Searching for multiple targets using Probabilistic Quadtrees

Abstract

Abstract-We consider the problem of searching for an unknown number of static targets inside an assigned area. The search problem is tackled using Probabilisitic Quadtrees (PQ), a data structure we recently introduced. Probabilistic quadtrees allow for a variable resolution representation and naturally induce a search problem where the searcher needs to choose not only where to sense, but also the sensing resolution. Through a Bayesian approach accommodating faulty sensors returning both false positives and missed detections, a posterior distribution about the location of the targets is propagated during the search effort. In this paper we extend our previous findings by considering the problem of searching for an unknown number of targets. Moreover, we substitute our formerly used heuristic with an approach based on information gain and expected costs. Finally, we provide some convergence results showing that in the worst case our model provides the same results as uniform grids, thus guaranteeing that the representation we propose gracefully degrades towards a known model. Extensive simulation results substantiate the properties of the method we propose, and we also show that our variable resolution method outperforms traditional methods based on uniform resolution grids.

Variable Resolution Search with Quadrotors: Theory and Practice

“…Any opinions, findings, and conclusions or recommendations expressed in these materials are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the funding agencies of the U.S. Government. This paper extends preliminary results presented at ICRA 2011 (Chung and Carpin, ) and IROS 2011 (Carpin et al., ). The authors thank Kevin Jones for having shared aerial images needed to obtain Figure .…”

“…Maintaining probabilistic knowledge about multiple targets or integrating a target's movement model in the decision process can challenge a search strategy's definition and obtained performance; see, for example, Carpin et al. (). To align with the performed field experiments and to primarily focus on probabilistic quadtrees, this work builds on that of Chung and Carpin () and considers a single and stationary target.…”

“…We refer the reader to Carpin et al. () for a discussion about the case with multiple targets. For the sake of completeness, in the following we include a comprehensive discussion about Type1 PQ.…”

Physics-aware informative coverage planning for autonomous vehicles

“…In [8], agents followed the gradient of mutual information to minimize total entropy. In [9], a data structure called a probabilistic quad tree was proposed and used to provide a tree structure to the total entropy in the environment during target search. Other examples of information-theoretic coverage planning work include [10], [11].…”