A Decision-Making Framework for Control Strategies in Probabilistic Search

Abstract

Abstract-This paper presents the search problem formulated as a decision problem, where the searcher decides whether the target is present in the search region, and if so, where it is located. Such decision-based search tasks are relevant to many research areas, including mobile robot missions, visual search and attention, and event detection in sensor networks. The effect of control strategies in search problems on decisionmaking quantities, namely time-to-decision, is investigated in this work. We present a Bayesian framework in which the objective is to improve the decision, rather than the sensing, using different control policies. Furthermore, derivations of closed-form expressions governing the evolution of the belief function are also presented. As this framework enables the study and comparison of the role of control for decision-making applications, the derived theoretical results provide greater insight into the sequential processing of decisions. Numerical studies are presented to verify and demonstrate these results. I. INTRODUCTIONThe goal in a search problem is to generate the search paths in uncertain environments that best enable the searcher to locate a target (perhaps among other objects) using one or more mobile sensor platforms, possibly under resource constraints. Inspired by the seminal works of B. Koopman [1] and L.D. Stone [2], this physical search theory has been extensively developed.Beyond the search for targets using mobile sensors, however, the search problem can be generalized to represent the class of problems where choice of observations is controlled to best search for an object or outcome. For instance, the scheduling of individual sensor nodes in a wireless sensor network or the selection of the focus-of-attention in visual systems can also be formulated as search problems, where a control policy is generated to improve the information obtained by observations. This paper presents a formal framework which casts the search problem as a decision between hypotheses about the decision-maker's current knowledge. In the specific case typically considered in the physical search theory literature, the decision reflects a belief of whether or not the target of interest is present in the search region. However, our general formulation allows for analysis of the belief evolution as more observations are taken, as well as the definition of measures of the quality of the decision, such as performance and robustness of the decision-making process.Given its relevance to a variety of autonomous, mobile sensor applications, search theory has been studied extensively in the literature. In addition to the defining works mentioned previously, [3] discusses various components of the search problem, including classes of search paths, models

Coordinated Search with a Swarm of UAVs

“…Following Chung [3], we model the problem as follows: 1) We are searching for a single, stationary target x T that might lie in the search area A. 2) A is decomposed into a set of |A| grid cells.…”

“…Let x T = a denote the event that the target lies in cell a. Each cell contains the probability that the target is present in that cell [3], [4].…”

“…To account for this dependence, we update all the cells in the belief map after each observation in a similar way as described in [3] and [5]. In addition, we also account for the fact that for each measurement, the k th UAV can observe a set of M h k cells simultaneously, where h k is the altitude of the UAV.…”

Stochastic surveillance strategies for spatial quickest detection

“…Castañón [4] poses the search problem as a dynamic hypothesis test, and determines the optimal routing policy that maximizes the probability of detection of a target. Chung et al [5] study the probabilistic search problem in a decision theoretic framework. They present various search policies including sequential hypothesis tests.…”

Optimized graph topologies for probabilistic search

“…Numerous works have considered optimization of searcher paths in both the OR (see [14] for a survey) and robotics communities (e.g., [15]), but few have investigated the structure of the search environment and its modification as they pertain to the probabilistic search process. The connection between algebraic connectivity and search performance has been studied in [16], leveraging a framework for decision making in probabilistic search found in [17]. To the best of our knowledge, this is the first work that provides insight in the relation between augmenting a given connected graph and probabilistic search performance.…”