Adaptive Searching in One and Two Dimensions

Searching in a geometric space is an active area of research, predating computer technology. The applications are varied ranging from robotics, to search-andrescue operations in the high seas [24, 23] as well as in land, such as in an avalanche [5] or an office space [12, 7, 13], to scheduling of heuristic algorithms for solvers searching an abstract solution space for a specific solution [16, 17, 22, 2, 19]. Within academia, the field has seen two marked boosts in activity. The first was motivated by the loss of weaponry off the coast of Spain in 1966 in what is known as the Palomares incident and of the USS Thresher and Scorpion submarines in 1963 and 1966 respectively [24, 26]. A second renewed thrust took place in the late 1980s when the applications for autonomous robots became apparent. Geometric searching has proved a fertile ground within computational geometry for the design and analysis of search and recognition strategies under various initial conditions [14, 12, 6, 7, 8, 18, 20]. The basic search scenarios consist of exploring a one dimensional object, such as a path or office corridor, usually modeled as the real line, and of exploring a two dimensional scene, such as a room or a factory floor, usually modelled as a polygonal scene. However, in spite of numerous advances in the theoretical understanding of both of these scenarios, so far such solutions have generally had a limited impact in practice. Over the years various efforts have been made to address this situation, both in terms of isolated research papers attempting to narrow the gap, as well as in organized efforts such as the Algorithmic Foundations of Robotics conference and the Dagstuhl seminars on on-line robotics which bring together theoreticians and practitioners. From these it is apparent that the cost model and hence the solutions obtained from theoretical analysis do not fully reflect real life constraints. Several efforts have been made to resolve this, such as including the turn cost, the scanning cost, and error in navigation and reckoning [9, 10, 15, 20, 18]. In this paper we address one more shortcoming of the standard model. Consider for example a vacuuming robot—such as Roomba(TM). Such a robot explores the environment using sophisticated motion planning algorithms with the goal of attaining complete coverage of