2010/12/23 by Daniel Herrmann, Herrmann, Daniel, Tom Kamphans +3
Computer Science · #Computational Geometry (cs.CG) #Computational Geometry and Mesh Generation #F.2.2 #FOS: Computer and information sciences #I.2.9 #I.3.5 #Optimization and Search Problems #Robotic Path Planning Algorithms #Robotics (cs.RO) #cs.CG #cs.RO
paper · pdf · doi:10.48550/arxiv.1012.5253
37 pages, 25 figures
arxiv created 2010/12/23 · openalex publication_date 2010/12/23 · arxiv updated 2010/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the online exploration problem (aka covering) of a short-sighted mobile robot moving in an unknown cellular environment with hexagons and triangles as types of cells. To explore a cell, the robot must enter it. Once inside, the robot knows which of the 3 or 6 adjacent cells exist and which are boundary edges. The robot's task is to visit every cell in the given environment and to return to the start. Our interest is in a short exploration tour; that is, in keeping the number of multiple cell visits small. For arbitrary environments containing no obstacles we provide a strategy producing tours of length S <= C + 1/4 E - 2.5 for hexagonal grids, and S <= C + E - 4 for triangular grids. C denotes the number of cells-the area-, E denotes the number of boundary edges-the perimeter-of the given environment. Further, we show that our strategy is 4/3-competitive in both types of grids, and we provide lower bounds of 14/13 for hexagonal grids and 7/6 for triangular grids.