Egerstedt

TL;DR

The paper tackles the challenge of ensuring there are no unmonitored holes between the FOVs of a team of quadcopters performing visual environmental monitoring. It introduces a distributed, constraint-based approach that uses nonsmooth control barrier functions (NCBFs) derived from a power-diagram representation to forbid holes, while a separate coverage-control law maximizes monitoring quality and minimizes FOV overlap. The method leverages the radical centers of the power diagram and a hybrid forward-invariance framework to handle switching network topologies, ensuring feasibility except for a few pathological cases. It is validated through extensive simulations and hardware experiments, demonstrating hole prevention without sacrificing coverage performance and confirming practical real-time applicability. Overall, the work advances distributed multi-robot sensing by guaranteeing hole-free coverage in dynamically changing formations and FOVs, with potential impact on robust environmental monitoring and surveillance tasks.

Abstract

This paper proposes a distributed coverage control strategy for quadcopters equipped with downward-facing cameras that prevents the appearance of unmonitored areas in between the quadcopters' fields of view (FOVs). We derive a necessary and sufficient condition for eliminating any unsurveilled area that may arise in between the FOVs among a trio of quadcopters by utilizing a power diagram, i.e. a weighted Voronoi diagram defined by radii of FOVs. Because this condition can be described as logically combined constraints, we leverage nonsmooth control barrier functions (NCBFs) to prevent the appearance of unmonitored areas among a team's FOV. We then investigate the symmetric properties of the proposed NCBFs to develop a distributed algorithm. The proposed algorithm can support the switching of the NCBFs caused by changes of the quadcopters composing trios. The existence of the control input satisfying NCBF conditions is analyzed by employing the characteristics of the power diagram. The proposed framework is synthesized with a coverage control law that maximizes the monitoring quality while reducing overlaps of FOVs. The proposed method is demonstrated in simulation and experiment.

Distributed Coverage Hole Prevention for Visual Environmental Monitoring with Quadcopters via Nonsmooth Control Barrier Functions

TL;DR

The paper tackles the challenge of ensuring there are no unmonitored holes between the FOVs of a team of quadcopters performing visual environmental monitoring. It introduces a distributed, constraint-based approach that uses nonsmooth control barrier functions (NCBFs) derived from a power-diagram representation to forbid holes, while a separate coverage-control law maximizes monitoring quality and minimizes FOV overlap. The method leverages the radical centers of the power diagram and a hybrid forward-invariance framework to handle switching network topologies, ensuring feasibility except for a few pathological cases. It is validated through extensive simulations and hardware experiments, demonstrating hole prevention without sacrificing coverage performance and confirming practical real-time applicability. Overall, the work advances distributed multi-robot sensing by guaranteeing hole-free coverage in dynamically changing formations and FOVs, with potential impact on robust environmental monitoring and surveillance tasks.

Abstract

This paper proposes a distributed coverage control strategy for quadcopters equipped with downward-facing cameras that prevents the appearance of unmonitored areas in between the quadcopters' fields of view (FOVs). We derive a necessary and sufficient condition for eliminating any unsurveilled area that may arise in between the FOVs among a trio of quadcopters by utilizing a power diagram, i.e. a weighted Voronoi diagram defined by radii of FOVs. Because this condition can be described as logically combined constraints, we leverage nonsmooth control barrier functions (NCBFs) to prevent the appearance of unmonitored areas among a team's FOV. We then investigate the symmetric properties of the proposed NCBFs to develop a distributed algorithm. The proposed algorithm can support the switching of the NCBFs caused by changes of the quadcopters composing trios. The existence of the control input satisfying NCBF conditions is analyzed by employing the characteristics of the power diagram. The proposed framework is synthesized with a coverage control law that maximizes the monitoring quality while reducing overlaps of FOVs. The proposed method is demonstrated in simulation and experiment.
Paper Structure (22 sections, 10 theorems, 63 equations, 20 figures, 1 algorithm)

This paper contains 22 sections, 10 theorems, 63 equations, 20 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Proposed Approach and Contributions
  4. Preliminaries
  5. Problem Statement
  6. Quadcopters and Environment
  7. Communication Graph and Power Diagram
  8. Unmonitored Areas to Be Prevented
  9. Prevention of Coverage Holes
  10. Control Barrier Functions Preventing a Hole
  11. Algorithm for Preventing a Hole
  12. Validity of the Proposed CBFs
  13. Coverage Control
  14. Simulations and Experiments
  15. Comparison between NCBF $h_{i, \Delta_{\iota}}^{\mathrm k}$ and CBF $h_{i, \Delta_{\iota}, \mathcal{F}}^{\mathrm k}$
  16. ...and 7 more sections

Key Result

Theorem 1

Glotfelter18 Let $h^{\mathrm k}:\mathcal{D}^{\mathrm k} \subset {\mathbb R}^n \to {\mathbb R}$ be a smoothly composed candidate NCBF, as in Definition def:alm_act_grad. If there exists $\epsilon > 0$ and a locally Lipschitz extended class-$\mathcal{K}$ function $\alpha: {\mathbb R}\to {\mathbb R}$ s with $A: \mathcal{D}^{\mathrm k} \subset {\mathbb R}^n \to {\mathbb R}^{m\times m}$, $b: \mathcal{D

Figures (20)

  • Figure 1: Proposed scenario. The team of quadcopters monitors a mission space $\mathcal{Q}$ specified within the environment $\mathcal{E}$. Each quadcopter mounts a downward-facing camera with a circular field of view (FOV) that is adjustable via its position $p_i$ and focal length $\lambda_i$. The hatched regions in between the FOVs of quadcopters represent unmonitored areas to be prevented.
  • Figure 2: An illustration of (a) Quadcopter $i$'s FOV $\mathcal{F}_i$ and (b) communication graph $\mathcal{G}$. In (b), a radical center $v_{ijk}$ is depicted as a green dot.
  • Figure 3: Power diagram generated by nine quadcopters, illustrated by black lines. The vertices of the power diagram shown in red dots, called radical centers, are generated by groups of three quadcopters depicted in black dots. The FOVs of quadcopters and the graph $\mathcal{G}(t)$ are depicted with the green circles and the blue lines, respectively. On the right, the boundary of $\cup_{i=1}^n \mathcal{F}_i$ has a dent with a radical center, but this is not regarded as a hole, which is formally defined in Definition \ref{['def:hole']}.
  • Figure 4: Three cases of FOV configurations with $\triangle{IJK}$ depicted as a purple triangle. (a) illustrates a hole in the sense of Definition \ref{['def:hole']}, where $v_{ijk}$ are not contained by any of a trio. Neither (b) nor (c) has a hole, but $v_{ijk}$ lies outside of FOVs in (c). This signifies that if we utilize a constraint $v_{ijk} \in \mathcal{F}_i$ only, the configuration (c) is also restricted as well as (a), even if (c) does not have any holes.
  • Figure 5: The coordinate frame $\Sigma_d$ introduced for calculation of partial derivatives of designed CBFs.
  • ...and 15 more figures

Theorems & Definitions (31)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Theorem 1
  • Remark 1
  • Theorem 2
  • Definition 6
  • Theorem 3
  • ...and 21 more