Visibility-based path planning algorithms in a polygon

Abstract

Path planning in an environment cluttered with obstacles is a basic problem in computational geometry and robotics. Recently, researches on the visibility-based path planning algorithms have attracted much attention, where the robot (or a person) has visibility. These researches divides into two categories: online navigations and pursuit-evasions. In online navigation problems, the robot has to find a target or explore the environment without knowing the geometry of the obstacles. In pursuit-evasions, the robot with visibility has to find a mobile target. In this thesis, we deal with various versions of the visibility-based path planning problems. These problems are natural extensions of the well-known geometric problems including the shortest path problem and watchman route problem and the art gallery problems. In the first part, we consider an online navigation problem, called online kernel-search problem. The online kernel-search problem is for a mobile robot with 360° visibility to move from a starting point s to the closest kernel point κ within an unknown star-shaped polygon. The goal is to minimize the ratio of the distance traveled by the robot to the length of the shortest s-t path. Icking and Klein first introduced this problem and presented a very intuitive strategy and showed that their strategy is 5.331-competitive. We show that their strategy is, in fact, π+1(?4.14)-competiive. Since it is known that their strategy is no better than (π+1)-competitive, our new analysis is tight. Next, we present a new simple strategy that is $1+2\sqrt{2};(＜ 3.829)$-competitive. In the second part, we consider visibility-based pursuit-evasion problems stated as follows: given a polygonal region, a searcher with visibility, and an {\em unpredictable} intruder that is arbitrarily faster than the searcher, plan the motion of the searcher so as to see the intruder. In particular, we mainly discuss about the following question. Given a simple polygon with a door (i.e.,...