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NavEX: A Multi-Agent Coverage in Non-Convex and Uneven Environments via Exemplar-Clustering

Donipolo Ghimire, Carlos Nieto-Granda, Solmaz S. Kia

TL;DR

The paper addresses multi-agent coverage in non-convex and uneven environments where Euclidean distances fail to capture navigability. It introduces NavEX, a framework that combines exemplar-based clustering with obstacle-aware shortest-path distances from visibility graphs in 2D and traversability-aware \\text{RRT}$^\ extstar$ in 3D, formulated as monotone submodular maximization under a matroid constraint. It supports two deployment tasks—fair-access (minimize the maximum target-to-agent distance) and hotspot deployment (prioritize high-density regions)—with provable near-optimal guarantees and scalable computation. Simulations across planar and rugged terrains demonstrate NavEX’s ability to yield feasible, equitable deployments while respecting environmental constraints, and the approach is extensible to heterogeneous and dynamic settings.

Abstract

This paper addresses multi-agent deployment in non-convex and uneven environments. To overcome the limitations of traditional approaches, we introduce Navigable Exemplar-Based Dispatch Coverage (NavEX), a novel dispatch coverage framework that combines exemplar-clustering with obstacle-aware and traversability-aware shortest distances, offering a deployment framework based on submodular optimization. NavEX provides a unified approach to solve two critical coverage tasks: (a) fair-access deployment, aiming to provide equitable service by minimizing agent-target distances, and (b) hotspot deployment, prioritizing high-density target regions. A key feature of NavEX is the use of exemplar-clustering for the coverage utility measure, which provides the flexibility to employ non-Euclidean distance metrics that do not necessarily conform to the triangle inequality. This allows NavEX to incorporate visibility graphs for shortest-path computation in environments with planar obstacles, and traversability-aware RRT* for complex, rugged terrains. By leveraging submodular optimization, the NavEX framework enables efficient, near-optimal solutions with provable performance guarantees for multi-agent deployment in realistic and complex settings, as demonstrated by our simulations.

NavEX: A Multi-Agent Coverage in Non-Convex and Uneven Environments via Exemplar-Clustering

TL;DR

The paper addresses multi-agent coverage in non-convex and uneven environments where Euclidean distances fail to capture navigability. It introduces NavEX, a framework that combines exemplar-based clustering with obstacle-aware shortest-path distances from visibility graphs in 2D and traversability-aware \\text{RRT} in 3D, formulated as monotone submodular maximization under a matroid constraint. It supports two deployment tasks—fair-access (minimize the maximum target-to-agent distance) and hotspot deployment (prioritize high-density regions)—with provable near-optimal guarantees and scalable computation. Simulations across planar and rugged terrains demonstrate NavEX’s ability to yield feasible, equitable deployments while respecting environmental constraints, and the approach is extensible to heterogeneous and dynamic settings.

Abstract

This paper addresses multi-agent deployment in non-convex and uneven environments. To overcome the limitations of traditional approaches, we introduce Navigable Exemplar-Based Dispatch Coverage (NavEX), a novel dispatch coverage framework that combines exemplar-clustering with obstacle-aware and traversability-aware shortest distances, offering a deployment framework based on submodular optimization. NavEX provides a unified approach to solve two critical coverage tasks: (a) fair-access deployment, aiming to provide equitable service by minimizing agent-target distances, and (b) hotspot deployment, prioritizing high-density target regions. A key feature of NavEX is the use of exemplar-clustering for the coverage utility measure, which provides the flexibility to employ non-Euclidean distance metrics that do not necessarily conform to the triangle inequality. This allows NavEX to incorporate visibility graphs for shortest-path computation in environments with planar obstacles, and traversability-aware RRT* for complex, rugged terrains. By leveraging submodular optimization, the NavEX framework enables efficient, near-optimal solutions with provable performance guarantees for multi-agent deployment in realistic and complex settings, as demonstrated by our simulations.
Paper Structure (7 sections, 6 equations, 5 figures, 2 algorithms)

This paper contains 7 sections, 6 equations, 5 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem setting
  3. NavEX: a multi-agent deployment in non-convex and uneven workspaces
  4. Distance metrics
  5. Utility function design
  6. Demonstrative examples
  7. Conclusion

Figures (5)

  • Figure 1: A non-convex environment overlaid with the corresponding visibility graph that is used as a distance metric. The shortest path is highlighted in red between two random points.
  • Figure 2: Distance metric via traversability-aware RRT$^{\star}$: two generated paths show the traversability impacts the distance between start and goal points. Depending on the terrain, the path may entirely circumvent the obstacle formed by hills, while in other traversable regions, the algorithm allows direct passage.
  • Figure 3: Fair-access deployment using NavEX in a workspace with (left plot) and without (right plot) obstacles.
  • Figure 4: Hotspot deployment using NavEX.
  • Figure 5: The outcome of fair-access deployment using NavEX in two distinct uneven terrains. Plots (a) and (d) show the terrains, with corresponding deployment scenarios to their right. Heatmaps show traversability maps.