Technical Report #SEHIR-IE-VA-12-1: Optimal Obstacle Placement with Disambiguations
Vural Aksakallı, Elvan Ceyhan · arXiv (Cornell University) · 2012
We introduce the optimal obstacle placement with disambiguations problem wherein the goal is to place true obstacles in an environment cluttered with false obstacles so as to maximize the total traversal length of a navigating agent (NAVA). Prior to the traversal, NAVA is given location information and probabilistic estimates of each disk-shaped hindrance (hereinafter referred to as disk) being a true obstacle. The NAVA can disambiguate a disk's status only when situated on its boundary. There exists an obstacle placing agent (OPA) that locates obstacles prior to NAVA's traversal. The goal of OPA is to place true obstacles in between the clutter in such a way that NAVA's traversal length is maximized in a game-theoretic sense. We assume OPA knows the clutter spatial distribution type (referred as clutter type for brevity henceforth), but not the exact locations of clutter disks. We consider various obstacle placement schemes against different clutter point realizations sampled from Poisson, clustered, and regular spatial point distributions. In our obstacle placement schemes, obstacles are located according to a Poisson distribution in various window types. We analyze the traversal length using repeated measures analysis of variance for various obstacle number, obstacle placing scheme, and clutter type combinations in order to identify the optimal combination. Our results indicate that as the clutter type becomes more regular (clustered), NAVA's traversal length gets longer (shorter). On the other hand, the traversal length tends to follow a concave-down trend (i.e., increases, reaches a peak, and then decreases) as the number of obstacles increases. We also provide a case study on a real-world maritime minefield data set.