Generalized Streets Revisited
نویسندگان
چکیده
We consider the problem of a robot inside an unknown polygon that has to nd a path from a starting point s to a target point t. We assume that it is equipped with an on-board vision system through which it can get the visibility map of its surroundings. Furthermore, we assume that the robot is contained in a simple polygon that belongs to the class of generalized streets. We consider three problems. 1. We present a strategy that allows the robot to search for t in an arbitrarily oriented generalized street where the distance travelled by the robot under our strategy is at most 80 times the length of the shortest path from s to t. 2. We show that there are orthogonal generalized streets for which the distance travelled by the robot under any searching strategy is at least 9.06 times the length of the shortest path from s to t. 3. Finally, we show that even if the location of the target is known, there are orthogonal generalized streets for which the distance travelled by the robot under any searching strategy is at least 9 times the length of the shortest path from s to t.
منابع مشابه
. so c - ph ] 2 9 O ct 2 00 7 Transport Networks Revisited : Why Dual Graphs ?
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the graph spanning the spatial network of a city naturally interpreted as random walks. Random walks assign absolute scores to all nodes of a graph and embed sp...
متن کاملA Competitive Strategy for Walking in Generalized Streets for a Simple Robot
In this study, we consider the problem of walking in an unknown generalized street or G-street, for a simple robot. The basic robot is equipped with a sensor that only detect the discontinuities in depth information (gaps). In the former recent researches some competitive strategies for walking the robot in street polygons have been presented. In this research we have empowered the robot by add...
متن کاملInformation projections revisited
The goal of this paper is to complete results available about -projections, reverse -projections, and their generalized versions, with focus on linear and exponential families. Pythagorean-like identities and inequalities are revisited and generalized, and generalized maximum-likelihood (ML) estimates for exponential families are introduced. The main tool is a new concept of extension of expone...
متن کاملGeneralized Geometry, T-duality, and Renormalization Group Flow
We interpret the physical B-field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural “Ricci flow” for generalized geometry. Next we show that the B-field renormalization group flow preserves T-duality in a natural sense. As corollaries we obtain new long time existence results for the B-field renormalization group flow.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996