Abstract
An autonomous search for sources of gamma radiation in an outdoor environment is a domain suitable for the deployment of a heterogeneous robotic team, consisting of an Unmanned Aerial (UAV) and an Unmanned Ground (UGV) Vehicle. The UAV is convenient for fast mapping of the area and identifying regions of interest, whereas the UGV can perform highly accurate localization. It is assumed that the regions of interest are identified by the UAV during an initial reconnaissance, while performing a simple motion pattern. This paper proposes a path planning algorithm for the UGV, which guarantees accurate source localization in multiple preselected regions and minimizes the total path length. The problem is formulated as the Generalized Travelling Salesman Problem (GTSP) defined for discrete sets of suitable maneuvers (circular arcs), ensuring source localization in the given regions. The problem is successfully solved by a modified version of the state of the art GTSP solver, Generalized Large Neighborhood Search with Arcs (GLNSarc). Apart from adapting the GLNS, other aspects of the planning task are addressed: problem discretization and informed sampling of valid circular arcs, variants of weighting the nonrestricted trajectory segments between the arcs and postprocessing of the discretely planned trajectory in the continuous domain.
Similar content being viewed by others
References
Arain MA et al (2015) Global coverage measurement planning strategies for mobile robots equipped with a remote gas sensor. In: Sensors (switzerland), vol 15.3, pp 6845–6871. issn: 14248220, https://doi.org/10.3390/s150306845
Bourne JR, Pardyjak ER, Leang KK (2019) Coordinated Bayesian-Based bioinspired plume source term estimation and source seeking for mobile robots. IEEE Trans Robot 35.4:967–986. issn: 19410468. https://doi.org/10.1109/TRO.2019.2912520
Chen W, Liu L (2019) Pareto monte carlo tree search for multi- objective informative planning. In: Robotics: Science and systems XV. https://doi.org/10.15607/rss.2019.xv.072
Christie G et al (2017) Radiation search operations using scene understanding with autonomous UAV and UGV. J Field Robo 34.8:1450–1468. issn: 15564959. https://doi.org/10.1002/rob.21723
De Geer LE (2004) Currie detection limits in gamma-ray spectroscopy. Appl Radiat Isotopes 61.2-3:151–160. issn: 09698043. https://doi.org/10.1016/j.apradiso.2004.03.037
Drexl M, Gutenberg J (2012) On the generalized directed rural postman problem. Tech. rep Gutenberg School of Management and Economics
Ebenezer J, Murty S (2016) Deployment of wireless sensor network for radiation monitoring. In: 2015 International conference on com- puting and network communications (coconet 2015). Institute of Electrical and Electronics Engineers Inc., pp 27–32. isbn: 9781467373098. https://doi.org/10.1109/CoCoNet.2015.7411163
Ferri G et al (2007) Explorative particle swarm optimization method for gas/odor source localization in an indoor environment with no strong air-flow. In: 2007 IEEE International conference on robotics and biomimetics, ROBIO. IEEE computer society, pp 841–846. isbn: 9781424417582. https://doi.org/10.1109/ROBIO.2007.4522272
Fischetti M, González JJS, Toth P (1997) A branchand- cut algorithm for the symmetric generalized traveling salesman problem. Oper Res 45.3:378–394. issn: 0030364x. https://doi.org/10.1287/opre.45.3.378
Fischetti M, González JJS, Toth P (1995) The symmetric generalized traveling salesman polytope. Networks 26.2:113–123. issn: 10970037. https://doi.org/10.1002/net.3230260206
Gabrlik P, Lazna T (2018) Simulation of gamma radiation mapping using an unmanned aerial system. In: IFAC-Papersonline 51.6:256–262. issn: 24058963. https://doi.org/10.1016/j.ifacol.2018.07.163
Gutin G, Karapetyan D (2010) A memetic algorithm for the generalized traveling salesman problem. Natural Comput 9.1:47–60. issn: 15677818. https://doi.org/10.1007/s11047-009-9111-6. arXiv:0804.0722
Han J et al (2013) Low-cost multi-UAV technologies for contour mapping of nuclear radiation field. J Intell Robot Syst: Theory Appl 70.1-4:401–410. issn: 09210296. https://doi.org/10.1007/s10846-012-9722-5
Helsgaun K (2000) An effective implementation of the Lin-Kernighan traveling salesman heuristic. Eur J Oper Res 126:106–130
Helsgaun K (2013) GTSP problem libraries BAF, MOM and GTSP+. http://akira.ruc.dk/~keld/research/GLKH/. accessed 2020-02-03
Helsgaun K (2015) Solving the equality generalized traveling salesman problem using the Lin-Kernighan-Helsgaun Algorithm. Math Programm Comput 7.3:269–287. issn: 18672957. https://doi.org/10.1007/s12532-015-0080-8
Hollinger G, Sukhatme G (2016) Sampling-based motion planning for robotic information gathering. In: Robotics: Science and systems. https://doi.org/10.15607/rss.2013.ix.051
Hoos HH, Thomas S (2014) On the empirical scaling of run-time for finding optimal solutions to the travelling salesman problem. Eur J Oper Res 238.1:87–94. issn: 03772217. https://doi.org/10.1016/j.ejor.2014.03.042
Isaacs JT, Hespanha JP (2013) Dubins traveling salesman problem with neighborhoods: A graph-based approach. Algorithms 6.1:84–99. issn: 19994893. https://doi.org/10.3390/a6010084. http://www.mdpi.com/1999-4893/6/1/84
Kalisiak M, Faigl J (2013) Motion planning maps - dataset. http://agents.fel.cvut.cz/~faigl/planning/. accessed 2020-07-07
Laporte G, Asef-Vaziri A, Sriskandarajah C (1996) Some applications of the generalized travelling salesman problem. J Oper Res Soci 47.12:1461–1467. issn: 14769360. https://doi.org/10.1057/jors.1996.190
Laporte G, Nobert Y (1983) Generalized traveling salesman problem through n sets of nodes: an integer programming approach. INFOR: Inf Syst Oper Res 21.1:61–75. issn: 03155986. https://doi.org/10.1080/03155986.1983.11731885
Lazna T Optimizing the localization of gamma radiation point sources using a UGV. In: 2018 ELEKTRO Conference Proceedings. Institute of Electrical and Electronics Engineers Inc., pp 1–6. (2018) https://doi.org/10.1109/ELEKTRO.2018.8398368
Lazna T, et al. (2018) Cooperation between an unmanned aerial vehicle and an unmanned ground vehicle in highly accurate localization of gamma radiation hotspots. Int J Adv Robot Syst 15.1:172988141775078. issn: 17298814. https://doi.org/10.1177/1729881417750787
Lilienthal A, Loutfi A, Duckett T (2006) Airborne chemical sensing with mobile robots. Sensors 6.11:1616–1678. issn: 1424-8220. https://doi.org/10.3390/s6111616
Liu Z, Abbaszadeh S, Sullivan CJ (2018) Spatial-temporal modeling of background radiation using mobile sensor networks. PLOS one, vol 13. Ed. by Raghuraman Mudumbai. issn, pp 1932–6203. https://doi.org/10.1371/journal.pone.0205092
Miller A., Machrafi R., Mohany A. (2015) Development of a semi-autonomous directional and spectroscopic radiation detection mobile platform. Radiat Measur 72:53–59. issn: 13504487. https://doi.org/10.1016/j.radmeas.2014.11.009
Noon CE, Bean JC (1993) An efficient transformation of the generalized traveling salesman problem. INFOR: Inf Syst Oper Res 31.1:39–44. issn: 0315-5986. https://doi.org/10.1080/03155986.1993.11732212
Obermeyer KJ, Contributors (2008) VisiLibity: A C++ Library for Visibility Computations in Planar Polygonal Environments. http://www.VisiLibity.org. accessed 2020-07-07
Pop PC. (2007) New integer programming formulations of the generalized travelling salesman problem. Amer J Appl Sci 4.11:932–937. issn: 15543641. https://doi.org/10.3844/ajassp.2007.932.937
de Julio Rozental J (2002) Two decades of radiological accidents direct causes, roots causes and consequences. Braz Arch Biol Technol 45.spe:125–133. issn: 1516-8913. https://doi.org/10.1590/s1516-89132002000500018
Smith SL, Frank I (2017) GLNS An effective large neighborhood search heuristic for the generalized traveling salesman problem. Comput Oper Res 87:1–19
Soin PK et al (2019) Application of a novel search method to handheld gamma radiation detectors. IEEE Sens J:1–1. issn: 1530-437X. https://doi.org/10.1109/jsen.2019.2945314
Uher J., et al. (2007) Directional radiation detector. IEEE Nuclear Sci Symp Conf Rec 2:1162–1166. isbn: 1424409233. https://doi.org/10.1109/NSSMIC.2007.4437213
Wendorf M (2020) Broken Arrows - The World’s Lost Nuclear Weapons. shorturl.at/ryBLO
Wheatley S, Sovacool BK, Sornette Didier (2016) Reassessing the safety of nuclear power. Energy Res Social Sci 15:96–100. issn: 22146296. https://doi.org/10.1016/j.erss.2015.12.026
Wiedemann T, Shutin D, Lilienthal AJ (2019) Modelbased gas source localization strategy for a cooperative multi-robot system— A probabilistic approach and experimental validation incorporating physical knowledge and model uncertainties. Robot Auton Syst 118:66–79. issn: 09218890. https://doi.org/10.1016/j.robot.2019.03.014
Woller D (2019) GTSP with arcs - 3 datasets. http://imr.ciirc.cvut.cz/Datasets/GTSP-arc. accessed 2020-02-03
Zakaria AH et al (2017) Development of autonomous radiation mapping robot. In: Procedia Computer Science. vol 105. Elsevier B.V., pp 81–86. https://doi.org/10.1016/j.procs.2017.01.203
Acknowledgements
This work has been supported by the European Regional Development Fund under the project Robotics for Industry 4.0 (registration no. CZ.02.1.01/0.0/0.0/15 003/0000470). The work of David Woller has been also supported by the Grant Agency of the Czech Technical University in Prague, grant SGS18/206/OHK3/3T /37.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Woller, D., Kulich, M. Path planning algorithm ensuring accurate localization of radiation sources. Appl Intell 52, 9574–9596 (2022). https://doi.org/10.1007/s10489-021-02941-y
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10489-021-02941-y