Abstract
We study the problem of mapping an initially unknown environment with autonomous mobile robots. More precisely, we consider simplistic agents that move from vertex to vertex along the boundary of a polygon and measure angles at each vertex. We show that such agents are already capable of drawing a map of any polygon in the sense that they can infer the exact geometry up to similarity. Often, such tasks require the agent to have some prior bound on the size of the environment. In this paper, we provide an efficient reconstruction algorithm that does not need any a priori knowledge about the total number of vertices.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transactions on Robotics and Automation 15(5), 818–828 (1999)
Biedl, T., Durocher, S., Snoeyink, J.: Reconstructing Polygons from Scanner Data. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 862–871. Springer, Heidelberg (2009)
Bilò, D., Disser, Y., Mihalák, M., Suri, S., Vicari, E., Widmayer, P.: Reconstructing visibility graphs with simple robots. Theoretical Computer Science 444, 52–59 (2012)
Brunner, J., Mihalák, M., Suri, S., Vicari, E., Widmayer, P.: Simple Robots in Polygonal Environments: A Hierarchy. In: Fekete, S.P. (ed.) ALGOSENSORS 2008. LNCS, vol. 5389, pp. 111–124. Springer, Heidelberg (2008)
Chalopin, J., Das, S., Disser, Y., Mihalák, M., Widmayer, P.: How Simple Robots Benefit from Looking Back. In: Calamoneri, T., Diaz, J. (eds.) CIAC 2010. LNCS, vol. 6078, pp. 229–239. Springer, Heidelberg (2010)
Chalopin, J., Das, S., Disser, Y., Mihalák, M., Widmayer, P.: Telling convex from reflex allows to map a polygon. In: Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science, pp. 153–164 (2011)
Chen, D., Wang, H.: An improved algorithm for reconstructing a simple polygon from the visibility angles. Computational Geometry: Theory and Applications 45, 254–257 (2012)
Coullard, C., Lubiw, A.: Distance visibility graphs. In: Proceedings of the 7th Annual Symposium on Computational Geometry, pp. 289–296 (1991)
Disser, Y., Mihalák, M., Widmayer, P.: A polygon is determined by its angles. Computational Geometry: Theory and Applications 44, 418–426 (2011)
Donald, B.R.: On information invariants in robotics. Artificial Intelligence 72(1-2), 217–304 (1995)
Ganguli, A., Cortés, J., Bullo, F.: Distributed deployment of asynchronous guards in art galleries. In: Proceedings of the 2006 American Control Conference, pp. 1416–1421 (2006)
Gfeller, B., Mihalák, M., Suri, S., Vicari, E., Widmayer, P.: Counting Targets with Mobile Sensors in an Unknown Environment. In: Kutyłowski, M., Cichoń, J., Kubiak, P. (eds.) ALGOSENSORS 2007. LNCS, vol. 4837, pp. 32–45. Springer, Heidelberg (2008)
Ghosh, S.K.: On recognizing and characterizing visibility graphs of simple polygons. Discrete and Computational Geometry 17(2), 143–162 (1997)
Ghosh, S.K.: Visibility Algorithms in the Plane. Cambridge University Press (2007)
Ghosh, S.K., Goswami, P.P.: Unsolved problems in visibility graph theory. In: Proceedings of the India-Taiwan Conference on Discrete Mathematics, pp. 44–54 (2009)
Jackson, L., Wismath, S.K.: Orthogonal polygon reconstruction from stabbing information. Computational Geometry 23(1), 69–83 (2002)
Katsev, M., Yershova, A., Tovar, B., Ghrist, R., LaValle, S.M.: Mapping and pursuit-evasion strategies for a simple wall-following robot. IEEE Transactions on Robotics 27(1), 113–128 (2011)
Komuravelli, A., Mihalák, M.: Exploring Polygonal Environments by Simple Robots with Faulty Combinatorial Vision. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 458–471. Springer, Heidelberg (2009)
O’Kane, J.M., LaValle, S.M.: On comparing the power of robots. International Journal of Robotics Research 27(1), 5–23 (2008)
O’Rourke, J.: Uniqueness of orthogonal connect-the-dots. In: Toussaint, G.T. (ed.) Computational Morphology, pp. 97–104. North-Holland (1988)
Rappaport, D.: On the complexity of computing orthogonal polygons from a set of points. Technical Report SOCS-86.9, McGill University, Montreal, Canada (1986)
Sidlesky, A., Barequet, G., Gotsman, C.: Polygon reconstruction from line cross-sections. In: Proceedings of the 18th Annual Canadian Conference on Computational Geometry, pp. 81–84 (2006)
Snoeyink, J.: Cross-ratios and angles determine a polygon. Discrete and Computational Geometry 22(4), 619–631 (1999)
Suri, S., Vicari, E., Widmayer, P.: Simple robots with minimal sensing: From local visibility to global geometry. International Journal of Robotics Research 27(9), 1055–1067 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Disser, Y., Mihalák, M., Widmayer, P. (2013). Mapping Polygons with Agents That Measure Angles. In: Frazzoli, E., Lozano-Perez, T., Roy, N., Rus, D. (eds) Algorithmic Foundations of Robotics X. Springer Tracts in Advanced Robotics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36279-8_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-36279-8_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36278-1
Online ISBN: 978-3-642-36279-8
eBook Packages: EngineeringEngineering (R0)