33 research outputs found
Robotic Surveillance Based on the Meeting Time of Random Walks
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
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
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
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A Theory of Collective Cell Migration and the Design of Stochastic Surveillance Strategies
In nature, complex emergent behavior arises in groups of biological entities often as a result of simple local interactions between neighbors in space or on a network. In such cases, scientific inquiry is typically aimed at inferring these local rules. Conversely, in teams of robots, the goal is to create decentralized control laws which results in efficient global behavior. These behaviors are designed for tasks such as maintaining formation control, performing effective coverage control or persistently monitoring an environment. With this in mind, we consider the following: 1> the emergence of collective cell migration from local contact and mechanical feedback and 2> the design of unpredictable surveillance strategies for teams of robots.Collective cell migration is an essential part of tissue and organ morphogenesis during embryonic development, as well as of various disease processes, such as cancer. The vast majority of theoretical descriptions of collective cell behavior focus on large numbers of cells, but fail to accurately capture the dynamics of small groups of cells. Here we introduce a low-dimensional theoretical description that successfully describes single cell migration, cell collisions, collective dynamics in small groups of cells, and force propagation during sheet expansion, all within a common theoretical framework. We also explain the counter-intuitive observation that pairs of cells repel each other upon collision while they coordinate their motion in larger clusters.Conventional monitoring strategies used by teams of robots are deterministic in nature making it possible for intelligent intruders who study the motion of the patrolling agent to compromise the patrol route. This problem can be solved by designing random walkers on graphs which naturally incorporate unpredictability. Within this framework, we study and provide the first analytic expression for the first meeting time of multiple random walkers, in terms of their transition matrices. We also study two problems related to maximizing unpredictability: given graph and visit frequency constraints, 1> maximize the entropy rate generated by a Markov chain, and 2> maximize the return time entropy associated with the Markov chain, where the return time entropy is the weighted average over all graph nodes of the entropy of the first return times of the Markov chain
Robotic Surveillance and Deployment Strategies
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