Abstract
This paper introduces a problem in which an agent (robot, human, or animal) travels among obstacles and binary detection beams. The task is to determine the possible agent path based only on the binary sensor data. This is a basic filtering problem encountered in many settings, which may arise from physical sensor beams or virtual beams that are derived from other sensing modalities. Methods are given for three alternative representations: 1) the possible sequences of regions visited, 2) path descriptions up to homotopy class, and 3) numbers of times winding around obstacles. The solutions are adapted to the minimal sensing setting; therefore, precise estimation, distances, and coordinates are replaced by topological expressions. Applications include sensor-based forensics, assisted living, security, and environmental monitoring.
This is a preview of subscription content, log in via an institution to check access.
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
Cabello, S., Liu, Y., Mantler, A., Snoeyink, J.: Testing homotopy for paths in the plane. In: Proceedings of the eighteenth annual symposium on Computational geometry, pp. 160–169. ACM, New York (2002)
Dudek, G., Romanik, K., Whitesides, S.: Global localization: Localizing a robot with minimal travel. SIAM Journal on Computing 27(2), 583–604 (1998)
Efrat, A., Kobourov, S., Lubiw, A.: Computing homotopic shortest paths efficiently. Computational Geometry 35(3), 162–172 (2006)
Goldberg, K.Y.: Orienting polygonal parts without sensors. Algorithmica 10, 201–225 (1993)
Guibas, L.J., Latombe, J.-C., LaValle, S.M., Lin, D., Motwani, R.: Visibility-based pursuitevasion in a polygonal environment. International Journal of Computational Geometry and Applications 9(5), 471–494 (1999)
Guibas, L.J., Motwani, R., Raghavan, P.: The robot localization problem. In: Goldberg, K., Halperin, D., Latombe, J.-C., Wilson, R. (eds.) Algorithmic oundations of Robotics, pp. 269–282. A.K. Peters, Wellesley (1995)
LaValle, S.M.: Planning Algorithms. Cambridge University Press, Cambridge (2006), http://planning.cs.uiuc.edu/
Lee, J.-H., Shin, S.Y., Chwa, K.-Y.: Visibility-based pursuit-evasions in a polygonal room with a door. In: Proceedings ACM Symposium on Computational Geometry (1999)
Magnus, W., Karrass, A., Solitar, D.: Combinatorial Group Theory, 2nd edn., revised edn. Dover (2004)
Singh, J., Madhow, U., Kumar, R., Suri, S., Cagley, R.: Tracking multiple targets using binary proximity sensors. In: Proceedings of the 6th international conference on Information processing in sensor networks, pp. 529–538. ACM, New York (2007)
Tovar, B., Freda, L., LaValle, S.M.: Mapping and navigation from permutations of landmarks. In: AMS Contemporary Mathematics Proc., vol. 438, pp. 33–45 (2007)
Yu, J., LaValle, S.M.: Tracking hidden agents through shadow information spaces. In: Proceedings IEEE International Conference on Robotics and Automation (2008) (under review)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Tovar, B., Cohen, F., LaValle, S.M. (2009). Sensor Beams, Obstacles, and Possible Paths. In: Chirikjian, G.S., Choset, H., Morales, M., Murphey, T. (eds) Algorithmic Foundation of Robotics VIII. Springer Tracts in Advanced Robotics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00312-7_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-00312-7_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00311-0
Online ISBN: 978-3-642-00312-7
eBook Packages: EngineeringEngineering (R0)