Extracting Surveillance Graphs from Robot Maps Andreas Kolling and Stefano Carpin Abstract— GRAPH-CLEAR is a recently introduced theo- retical framework to model surveillance tasks accomplished by multiple robots patrolling complex indoor environments. In this paper we provide a first step to close the loop between its graph- based theoretical formulation and practical scenarios. We show how it is possible to algorithmically extract suitable so-called surveillance graphs from occupancy grid maps. We also identify local graph modification operators, called contractions, that alter the graph being extracted so that the original surveillance problem can be solved using less robots. The algorithm we present is based on the Generalized Voronoi Diagram, a structure that can be simply computed using watershed like algorithms. Our algorithm is evaluated by processing maps produced by mobile robots exploring indoor environments. It turns out that the proposed algorithm is fast, robust to noise, and opportunistically modifies the graph so that less expensive strategies can be computed. I. I NTRODUCTION We recently introduced a theoretical framework called GRAPH-CLEAR to model surveillance tasks performed by teams of robots [1][2]. One of its peculiar aspects resides in a conceptual mechanism that allows to model and study different search and clear strategies abstracting from the un- derlying robotic platforms used. GRAPH-CLEAR in partic- ular aims to model surveillance tasks where multiple robots with limited sensing capabilities cooperate to detect intruders in complex environments. The name GRAPH-CLEAR stems from the fact that environments to be cleared are modeled as surveillance graphs, i.e. a special graph class that will be later defined. Theoretical properties of GRAPH-CLEAR, as well as solving algorithms have been extensively studied in an earlier stage of this research, and will be summarized in the remaining part of the paper. In this manuscript we present the first steps towards the practical deployment of robot teams that clear complex environments using the formalism we formerly investigated. In particular we address the problem of automatic extraction of surveillance graphs from occupancy grid maps. Informally speaking, this task entails allocating graph vertices on rooms and graph edges on corridors or connections between rooms. The reader will realize that this step is similar to creating topological maps from occupancy grid maps. However, our task is more complex and our contribution more articulated. In order to enable the GRAPH-CLEAR framework it is also necessary to determine certain weights associated with edges and vertices. These weights measure the effort, i.e. the number of robots, needed to enforce relevant properties on the graph, like for example preventing intruders from passing through a door, or from hiding in a room. The method to assign weights School of Engineering, University of California,Merced, CA, USA presented in this paper is parametric with regard to the sensing capabilities of the robots used to implement the clearing strategies, and has therefore general applicability. In addition, while extracting graphs from occupancy grid maps we have identified certain opportunistic operations that modify the graph so that the algorithm generating clearing strategies produces solutions requiring less robots. While most ideas herein generalize to varying implementations of the basic GRAPH-CLEAR actions, i.e. blocking edges and clearing vertices, we will present experimental results for particular implementations of these actions on two realistic robot maps, one collected for a P3AT at UCMerced and one generated from the Radish online robotics data repository [3] called ”sdr site b”. The remaining part of the paper is organized as follows. Section II shortly revises related work in the area of robot aided surveillance systems, and pursuit evasion games. GRAPH-CLEAR and its solving algorithm are informally presented in section III. Section IV illustrates how graphs are created starting from occupancy grids, and how these graphs can be modified in order to yield better solving strategies. Strategies to block edges and clear vertices are presented in section V. Finally, experimental results are shown in section VI, and conclusions are drawn in section VII. II. RELATED WORK Surveillance tasks have been studied in a great number of variations. One version with strong theoretical results are visibility-based pursuit-evasion games, first investigated by Suzuki and Yamashita for detecting targets with an unlimited range beam sensor in [4]. Subsequently many variants of this problem were studied, most notably the variant of a robot with an unlimited range omnidirectional gap sensor [5] which can detect intruders robustly and in manifold environments. An entirely different approach was taken by Parker who investigated the surveillance of multiple moving targets in simple planar environments by large robot teams in [6]. Also in open planar environments we find a capturing strategy presented in [7] in which robots form a so called trapping chain to ensure that the target once detected by any robot in the chain will subsequently be caught. Probabilistic detection guarantees are given for traversing an environment with such chains for varying conditions. A probabilistic approach which works in cluttered environments is presented in [8]. The GRAPH-CLEAR problem was formalized in [2] in which we presented algorithms to compute strategies for GRAPH-CLEAR on trees and heuristics to apply tree strategies to graphs. Improved algorithms were presented in [1]. GRAPH-CLEAR is an extension of edge-search another