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Multi-Agent Patrolling Problems consist in moving agents throughout a graph in order to optimize a collective performance metric. Some strategies from the literature tackle this problem by dispatching decentralized autonomous agents that coordinate themselves merely by sensing and writing information in the nodes. In this work, they are called k-range local strategies , were k indicates the range, in number of edges, of the agents’ sensing capabilities. The 1-range strategies (where agents can sense up to its neighbor nodes) are certainly the most common case in the literature. And only few 0-range strategies (where agents can only sense its current node) were found, although this type of strategy has the advantage of requiring simpler hardware, when applied in the design of real robots. In this work, we propose two higher-level procedures to reduce the perception range of 1-range strategies to 0: the Zr Method and the EZr Method . Applying both methods in 1-range strategies found in the literature, we created twenty new 0-range strategies, which were evaluated in a simulation experiment described and analyzed here. We also developed a prototype of a low-cost patrolling robot that is able to run the 0-range strategies proposed in this work.

A patrolling strategy that defines fare inspection frequencies on a proof-of-payment transportation system is operationally useful to the transit authority when there is a mechanism for its practical implementation. This study addresses the operational implementation of a fare inspection patrolling strategy under an in-station selective inspection policy using an unpredictable patrolling schedule, where the transit authority select a patrolling schedule each day with some probability. The challenge is to determine the set of patrolling schedules and their respective probabilities of being selected whose systematic day-to-day application matches the inspection frequencies that inhibit the action of opportunistic passengers in the medium term. A Stackelberg game approach is used to represent the hierarchical decision making process between the transit authority and opportunistic passengers. The heterogeneity of opportunistic passengers’ decisions to evade fare payment is taken into account. Numerical experiments show that a joint strategy-schedule approach provides good-quality unpredictable patrolling schedules with respect to the optimality gap for large-scale networks.

Multi-robot patrolling is a key feature for various applications related to surveillance and security, and it has been studied from several different perspectives, ranging from techniques that devise optimal off-line strategies to implemented systems. However, still few approaches consider on-line decision techniques that can cope with uncertainty and non-determinism in robot behaviors. In this article we address on-line coordination, by casting the multi-robot patrolling problem as a task assignment problem and proposing two solution techniques: DTA-Greedy, which is a baseline greedy approach, and DTAP, which is based on sequential single-item auctions. We evaluate the performance of our system in a realistic simulation environment (built with ROS and stage) as well as on real robotic platforms. In particular, in the simulated environment we compare our task assignment approaches with previous off-line and on-line methods. Our results confirm that on-line coordination approaches improve the performance of the multi-robot patrolling system in real environments, and that coordination approaches that employ more informed coordination protocols (e.g., DTAP) achieve better performances with respect to state-of-the-art online approaches (e.g., SEBS) in scenarios where interferences among robots are likely to occur. Moreover, the deployment on real platforms (three Turtlebots in an office environment) shows that our on-line approaches can successfully coordinate the robots achieving good patrolling behaviors when facing typical uncertainty and noise (e.g., localization and navigation errors) associated to real platforms.

Patrolling an environment with multiple robots is a problem with applicability to both military activities and other areas requiring security. In an adversarial environment, wireless communication between the robots may be jammed, and their sensor ranges may be limited to visibility. This increases the difficulty of the problem, but solutions will be widely applicable regardless of the environment. Robot paths that are deterministic can be observed and predicted by an adversary, permitting exploitation of known gaps in coverage. We also wish to avoid requirements for synchronization or a particular form of the environment. We, therefore, propose a method of finding patrolling policies for multiple robots that monitor any polygonal environment using limited visibility regions and non-deterministic patrolling paths. First, visibility regions are calculated for a subset of locations that cover the whole environment or a part of the environment. Then, we find distributed patrolling policies in the form of Markov chains, using convex optimization to minimize the average expected commute time for the subset of the locations permitting each robot to cover the whole environment independently. We also find centralized and Markov chain based patrolling policies that minimize the average expected commute time for the subset of locations permitting each robot to cover a part of the environment while communicating with a central base station. Finally, we evaluate the vulnerability of our patrolling policies by finding the probability of capturing an adversary and the maximum unguarded time for a location in our proposed patrolling scenarios. We present multiple simulation results and a physical implementation to show the effectiveness of our visibility-based non-deterministic patrolling method.

Today, mobile robots have a wide range of real-world applications where they can replace or assist humans in many tasks, such as search and rescue, surveillance, patrolling, inspection, environmental monitoring, etc. These tasks usually require a robot to navigate through a dynamic environment with smooth, efficient, and safe motion. In this paper, we propose an online smooth-motion-planning method that generates a smooth, collision-free patrolling trajectory based on clothoid curves. Moreover, the proposed method combines global and local planning methods, which are suitable for changing large environments and enabling efficient path replanning with an arbitrary robot orientation. We propose a method for planning a smoothed path based on the golden ratio wherein a robot’s orientation is aligned with a new path that avoids unknown obstacles. The simulation results show that the proposed algorithm reduces the patrolling execution time, path length, and deviation of the tracked trajectory from the patrolling route compared to the original patrolling method without smoothing. Furthermore, the proposed algorithm is suitable for real-time operation due to its computational simplicity, and its performance was validated through the results of an experiment employing a differential-drive mobile robot.

The remarkable development of various sensor equipment and communication technologies has stimulated many application platforms of automation. A drone is a sensing platform with strong environmental adaptability and expandability, which is widely used in aerial photography, transmission line inspection, remote sensing mapping, auxiliary communication, traffic patrolling, and other fields. A drone is an effective supplement to the current patrolling business in road traffic patrolling with complex urban buildings and road conditions and a limited ground perspective. However, the limited endurance of patrol drones can be directly solved by vehicles that cooperate with drones on patrolling missions. In this paper, we first proposed and studied the traffic patrolling routing problem with drones (TPRP-D) in an urban road system. Considering road network equations and the heterogeneity of patrolling tasks in the actual patrolling process, we modeled the problem as a double-layer arc routing problem (DL-ARP). Based on graph theory and related research work, we present the mixed integer linear programming formulations and two-stage heuristic solution approaches to solve practical-sized problems. Through analysis of numerical experiments, the solution method proposed in this paper can quickly provide an optimal path planning scheme for different test sets, which can save 9%–16% of time compared with traditional vehicle patrol. At the same time, we analyze several relevant parameters of the patrol process to determine the effect of coordinated traffic patrol. Finally, a case study was completed to verify the practicability of the algorithm.

Teams of UGVs patrolling harsh and complex 3D environments can experience interference and spatial conflicts with one another. Neglecting the occurrence of these events crucially hinders both soundness and reliability of a patrolling process. This work presents a distributed multi-robot patrolling technique, which uses a two-level coordination strategy to minimize and explicitly manage the occurrence of conflicts and interference. The first level guides the agents to single out exclusive target nodes on a topological map. This target selection relies on a shared idleness representation and a coordination mechanism preventing topological conflicts. The second level hosts coordination strategies based on a metric representation of space and is supported by a 3D SLAM system. Here, each robot path planner negotiates spatial conflicts by applying a multi-robot traversability function. Continuous interactions between these two levels ensure coordination and conflicts resolution. Both simulations and real-world experiments are presented to validate the performances of the proposed patrolling strategy in 3D environments. Results show this is a promising solution for managing spatial conflicts and preventing deadlocks.

Poaching is driving many species toward extinction, and as a result, lowering poaching pressure is a conservation priority. This requires understanding where poaching pressure is high and which factors determine these spatial patterns. However, the cryptic and illegal nature of poaching makes this difficult. Ranger patrol data, typically recorded in protected area logbooks, contain information on patrolling efforts and poaching detection and should thus provide opportunities for a better understanding of poaching pressure. However, these data are seldom analyzed and rarely used to inform adaptive management strategies. We developed a novel approach to making use of analog logbook records to map poaching pressure and to test environmental criminology and predator–prey relationship hypotheses explaining poaching patterns. We showcase this approach for Golestan National Park in Iran, where poaching has substantially depleted ungulate populations. We digitized data from >4800 ranger patrols from 2014 to 2016 and used an occupancy modeling framework to relate poaching to (1) accessibility, (2) law enforcement, and (3) prey availability factors. Based on predicted poaching pressure and patrolling intensity, we provide suggestions for future patrol allocation strategies. Our results revealed a low probability (12%) of poacher detection during patrols. Poaching distribution was best explained by prey availability, indicating that poachers target areas with high concentrations of ungulates. Poaching pressure was estimated to be high (>0.49) in 39% of our study area. To alleviate poaching pressure, we recommend ramping up patrolling intensity in 12% of the national park, which could be achievable by reducing excess patrols in about 20% of the park. However, our results suggest that for 27% of the park, it is necessary to improve patrolling quality to increase detection probability of poaching, for example, by closing temporal patrolling gaps or expanding informant networks. Our approach illustrates that analog ranger logbooks are an untapped resource for evidence-based and adaptive planning of protected area management. Using this wealth of data can open up new avenues to better understand poaching and its determinants, to expand effectiveness assessments to the past, and, more generally, to allow for strategic conservation planning in protected areas.

We investigate a combinatorial optimization problem that involves patrolling the edges of an acute triangle using a unit-speed agent. The goal is to minimize the maximum (1-gap) idle time of any edge, which is defined as the time gap between consecutive visits to that edge. This problem has roots in a centuries-old optimization problem posed by Fagnano in 1775, who sought to determine the inscribed triangle of an acute triangle with the minimum perimeter. It is well-known that the orthic triangle, giving rise to a periodic and cyclic trajectory obeying the laws of geometric optics, is the optimal solution to Fagnano's problem. Such trajectories are known as Fagnano orbits, or more generally as billiard trajectories. We demonstrate that the orthic triangle is also an optimal solution to the patrolling problem. Our main contributions pertain to new connections between billiard trajectories and optimal patrolling schedules in combinatorial optimization. In particular, as an artifact of our arguments, we introduce a novel 2-gap patrolling problem that seeks to minimize the visitation time of objects every three visits. We prove that there exist infinitely many well-structured billiard-type optimal trajectories for this problem, including the orthic trajectory, which has the special property of minimizing the visitation time gap between any two consecutively visited edges. Complementary to that, we also examine the cost of dynamic, sub-optimal trajectories to the 1-gap patrolling optimization problem. These trajectories result from a greedy algorithm and can be implemented by a computationally primitive mobile agent.

Recovering small populations of threatened species is an important global conservation strategy. Monitoring the anticipated recovery, however, often relies on uncertain abundance indices rather than on rigorous demographic estimates. To counter the severe threat from poaching of wild tigers (Panthera tigris), the Government of Thailand established an intensive patrolling system in 2005 to protect and recover its largest source population in Huai Kha Khaeng Wildlife Sanctuary. Concurrently, we assessed the dynamics of this tiger population over the next 8 years with rigorous photographic capture-recapture methods. From 2006 to 2012, we sampled across 624-1026 km² with 137-200 camera traps. Cameras deployed for 21,359 trap days yielded photographic records of 90 distinct individuals. We used closed model Bayesian spatial capture-recapture methods to estimate tiger abundances annually. Abundance estimates were integrated with likelihood-based open model analyses to estimate rates of annual and overall rates of survival, recruitment, and changes in abundance. Estimates of demographic parameters fluctuated widely: annual density ranged from 1.25 to 2.01 tigers/100 km², abundance from 35 to 58 tigers, survival from 79.6% to 95.5%, and annual recruitment from 0 to 25 tigers. The number of distinct individuals photographed demonstrates the value of photographic capture-recapture methods for assessments of population dynamics in rare and elusive species that are identifiable from natural markings. Possibly because of poaching pressure, overall tiger densities at Huai Kha Khaeng were 82-90% lower than in ecologically comparable sites in India. However, intensified patrolling after 2006 appeared to reduce poaching and was correlated with marginal improvement in tiger survival and recruitment. Our results suggest that population recovery of low-density tiger populations may be slower than anticipated by current global strategies aimed at doubling the number of wild tigers in a decade. Recuperar las poblaciones pequeñas de las especies amenazadas es una importante estrategia global de conservación. Sin embargo, monitorear la recuperación esperada generalmente depende de índices inciertos de abundancia en lugar de estimados demográficos rigurosos. Para contrarrestar la gran amenaza causada por la cacería furtiva de tigres (Panthera tigris), el Gobierno de Tailandia estableció un sistema intensivo de patrullaje en 2005 para proteger y recuperar la población fuente más grande en el Santuario Huai Kha Khaeng. Simultáneamente, evaluamos las dinámicas de esta población de tigres durante los siguientes ocho años con rigurosos métodos fotográficos de captura-recaptura. De 2006 a 2012 muestreamos a lo largo de 624-1026 km² con 137-200 trampas cámara. Las cámaras desplegadas durante 21,359 días de trampa produjeron registros fotográficos de 90 individuos distinguibles. Usamos métodos espaciales de capturarecaptura y modelo bayesiano cerrado para estimar anualmente la abundancia de los tigres. Los estimados de abundancia estuvieron integrados por análisis de modelo abierto basados en la probabilidad para estimar la tasa anual y las tasas generales de supervivencia, reclutamiento y cambios en la abundancia. Los estimados de los parámetros demográficos fluctuaron ampliamente: la densidad anual varió entre 1.25 y 2.01 tigres/100 km², la abundancia entre 35 a 58 tigres, la supervivencia entre 79-6 y 95.5% y el reclutamiento anual de 0 a 25 tigres. El número de individuos distinguibles que fue fotografiado demuestra el valor de los métodos de captura-recaptura para la evaluación de las dinámicas poblacionales de especies raras y elusivas que son identificables gracias a marcas naturales. Posiblemente por causa de la presión ejercida por la caza furtiva, la densidad general de los tigres en Huai Kha Khaeng fue 82-90% más baja que en sitios ecológicamente comparables de India. Sin embargo, el patrullaje intensivo después de 2006 pareció reducir la caza furtiva y estuvo correlacionado con el mejoramiento marginal de la supervivencia y reclutamiento de los tigres. Nuestros resultados sugieren que la recuperación de las poblaciones de tigres con baja densidad puede ser más lenta de lo esperado por las estrategias globales actuales enfocadas en la duplicación del número de tigres en una década.