Exploring Unknown Environments with Obstacles

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 three-dimensional 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 algorithm for exploring grids with rectangular obstacles. We present an e cient strategy for piecemeal exploration of grids with arbitrary obstacles.

• Type: Journal
• Year: 2002
• Where: ALGORITHMICA
• Authors: Susanne Albers, Klaus Kursawe, Sven Schuierer
• Keywords: ALGORITHMICA 2002, Piecemeal, Robot, Three-dimensional Rectilinear Polyhedra