 
Summary: Exploring Unknown Environments with Obstacles
Susanne Albers Klaus Kursawey Sven Schuiererz
Abstract
We study exploration problems where a robot has to construct a complete map of an unknown
environment using a path that is as short as possible.
In the rst problem setting we consider, a robot has to explore n rectangles. We show that
no deterministic or randomized online algorithm can be better than (
pn)competitive, solving
an open problem by Deng, Kameda and Papadimitriou 5]. We also generalize this bound to the
problem of exploring threedimensional rectilinear polyhedra without obstacles.
In the second problem setting we study, a robot has to explore a grid graph with obstacles
in a piecemeal fashion. The piecemeal constraint was de ned by Betke, Rivest and Singh 3] and
implies that the robot has to return a start node every so often. Betke et al. gave an e cient algo
rithm for exploring grids with rectangular obstacles. We present an e cient strategy for piecemeal
exploration of grids with arbitrary obstacles.
1 Introduction
In robot exploration problems, a robot has to construct a complete map of an unknown environment
using a path that is as short as possible. Many geometric and graph theoretic versions of this problem
have been studied in the past 1, 2, 3, 4, 5, 6, 8, 9, 10, 11]. A general problem setting was introduced
by Deng, Kameda and Papadimitriou 5]. The robot is placed in a room with obstacles. The exterior
