Markov Chain-Based Stochastic Strategies for Robotic Surveillance

Abstract

This article surveys recent advancements of strategy designs for persistent robotic surveillance tasks with the focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way where the efficiency is defined with respect to relevant underlying performance metrics. We first start by reviewing the basics of Markov chains, which is the primary motion model for stochastic robotic surveillance. Then two main criteria regarding the speed and unpredictability of surveillance strategies are discussed. The central objects that appear throughout the treatment is the hitting times of Markov chains, their distributions and expectations. We formulate various optimization problems based on the concerned metrics in different scenarios and establish their respective properties.

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• Persistent Robotic Tasks: Monitoring and Sweeping in Changing Environments
• On cooperative patrolling: optimal trajectories, complexity analysis, and approximation algorithms
• Localization of maximal entropy random walk
• The Role of Kemeny's Constant in Properties of Markov Chains
• Approximation Algorithms for Multi-Robot Patrol-Scheduling with Min-Max Latency