33 research outputs found

    Robotic Surveillance Based on the Meeting Time of Random Walks

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    This paper analyzes the meeting time between a pair of pursuer and evader performing random walks on digraphs. The existing bounds on the meeting time usually work only for certain classes of walks and cannot be used to formulate optimization problems and design robotic strategies. First, by analyzing multiple random walks on a common graph as a single random walk on the Kronecker product graph, we provide the first closed-form expression for the expected meeting time in terms of the transition matrices of the moving agents. This novel expression leads to necessary and sufficient conditions for the meeting time to be finite and to insightful graph-theoretic interpretations. Second, based on the closed-form expression, we setup and study the minimization problem for the expected capture time for a pursuer/evader pair. We report theoretical and numerical results on basic case studies to show the effectiveness of the design.Comment: arXiv admin note: substantial text overlap with arXiv:1806.0884

    Robot Patrolling for Stochastic and Adversarial Events

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    In this thesis, we present and analyze two robot patrolling problems. The first problem discusses stochastic patrolling strategies in adversarial environments where intruders use the information about a patrolling path to increase chances of successful attacks on the environment. We use Markov chains to design the random patrolling paths on graphs. We present four different intruder models, each of which use the information about patrolling paths in a different manner. We characterize the expected rewards for those intruder models as a function of the Markov chain that is being used for patrolling. We show that minimizing the reward functions is a non convex constrained optimization problem in general. We then discuss the application of different numerical optimization methods to minimize the expected reward for any given type of intruder and propose a pattern search algorithm to determine a locally optimal patrolling strategy. We also show that for a certain type of intruder, a deterministic patrolling policy given by the orienteering tour of the graph is the optimal patrolling strategy. The second problem that we define and analyze is the Event Detection and Confirmation Problem in which the events arrive randomly on the vertices of a graph and stay active for a random amount of time. The events that stay longer than a certain amount of time are defined to be true events. The monitoring robot can traverse the graph to detect newly arrived events and can revisit these events in order to classify them as true events. The goal is to maximize the number of true events that are correctly classified by the robot. We show that the off-line version of the problem is NP-hard. We then consider a simple patrolling policy based on the TSP tour of the graph and characterize the probability of correctly classifying a true event. We investigate the problem when multiple robots follow the same path, and show that the optimal spacing between the robots in that case can be non uniform

    RoSSO: A High-Performance Python Package for Robotic Surveillance Strategy Optimization Using JAX

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    To enable the computation of effective randomized patrol routes for single- or multi-robot teams, we present RoSSO, a Python package designed for solving Markov chain optimization problems. We exploit machine-learning techniques such as reverse-mode automatic differentiation and constraint parametrization to achieve superior efficiency compared to general-purpose nonlinear programming solvers. Additionally, we supplement a game-theoretic stochastic surveillance formulation in the literature with a novel greedy algorithm and multi-robot extension. We close with numerical results for a police district in downtown San Francisco that demonstrate RoSSO's capabilities on our new formulations and the prior work.Comment: 7 pages, 4 figures, 3 tables, submitted to the 2024 IEEE International Conference on Robotics and Automation. See https://github.com/conhugh/RoSSO for associated codebas

    Robotic Surveillance and Deployment Strategies

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    Autonomous mobile systems are becoming more common place, and have the opportunity to revolutionize many modern application areas. They include, but are not limited to, tasks such as search and rescue operations, ad-hoc mobile wireless networks and warehouse management; each application having its own complexities and challenging problems that need addressing. In this thesis, we explore and characterize two application areas in particular. First, we explore the problem of autonomous stochastic surveillance. In particular, we study random walks on a finite graph that are described by a Markov chain. We present strategies that minimize the first hitting time of the Markov chain, and look at both the single agent and multi-agent cases. In the single agent case, we provide a formulation and convex optimization scheme for the hitting time on graphs with travel distances. In addition, we provide detailed simulation results showing the effectiveness of our strategy versus other well-known Markov chain design strategies. In the multi-agent case, we provide the first characterization of the hitting time for multiple random walkers, which we denote the "group hitting time". We also provide a closed form solution for calculating the hitting time between specified nodes for both the single and multiple random walker cases. Our results allow for the multiple random walks to be different and, moreover, for the random walks to operate on different subgraphs. Finally, we use sequential quadratic programming to find the transition matrices that generate minimal "group hitting time".Second, we consider the problem of optimal coverage with a group of mobile agents. For a planar environment with an associated density function, this problem is equivalent to dividing the environment into optimal subregions such that each agent is responsible for the coverage of its own region. We study this problem for the discrete time and space case and the continuous time and space case. For the discrete time and space case, we present algorithms that provide optimal coverage control in a non-convex environment when each robot has only asynchronous and sporadic communication with a base station. We introduce the notion of coverings, a generalization of partitions, to do this. For the continuous time and space case, we present a continuous-time distributed policy which allows a team of agents to achieve a convex area-constrained partition in a convex workspace. This work is related to the classic Lloyd algorithm, and makes use of generalized Voronoi diagrams. For both cases we provide detailed simulation results and discuss practical implementation issues
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