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Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations
Robotics · Submitted 24 Sep 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our constructive proof also produces an efficient algorithm for computing the unique optimal solution with $O(n)$ time complexity, in which $n$ is the number of stations, with $O(\log n)$ time complexity for incrementally adding or removing stations.
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The abstract, sentence by sentence
This paper introduces a new mobile sensor scheduling problem, involving a single robot tasked with monitoring several events of interest that occur at different locations. Of particular interest is the monitoring of transient events that can not be easily forecast. Application areas range from natural phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano using a ground robot) to urban activities ({\em e.g.}, monitoring early formations of traffic congestion using an aerial robot). Motivated by those and many other examples, this paper focuses on problems in which the precise occurrence times of the events are unknown {\em a priori}, but statistics for their inter-arrival times are available. The robot's task is to monitor the events to optimize the following two objectives: {\em (i)} maximize the number of events observed and {\em (ii)} minimize the delay between two consecutive observations of events occurring at the same location. The paper considers the case when a robot is tasked with optimizing the event observations in a balanced manner, following a cyclic patrolling route. First, assuming the cyclic ordering of stations is known, we prove the existence and uniqueness of the optimal solution, and show that the optimal solution has desirable convergence and robustness properties. Our constructive proof also produces an efficient algorithm for computing the unique optimal solution with $O(n)$ time complexity, in which $n$ is the number of stations, with $O(\log n)$ time complexity for incrementally adding or removing stations. Except for the algorithm, most of the analysis remains valid when the cyclic order is unknown. We then provide a polynomial-time approximation scheme that gives a $(1+\epsilon)$-optimal solution for this more general, NP-hard problem.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper introduces a new mobile sensor scheduling problem, involving a single robot tasked with monitoring several events of interest that occur at different locations. | contribution 0.82 | 0.75 | 0.04 | asserted 1.00 |
| s1 | Of particular interest is the monitoring of transient events that can not be easily forecast. | background 0.99 | 0.07 | 0.02 | asserted 0.97 |
| s2 | Application areas range from natural phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano using a ground robot) to urban activities ({\em e.g.}, monitoring early formations of traffic congestion using an aerial robot). | background 1.00 | 0.07 | 0.02 | asserted 0.96 |
| s3 | Motivated by those and many other examples, this paper focuses on problems in which the precise occurrence times of the events are unknown {\em a priori}, but statistics for their inter-arrival times are available. | background 0.91 | 0.16 | 0.03 | asserted 0.98 |
| s4 | The robot's task is to monitor the events to optimize the following two objectives: {\em (i)} maximize the number of events observed and {\em (ii)} minimize the delay between two consecutive observations of events occurring at the same location. | background 0.63 | 0.28 | 0.07 | asserted 0.99 |
| s5 | The paper considers the case when a robot is tasked with optimizing the event observations in a balanced manner, following a cyclic patrolling route. | contribution 0.38 | 0.34 | 0.05 | asserted 0.98 |
| s6 | First, assuming the cyclic ordering of stations is known, we prove the existence and uniqueness of the optimal solution, and show that the optimal solution has desirable convergence and robustness properties. | result 0.76 | 0.94 | 0.27 | asserted 1.00 |
| s7 | Our constructive proof also produces an efficient algorithm for computing the unique optimal solution with $O(n)$ time complexity, in which $n$ is the number of stations, with $O(\log n)$ time complexity for incrementally adding or removing stations. | contribution 0.57 | 0.96 | 0.21 | asserted 1.00 |
| s8 | Except for the algorithm, most of the analysis remains valid when the cyclic order is unknown. | result 0.61 | 0.80 | 0.07 | asserted 0.89 |
| s9 | We then provide a polynomial-time approximation scheme that gives a $(1+\epsilon)$-optimal solution for this more general, NP-hard problem. | contribution 0.81 | 0.94 | 0.22 | asserted 1.00 |
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The paper
Original abstract
This paper introduces a new mobile sensor scheduling problem, involving a single robot tasked with monitoring several events of interest that occur at different locations. Of particular interest is the monitoring of transient events that can not be easily forecast. Application areas range from natural phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano using a ground robot) to urban activities ({\em e.g.}, monitoring early formations of traffic congestion using an aerial robot). Motivated by those and many other examples, this paper focuses on problems in which the precise occurrence times of the events are unknown {\em a priori}, but statistics for their inter-arrival times are available. The robot's task is to monitor the events to optimize the following two objectives: {\em (i)} maximize the number of events observed and {\em (ii)} minimize the delay between two consecutive observations of events occurring at the same location. The paper considers the case when a robot is tasked with optimizing the event observations in a balanced manner, following a cyclic patrolling route. First, assuming the cyclic ordering of stations is known, we prove the existence and uniqueness of the optimal solution, and show that the optimal solution has desirable convergence and robustness properties. Our constructive proof also produces an efficient algorithm for computing the unique optimal solution with $O(n)$ time complexity, in which $n$ is the number of stations, with $O(\log n)$ time complexity for incrementally adding or removing stations. Except for the algorithm, most of the analysis remains valid when the cyclic order is unknown. We then provide a polynomial-time approximation scheme that gives a $(1+\epsilon)$-optimal solution for this more general, NP-hard problem.
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How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as background 2 papers
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For the problem of observing stochastically arriving events at multiple locations with a single mobile robot, a $(1+ϵ)$-optimal algorithm was proposed in [ref] to solve the multi-objective optimization problem of maximizing event observation in a balanced manner and minimizing delay between event observations across the locations.
Optimal Tourist Problem and Anytime Planning of Trip Itineraries · Introduction · 0.95
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The literature on informative path and policy planning for persistent monitoring is fairly rich [ref] , covering theories, systems, algorithm designs, and applications.
Correlated Orienteering Problem and it Application to Persistent Monitoring Tasks · Introduction · 0.98
What it cites
Cites as background 1 paper
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Motivated by a variety of potential applications, such as aerial [ref] and underwater [ref] data collection, several authors have studied persistent monitoring problems [ref] .
Memoryless Control Design for Persistent Surveillance under Safety Constraints · Introduction · 0.97
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