Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations

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

Monitoring using Heterogeneous Autonomous Agents.

This dissertation studies problems involving different types of autonomous agents observing objects of interests in an area. Three types of agents are considered: mobile agents, stationary agents, and marsupial agents, i.e., agents capable of deploying other agents or being deployed themselves. Objects can be mobile or stationary. The problem of a mobile agent without fuel constraints revisiting stationary objects is formulated. Visits to objects are dictated by revisit deadlines, i.e., the maximum time that can elapse between two visits to the same object. The problem is shown to be NP-complete and heuristics are provided to generate paths for the agent. Almost periodic paths are proven to exist. The efficacy of the heuristics is shown through simulation. A variant of the problem where the agent has a finite fuel capacity and purchases fuel is treated. Almost periodic solutions to this problem are also shown to exist and an algorithm to compute the minimal cost path is provided. A problem where mobile and stationary agents cooperate to track a mobile object is formulated, shown to be NP-hard, and a heuristic is given to compute paths for the mobile agents. Optimal configurations for the stationary agents are then studied. Several methods are provided to optimally place the stationary agents; these methods are the maximization of Fisher information, the minimization of the probability of misclassification, and the minimization of the penalty incurred by the placement. A method to compute optimal revisit deadlines for the stationary agents is given. The placement methods are compared and their effectiveness shown using numerical results. The problem of two marsupial agents, one carrier and one passenger, performing a general monitoring task using a constrained optimization formulation is stated. Necessary conditions for optimal paths are provided for cases accounting for constrained release of the passenger, termination conditions for the task, as well as retrieval and constrained retrieval of the passenger. A problem involving two marsupial agents collecting information about a stationary object while avoiding detection is then formulated. Necessary conditions for optimal paths are provided and rectilinear motion is demonstrated to be optimal for both agents.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111439/1/jfargeas_1.pd