Omnidirectional Sensor Placement: A Large-Scale Computational Study and Novel Hybrid Accelerated-Refinement Heuristics

TL;DR

The paper tackles omnidirectional sensor placement in a 2D environment to minimize sensor count while achieving coverage close to $(1-\epsilon)$. It introduces Hybrid Accelerated-Refinement (HAR), a framework that combines multiple guard-placement methods and employs preprocessing to accelerate refinement, and demonstrates its superiority over classical convex-partitioning and sampling heuristics on large polygonal maps. HAR achieves the lowest sensor counts and favorable runtimes, with strong performance even after adapting to localization-uncertainty visibility for small to moderate uncertainty. The findings highlight HAR’s potential for visibility-based route planning in mobile robotics and point to future work on formal coverage guarantees under uncertainty and extensions to route planning tasks.

Abstract

This paper studies the omnidirectional sensor-placement problem (OSPP), which involves placing static sensors in a continuous 2D environment to achieve a user-defined coverage requirement while minimizing sensor count. The problem is motivated by applications in mobile robotics, particularly for optimizing visibility-based route planning tasks such as environment inspection, target search, and region patrolling. We focus on omnidirectional visibility models, which eliminate sensor orientation constraints while remaining relevant to real-world sensing technologies like LiDAR, 360-degree cameras, and multi-sensor arrays. Three key models are considered: unlimited visibility, limited-range visibility to reflect physical or application-specific constraints, and localization-uncertainty visibility to account for sensor placement uncertainty in robotics. Our first contribution is a large-scale computational study comparing classical convex-partitioning and sampling-based heuristics for the OSPP, analyzing their trade-off between runtime efficiency and solution quality. Our second contribution is a new class of hybrid accelerated-refinement (HAR) heuristics, which combine and refine outputs from multiple sensor-placement methods while incorporating preprocessing techniques to accelerate refinement. Results demonstrate that HAR heuristics significantly outperform traditional methods, achieving the lowest sensor counts and improving the runtime of sampling-based approaches. Additionally, we adapt a specific HAR heuristic to the localization-uncertainty visibility model, showing that it achieves the required coverage for small to moderate localization uncertainty. Future work may apply HAR to visibility-based route planning tasks or explore novel sensor-placement approaches to achieve formal coverage guarantees under uncertainty.

Figures (9)

• Figure 1: The hybrid refinement (HR) framework follows two key principles: (1) combining outputs from multiple methods and (2) applying a refinement step. KA, CCDT, and RV are existing sensor-placement methods, while HR-KA,CCDT,RV represents their refined combination. Notably, HR-KA,CCDT,RV achieves the lowest guard count post-refinement. The final class of proposed methods, HAR heuristics, further improves efficiency by incorporating preprocessing techniques to accelerate refinement.
• Figure 2: Examples of visibility models for the same guard location in a $20\,\mathrm{m} {\times} 20\,\mathrm{m}$ polygonal environment. Visibility regions are shown in green, with the guard represented as a central violet dot. For the localization-uncertainty models, the guard's own visibility region is displayed in semi-transparent violet, while the sampled points on the uncertainty region boundary form rings around the guard, with their visibility regions shown in semi-transparent yellow. All parameters are in meters.
• Figure 3: Showcase of the visibility models used in the study on the 2p01 map. The guard location is marked by a yellow central dot in all images. The left image displays the unlimited visibility model $\mathrm{Vis}_\infty$ and the range-limited model $\mathrm{Vis}_{d}$, stacked in sequence from blue ($\mathrm{Vis}_\infty$) to red ($\mathrm{Vis}_{d=4}$). The middle and right images depict the localization-uncertainty models $\mathrm{Vis}_{\infty, \mathrm{Unc}_r}$ and $\mathrm{Vis}_{d=16, \mathrm{Unc}_r}$, with colors transitioning from blue ($r {=} 0$) to cyan ($r {=} 1.6\,\mathrm{m}$) and from purple ($r {=} 0$) to green ($r {=} 1.6\,\mathrm{m}$), respectively.
• Figure 4: Close-up views of $\mathrm{Vis}_{d=16}$ and $\mathrm{Vis}_{d=16, \mathrm{Unc}_r}$. The middle and right images show the samples used to approximate the visibility regions. In $\mathrm{Vis}_{d=16}$ (purple), a single sample represents the guard. For uncertainty models, additional samples form concentric rings at distance $r$, transitioning from purple to green as $r$ increases.
• Figure 5: The preliminary results for five visibility models and 39 evaluated methods. The top row corresponds to $\mathrm{Vis}_\infty$, while the remaining rows represent range-limited models $\mathrm{Vis}_d$ with $d {=} 64{,} 32{,} 16{,} 8$. The left column uses a logarithmic scale, while the right column provides a zoomed-in linear-scale view of the blue-shaded region from the left column. Each scatterplot point represents a method as $(\overline{t}, \overline{n})$, where $\overline{t}$ is the mean runtime and $\overline{n}$ is the mean guard count, averaged over 10 maps and 10 runs for non-deterministic methods. Marker shapes indicate method types: circles for baselines, crosses for HR, and squares for HAR. Colors represent different method sets (see the legend), with non-dominated methods marked with pink circles.