Multi-robot searching with limited sensing range for static and mobile intruders

TL;DR

The paper addresses multi-robot search with limited sensing in a simply connected orthogonal polygon, proving NP-hardness for guaranteed interception and formulating MRS and DMRS. It proposes three algorithmic families—space-filling-curves (with rectangulation), random search, and cooperative random search—and analyzes the trade-off between the number of robots $k$ and search time under static and mobile intruder models. Through Monte-Carlo simulations, RS and CRS emerge as effective with small $k$, while SFC approaches baselines more closely only when the region is decomposed into many rectangles; geometry and area can significantly affect performance. The work provides practical insights for robust search strategies in constrained environments and suggests directions for handling multiple or intelligent intruders and more complex polygons.

Abstract

We consider the problem of searching for an intruder in a geometric domain by utilizing multiple search robots. The domain is a simply connected orthogonal polygon with edges parallel to the cartesian coordinate axes. Each robot has a limited sensing capability. We study the problem for both static and mobile intruders. It turns out that the problem of finding an intruder is NP-hard, even for a stationary intruder. Given this intractability, we turn our attention towards developing efficient and robust algorithms, namely methods based on space-filling curves, random search, and cooperative random search. Moreover, for each proposed algorithm, we evaluate the trade-off between the number of search robots and the time required for the robots to complete the search process while considering the geometric properties of the connected orthogonal search area.

Figures (11)

• Figure 1: (a) Polygonal region $\mathcal{P}$ with intruder ($\mathcal{I}$) in red color and the search robots ($\mathcal{R'}\subseteq \mathcal{R}$) in green. The red square boxes around the robots is the robot sensing range, $l^s$. (b) The grid graph $G(\mathcal{P})$ shown in black solid lines of the region. The dual of $G(\mathcal{P})$, $\mathcal{D}_G$, is shown with red dotted lines. The robots move (horizontally/vertically) from the center of each black pixel (square) to the center of another at each time step $t$.
• Figure 2: Comb structure for the polygon $\mathcal{P}$. The base $b$, of the structure has a diameter $O(q)$. The spikes $s_0,s_1, \ldots, s_{3q}$ represent sub-regions that are connected to the base. Each spike has a width that is equal to the shortest edge of the polygon that appears in that spike.
• Figure 3: (a) Rectangular decomposition of simply connected rectilinear polygons, (b) Splitting of rectangle for computing space-filling curves
• Figure 4: Illustration for the arrangement and distribution of search robots in Space-filling curve approach. The polygonal region is decomposed into many sub-rectangular regions ($d_i$) and each sub-rectangular region is filled with a space-filling curve $c_i$. The trail behind each agent shows the trajectory during its past few time steps.
• Figure 5: A snapshot of cost map from the random search algorithm. The intruder and the robot are depicted in red and green circles, respectively. The trajectory of the searcher is shown with a green trail and the intruder with a red trail. The grid colours indicate the cost of re-traversal. The higher (brighter) the intensity, the lower the cost.

Theorems & Definitions (2)

• Theorem 1
• proof