The Fagnano Triangle Patrolling Problem

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

3D multi-robot patrolling with a two-level coordination strategy

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

Efficient Mission Planning for Robot Networks in Communication Constrained Environments

Many robotic systems are remotely operated nowadays that require uninterrupted connection and safe mission planning. Such systems are commonly found in military drones, search and rescue operations, mining robotics, agriculture, and environmental monitoring. Different robotic systems may employ disparate communication modalities such as radio network, visible light communication, satellite, infrared, Wi-Fi. However, in an autonomous mission where the robots are expected to be interconnected, communication constrained environment frequently arises due to the out of range problem or unavailability of the signal. Furthermore, several automated projects (building construction, assembly line) do not guarantee uninterrupted communication, and a safe project plan is required that optimizes collision risks, cost, and duration. In this thesis, we propose four pronged approaches to alleviate some of these issues: 1) Communication aware world mapping; 2) Communication preserving using the Line-of-Sight (LoS); 3) Communication aware safe planning; and 4) Multi-Objective motion planning for navigation. First, we focus on developing a communication aware world map that integrates traditional world models with the planning of multi-robot placement. Our proposed communication map selects the optimal placement of a chain of intermediate relay vehicles in order to maximize communication quality to a remote unit. We also vi propose an algorithm to build a min-Arborescence tree when there are multiple remote units to be served. Second, in communication denied environments, we use Line-of-Sight (LoS) to establish communication between mobile robots, control their movements and relay information to other autonomous units. We formulate and study the complexity of a multi-robot relay network positioning problem and propose approximation algorithms that restore visibility based connectivity through the relocation of one or more robots. Third, we develop a framework to quantify the safety score of a fully automated robotic mission where the coexistence of human and robot may pose a collision risk. A number of alternate mission plans are analyzed using motion planning algorithms to select the safest one. Finally, an efficient multi-objective optimization based path planning for the robots is developed to deal with several Pareto optimal cost attributes

Developing Police Patrol Strategies Based on the Urban Street Network

In urban areas, crime and disorder have been long-lasting problems that spoil the economic and emotional well-being of residents. A significant way to deter crime, and maintain public safety is through police patrolling. So far, the deployment of police forces in patrolling has relied mainly on expert knowledge, and is usually based on two-dimensional spatial units, giving insufficient consideration to the underlying urban structure and collaboration among patrol officers. This approach has led to impractical and inefficient police patrol strategies, as well as a workload imbalance among officers. Therefore, it is of essential importance to devise advanced police patrol strategies that incorporate urban structure, the collaboration of the patrol officers, and a workload balance. This study aims to develop police patrol strategies that would make intelligent use of the street network layout in urban areas. The street network is a key component in urban structure and is the domain in which crime and policing take place. By explicitly considering street network configurations in their operations, police forces are enabled to provide timely responses to emergency calls and essential coverage to crime hotspots. Although some models have considered street networks in patrolling to some extent, challenges remain. First, most existing methods for the design of police districts use two-dimensional units, such as grid cells, as basic units, but using streets as basic units would lead to districts that are more accessible and usable. Second, the routing problem in police patrolling has several unique characteristics, such as patrollers potentially starting from different stations, but most existing routing strategies have failed to consider these. Third, police patrolling strategies should be validated using real-world scenarios, whilst most existing strategies in the literature have only been tested in small hypothetical instances without realistic settings. In this thesis, a framework for developing police patrol strategies based on the urban street network is proposed, to effectively cover crime hotspots, as well as the rest of the territory. This framework consists of three strategies, including a districting model, a patrol routing strategy for repeated coverage, and a patrol routing strategy for infrequent coverage. Various relevant factors have been considered in the strategy design, including the underlying structure of the street network and the collaboration among patrollers belonging to different stations. Moreover, these strategies have been validated by the patrolling scenarios in London. The results demonstrate that these strategies outperform the current corresponding benchmark strategies, which indicates that they may have considerable potential in future police operations

Aerial Drone-based System for Wildfire Monitoring and Suppression

Wildfire, also known as forest fire or bushfire, being an uncontrolled fire crossing an area of combustible vegetation, has become an inherent natural feature of the landscape in many regions of the world. From local to global scales, wildfire has caused substantial social, economic and environmental consequences. Given the hazardous nature of wildfire, developing automated and safe means to monitor and fight the wildfire is of special interest. Unmanned aerial vehicles (UAVs), equipped with appropriate sensors and fire retardants, are available to remotely monitor and fight the area undergoing wildfires, thus helping fire brigades in mitigating the influence of wildfires. This thesis is dedicated to utilizing UAVs to provide automated surveillance, tracking and fire suppression services on an active wildfire event. Considering the requirement of collecting the latest information of a region prone to wildfires, we presented a strategy to deploy the estimated minimum number of UAVs over the target space with nonuniform importance, such that they can persistently monitor the target space to provide a complete area coverage whilst keeping a desired frequency of visits to areas of interest within a predefined time period. Considering the existence of occlusions on partial segments of the sensed wildfire boundary, we processed both contour and flame surface features of wildfires with a proposed numerical algorithm to quickly estimate the occluded wildfire boundary. To provide real-time situational awareness of the propagated wildfire boundary, according to the prior knowledge of the whole wildfire boundary is available or not, we used the principle of vector field to design a model-based guidance law and a model-free guidance law. The former is derived from the radial basis function approximated wildfire boundary while the later is based on the distance between the UAV and the sensed wildfire boundary. Both vector field based guidance laws can drive the UAV to converge to and patrol along the dynamic wildfire boundary. To effectively mitigate the impacts of wildfires, we analyzed the advancement based activeness of the wildfire boundary with a signal prominence based algorithm, and designed a preferential firefighting strategy to guide the UAV to suppress fires along the highly active segments of the wildfire boundary

Multi-Robot Path Planning for Persistent Monitoring in Stochastic and Adversarial Environments

In this thesis, we study multi-robot path planning problems for persistent monitoring tasks. The goal of such persistent monitoring tasks is to deploy a team of cooperating mobile robots in an environment to continually observe locations of interest in the environment. Robots patrol the environment in order to detect events arriving at the locations of the environment. The events stay at those locations for a certain amount of time before leaving and can only be detected if one of the robots visits the location of an event while the event is there. In order to detect all possible events arriving at a vertex, the maximum time spent by the robots between visits to that vertex should be less than the duration of the events arriving at that vertex. We consider the problem of finding the minimum number of robots to satisfy these revisit time constraints, also called latency constraints. The decision version of this problem is PSPACE-complete. We provide an O(log p) approximation algorithm for this problem where p is the ratio of the maximum and minimum latency constraints. We also present heuristic algorithms to solve the problem and show through simulations that a proposed orienteering-based heuristic algorithm gives better solutions than the approximation algorithm. We additionally provide an algorithm for the problem of minimizing the maximum weighted latency given a fixed number of robots. In case the event stay durations are not fixed but are drawn from a known distribution, we consider the problem of maximizing the expected number of detected events. We motivate randomized patrolling paths for such scenarios and use Markov chains to represent those random patrolling paths. We characterize the expected number of detected events as a function of the Markov chains used for patrolling and show that the objective function is submodular for randomly arriving events. We propose an approximation algorithm for the case where the event durations for all the vertices is a constant. We also propose a centralized and an online distributed algorithm to find the random patrolling policies for the robots. We also consider the case where the events are adversarial and can choose where and when to appear in order to maximize their chances of remaining undetected. The last problem we study in this thesis considers events triggered by a learning adversary. The adversary has a limited time to observe the patrolling policy before it decides when and where events should appear. We study the single robot version of this problem and model this problem as a multi-stage two player game. The adversary observes the patroller’s actions for a finite amount of time to learn the patroller’s strategy and then either chooses a location for the event to appear or reneges based on its confidence in the learned strategy. We characterize the expected payoffs for the players and propose a search algorithm to find a patrolling policy in such scenarios. We illustrate the trade off between hard to learn and hard to attack strategies through simulations