Skip to main content
Erschienen in: Swarm Intelligence 2/2016

28.04.2016

Modeling multi-robot task allocation with limited information as global game

verfasst von: Anshul Kanakia, Behrouz Touri, Nikolaus Correll

Erschienen in: Swarm Intelligence | Ausgabe 2/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Continuous response threshold functions to coordinate collaborative tasks in multi-agent systems are commonly employed models in a number of fields including ethology, economics, and swarm robotics. Although empirical evidence exists for the response threshold model in predicting and matching swarm behavior for social insects, there has been no formal argument as to why natural swarms use this approach and why it should be used for engineering artificial ones. In this paper, we show, by formulating task allocation as a global game, that continuous response threshold functions used for communication-free task assignment result in system level Bayesian Nash equilibria. Building up on these results, we show that individual agents not only do not need to communicate with each other, but also do not need to model each other’s behavior, which makes this coordination mechanism accessible to very simple agents, suggesting a reason for their prevalence in nature and motivating their use in an engineering context.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Amstutz, P., Correll, N., & Martinoli, A. (2008). Distributed boundary coverage with a team of networked miniature robots using a robust market-based algorithm. Annals of Mathematics and Artificial Intelligence, 52(2–4), 307–333.MathSciNetCrossRefMATH Amstutz, P., Correll, N., & Martinoli, A. (2008). Distributed boundary coverage with a team of networked miniature robots using a robust market-based algorithm. Annals of Mathematics and Artificial Intelligence, 52(2–4), 307–333.MathSciNetCrossRefMATH
Zurück zum Zitat Arslan, G., Marden, J. R., & Shamma, J. S. (2007). Autonomous vehicle-target assignment: A game-theoretical formulation. Journal of Dynamic Systems, Measurement, and Control, 129(5), 584–596.CrossRef Arslan, G., Marden, J. R., & Shamma, J. S. (2007). Autonomous vehicle-target assignment: A game-theoretical formulation. Journal of Dynamic Systems, Measurement, and Control, 129(5), 584–596.CrossRef
Zurück zum Zitat Berman, S., Halász, Á., Hsieh, M. A., & Kumar, V. (2009). Optimized stochastic policies for task allocation in swarms of robots. IEEE Transactions on Robotics, 25(4), 927–937.CrossRef Berman, S., Halász, Á., Hsieh, M. A., & Kumar, V. (2009). Optimized stochastic policies for task allocation in swarms of robots. IEEE Transactions on Robotics, 25(4), 927–937.CrossRef
Zurück zum Zitat Bonabeau, E., Sobkowski, A., Theraulaz, G., & Deneubourg, J.-L. (1997). Adaptive task allocation inspired by a model of division of labor in social insects. In Biocomputing and emergent computation: Proceedings of BCEC97 (pp. 36–45). World Scientific Press. Bonabeau, E., Sobkowski, A., Theraulaz, G., & Deneubourg, J.-L. (1997). Adaptive task allocation inspired by a model of division of labor in social insects. In Biocomputing and emergent computation: Proceedings of BCEC97 (pp. 36–45). World Scientific Press.
Zurück zum Zitat Bonabeau, E., Theraulaz, G., & Deneubourg, J.-L. (1996). Quantitative study of the fixed threshold model for the regulation of division of labour in insect societies. Proceedings of the Royal Society of London Series B: Biological Sciences, 263(1376), 1565–1569.CrossRef Bonabeau, E., Theraulaz, G., & Deneubourg, J.-L. (1996). Quantitative study of the fixed threshold model for the regulation of division of labour in insect societies. Proceedings of the Royal Society of London Series B: Biological Sciences, 263(1376), 1565–1569.CrossRef
Zurück zum Zitat Bonabeau, E., Theraulaz, G., & Deneubourg, J.-L. (1998). Fixed response thresholds and the regulation of division of labor in insect societies. Bulletin of Mathematical Biology, 60(4), 753–807.CrossRefMATH Bonabeau, E., Theraulaz, G., & Deneubourg, J.-L. (1998). Fixed response thresholds and the regulation of division of labor in insect societies. Bulletin of Mathematical Biology, 60(4), 753–807.CrossRefMATH
Zurück zum Zitat Border, K. C. (1990). Fixed point theorems with applications to economics and game theory. Cambridge: Cambridge Books.MATH Border, K. C. (1990). Fixed point theorems with applications to economics and game theory. Cambridge: Cambridge Books.MATH
Zurück zum Zitat Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7(1), 1–41.CrossRef Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7(1), 1–41.CrossRef
Zurück zum Zitat Camilli, G. (1994). Teachers corner: Origin of the scaling constant d = 1.7 in item response theory. Journal of Educational and Behavioral Statistics, 19(3), 293–295.MathSciNet Camilli, G. (1994). Teachers corner: Origin of the scaling constant d = 1.7 in item response theory. Journal of Educational and Behavioral Statistics, 19(3), 293–295.MathSciNet
Zurück zum Zitat Carlsson, H., & Van Damme, E. (1993). Global games and equilibrium selection. Econometrica: Journal of the Econometric Society, 61(5), 989–1018.MathSciNetCrossRefMATH Carlsson, H., & Van Damme, E. (1993). Global games and equilibrium selection. Econometrica: Journal of the Econometric Society, 61(5), 989–1018.MathSciNetCrossRefMATH
Zurück zum Zitat Castello, E., Yamamoto, T., Dalla Libera, F., Liu, W., Winfield, A. F., Nakamura, Y., et al. (2016). Adaptive foraging for simulated and real robotic swarms: The dynamical response threshold approach. Swarm Intelligence, 10(1), 1–31.CrossRef Castello, E., Yamamoto, T., Dalla Libera, F., Liu, W., Winfield, A. F., Nakamura, Y., et al. (2016). Adaptive foraging for simulated and real robotic swarms: The dynamical response threshold approach. Swarm Intelligence, 10(1), 1–31.CrossRef
Zurück zum Zitat Chen, J., & Sun, D. (2011). Resource constrained multirobot task allocation based on leader–follower coalition methodology. The International Journal of Robotics Research, 30(12), 1423–1434.CrossRef Chen, J., & Sun, D. (2011). Resource constrained multirobot task allocation based on leader–follower coalition methodology. The International Journal of Robotics Research, 30(12), 1423–1434.CrossRef
Zurück zum Zitat Choi, H.-L., Brunet, L., & How, J. P. (2009). Consensus-based decentralized auctions for robust task allocation. IEEE Transactions on Robotics, 25(4), 912–926.CrossRef Choi, H.-L., Brunet, L., & How, J. P. (2009). Consensus-based decentralized auctions for robust task allocation. IEEE Transactions on Robotics, 25(4), 912–926.CrossRef
Zurück zum Zitat Conradt, L., & Roper, T. J. (2003). Group decision-making in animals. Nature, 421(6919), 155–158.CrossRef Conradt, L., & Roper, T. J. (2003). Group decision-making in animals. Nature, 421(6919), 155–158.CrossRef
Zurück zum Zitat Conradt, L., & Roper, T. J. (2005). Consensus decision making in animals. Trends in Ecology and Evolution, 20(8), 449–456.CrossRef Conradt, L., & Roper, T. J. (2005). Consensus decision making in animals. Trends in Ecology and Evolution, 20(8), 449–456.CrossRef
Zurück zum Zitat Correll, N. (2007). Coordination schemes for distributed boundary coverage with a swarm of miniature robots: Synthesis, analysis and experimental validation. PhD thesis, Ecole Polytechnique Fédérale, Lausanne, CH. Correll, N. (2007). Coordination schemes for distributed boundary coverage with a swarm of miniature robots: Synthesis, analysis and experimental validation. PhD thesis, Ecole Polytechnique Fédérale, Lausanne, CH.
Zurück zum Zitat Correll, N. (2008). Parameter estimation and optimal control of swarm-robotic systems: A case study in distributed task allocation. In IEEE international conference on robotics and automation (ICRA) (pp. 3302–3307). IEEE. Correll, N. (2008). Parameter estimation and optimal control of swarm-robotic systems: A case study in distributed task allocation. In IEEE international conference on robotics and automation (ICRA) (pp. 3302–3307). IEEE.
Zurück zum Zitat Dantu, K., Berman, S., Kate, B., & Nagpal, R. (2012). A comparison of deterministic and stochastic approaches for allocating spatially dependent tasks in micro-aerial vehicle collectives. In IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 793–800). IEEE. Dantu, K., Berman, S., Kate, B., & Nagpal, R. (2012). A comparison of deterministic and stochastic approaches for allocating spatially dependent tasks in micro-aerial vehicle collectives. In IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 793–800). IEEE.
Zurück zum Zitat Durrett, R. (2010). Probability: Theory and examples (4th ed.). Cambridge: Cambridge University Press.CrossRefMATH Durrett, R. (2010). Probability: Theory and examples (4th ed.). Cambridge: Cambridge University Press.CrossRefMATH
Zurück zum Zitat Fudenberg, D. (1998). The theory of learning in games (Vol. 2). Cambridge, MA: MIT Press.MATH Fudenberg, D. (1998). The theory of learning in games (Vol. 2). Cambridge, MA: MIT Press.MATH
Zurück zum Zitat Gerkey, B. P. (2004). A formal analysis and taxonomy of task allocation in multi-robot systems. The International Journal of Robotics Research, 23(9), 939–954.CrossRef Gerkey, B. P. (2004). A formal analysis and taxonomy of task allocation in multi-robot systems. The International Journal of Robotics Research, 23(9), 939–954.CrossRef
Zurück zum Zitat Gerkey, B. P., & Mataric, M. J. (2003). Multi-robot task allocation: Analyzing the complexity and optimality of key architectures. In IEEE international conference on robotics and automation (Vol. 3, pp. 3862–3868). IEEE. Gerkey, B. P., & Mataric, M. J. (2003). Multi-robot task allocation: Analyzing the complexity and optimality of key architectures. In IEEE international conference on robotics and automation (Vol. 3, pp. 3862–3868). IEEE.
Zurück zum Zitat Gordon, D. M. (1996). The organization of work in social insect colonies. Nature, 380(6570), 121–124.CrossRef Gordon, D. M. (1996). The organization of work in social insect colonies. Nature, 380(6570), 121–124.CrossRef
Zurück zum Zitat Grenager, T., Powers, R., & Shoham, Y. (2002). Dispersion games: General definitions and some specific learning results. In AAAI innovative applications of artificial intelligence conference (IAAI) (pp. 398–403). AAAI. Grenager, T., Powers, R., & Shoham, Y. (2002). Dispersion games: General definitions and some specific learning results. In AAAI innovative applications of artificial intelligence conference (IAAI) (pp. 398–403). AAAI.
Zurück zum Zitat Harsanyi, J. C. (2004). Games with incomplete information played by Bayesian players, I-III Part I. The basic model. Management Science, 50(12–supplement), 1804–1817.MathSciNetCrossRef Harsanyi, J. C. (2004). Games with incomplete information played by Bayesian players, I-III Part I. The basic model. Management Science, 50(12–supplement), 1804–1817.MathSciNetCrossRef
Zurück zum Zitat Kalra, N., & Martinoli, A. (2006). Comparative study of market-based and threshold-based task allocation. In Distributed autonomous robotic systems 7 (pp. 91–101). Springer. Kalra, N., & Martinoli, A. (2006). Comparative study of market-based and threshold-based task allocation. In Distributed autonomous robotic systems 7 (pp. 91–101). Springer.
Zurück zum Zitat Kanakia, A., & Correll, N. (2016). A response threshold sigmoid function model for swarm robot collaboration. Distributed and autonomous robotic systems (DARS), volume 112 of the series springer tracts in advanced robotics (pp. 193–206). Heidelberg: Springer.CrossRef Kanakia, A., & Correll, N. (2016). A response threshold sigmoid function model for swarm robot collaboration. Distributed and autonomous robotic systems (DARS), volume 112 of the series springer tracts in advanced robotics (pp. 193–206). Heidelberg: Springer.CrossRef
Zurück zum Zitat Krieger, M. J., Billeter, J.-B., & Keller, L. (2000). Ant-like task allocation and recruitment in cooperative robots. Nature, 406(6799), 992–995.CrossRef Krieger, M. J., Billeter, J.-B., & Keller, L. (2000). Ant-like task allocation and recruitment in cooperative robots. Nature, 406(6799), 992–995.CrossRef
Zurück zum Zitat Kube, C. R., & Bonabeau, E. (2000). Cooperative transport by ants and robots. Robotics and Autonomous Systems, 30(1), 85–101.CrossRef Kube, C. R., & Bonabeau, E. (2000). Cooperative transport by ants and robots. Robotics and Autonomous Systems, 30(1), 85–101.CrossRef
Zurück zum Zitat Lerman, K., Galstyan, A., Martinoli, A., & Ijspeert, A. (2001). A macroscopic analytical model of collaboration in distributed robotic systems. Artificial Life, 7, 375–393.CrossRef Lerman, K., Galstyan, A., Martinoli, A., & Ijspeert, A. (2001). A macroscopic analytical model of collaboration in distributed robotic systems. Artificial Life, 7, 375–393.CrossRef
Zurück zum Zitat Lerman, K., Jones, C., Galstyan, A., & Matarić, M. J. (2006). Analysis of dynamic task allocation in multi-robot systems. The International Journal of Robotics Research, 25(3), 225–241.CrossRef Lerman, K., Jones, C., Galstyan, A., & Matarić, M. J. (2006). Analysis of dynamic task allocation in multi-robot systems. The International Journal of Robotics Research, 25(3), 225–241.CrossRef
Zurück zum Zitat Liu, W., & Winfield, A. (2010). Modelling and optimisation of adaptive foraging in swarm robotic systems. The International Journal of Robotics Research, 29(14), 1743–1760.CrossRef Liu, W., & Winfield, A. (2010). Modelling and optimisation of adaptive foraging in swarm robotic systems. The International Journal of Robotics Research, 29(14), 1743–1760.CrossRef
Zurück zum Zitat Marden, J. R., Arslan, G., & Shamma, J. S. (2009). Joint strategy fictitious play with inertia for potential games. IEEE Transactions on Automatic Control, 54(2), 208–220.MathSciNetCrossRef Marden, J. R., Arslan, G., & Shamma, J. S. (2009). Joint strategy fictitious play with inertia for potential games. IEEE Transactions on Automatic Control, 54(2), 208–220.MathSciNetCrossRef
Zurück zum Zitat Martinoli, A., Easton, K., & Agassounon, W. (2004). Modeling swarm robotic systems: A case study in collaborative distributed manipulation. The International Journal of Robotics Research, 23(4–5), 415–436.CrossRef Martinoli, A., Easton, K., & Agassounon, W. (2004). Modeling swarm robotic systems: A case study in collaborative distributed manipulation. The International Journal of Robotics Research, 23(4–5), 415–436.CrossRef
Zurück zum Zitat Martinoli, A., Ijspeert, A. J., & Mondada, F. (1999). Understanding collective aggregation mechanisms: From probabilistic modelling to experiments with real robots. Robotics and Autonomous Systems, 29(1), 51–63.CrossRef Martinoli, A., Ijspeert, A. J., & Mondada, F. (1999). Understanding collective aggregation mechanisms: From probabilistic modelling to experiments with real robots. Robotics and Autonomous Systems, 29(1), 51–63.CrossRef
Zurück zum Zitat Matarić, M. J., Sukhatme, G. S., & Astergaard, E. H. (2003). Multi-robot task allocation in uncertain environments. Autonomous Robots, 14(2–3), 255–263.CrossRefMATH Matarić, M. J., Sukhatme, G. S., & Astergaard, E. H. (2003). Multi-robot task allocation in uncertain environments. Autonomous Robots, 14(2–3), 255–263.CrossRefMATH
Zurück zum Zitat Mather, T. W., Hsieh, M. A., & Frazzoli, E. (2010). Towards dynamic team formation for robot ensembles. In IEEE international conference on robotics and automation (ICRA) (pp. 4970–4975). IEEE. Mather, T. W., Hsieh, M. A., & Frazzoli, E. (2010). Towards dynamic team formation for robot ensembles. In IEEE international conference on robotics and automation (ICRA) (pp. 4970–4975). IEEE.
Zurück zum Zitat McEvoy, M., & Correll, N. (2015). Materials that couple sensing, actuation, computation, and communication. Science, 347(6228), 1261689.CrossRef McEvoy, M., & Correll, N. (2015). Materials that couple sensing, actuation, computation, and communication. Science, 347(6228), 1261689.CrossRef
Zurück zum Zitat Morris, S. E., & Shin, H. S. (2000). Global games: Theory and applications. New Haven, CT: Cowles Foundation for Research in Economics. Morris, S. E., & Shin, H. S. (2000). Global games: Theory and applications. New Haven, CT: Cowles Foundation for Research in Economics.
Zurück zum Zitat Nisan, N., Roughgarden, T., Tardos, E., & Vazirani, V. V. (2007). Algorithmic game theory (Vol. 1). Cambridge: Cambridge University Press.CrossRefMATH Nisan, N., Roughgarden, T., Tardos, E., & Vazirani, V. V. (2007). Algorithmic game theory (Vol. 1). Cambridge: Cambridge University Press.CrossRefMATH
Zurück zum Zitat Parsons, S., & Wooldridge, M. (2002). Game theory and decision theory in multi-agent systems. Autonomous Agents and Multi-Agent Systems, 5(3), 243–254.MathSciNetCrossRefMATH Parsons, S., & Wooldridge, M. (2002). Game theory and decision theory in multi-agent systems. Autonomous Agents and Multi-Agent Systems, 5(3), 243–254.MathSciNetCrossRefMATH
Zurück zum Zitat Pini, G., Gagliolo, M., Brutschy, A., Dorigo, M., & Birattari, M. (2013). Task partitioning in a robot swarm: A study on the effect of communication. Swarm Intelligence, 7(2–3), 173–199.CrossRef Pini, G., Gagliolo, M., Brutschy, A., Dorigo, M., & Birattari, M. (2013). Task partitioning in a robot swarm: A study on the effect of communication. Swarm Intelligence, 7(2–3), 173–199.CrossRef
Zurück zum Zitat Pynadath, D. V., & Tambe, M. (2002). Multiagent teamwork: Analyzing the optimality and complexity of key theories and models. In Proceedings of the first international joint conference on autonomous agents and multiagent systems (AAMAS): Part 2 (pp. 873–880). ACM. Pynadath, D. V., & Tambe, M. (2002). Multiagent teamwork: Analyzing the optimality and complexity of key theories and models. In Proceedings of the first international joint conference on autonomous agents and multiagent systems (AAMAS): Part 2 (pp. 873–880). ACM.
Zurück zum Zitat Raafat, R. M., Chater, N., & Frith, C. (2009). Herding in humans. Trends in Cognitive Sciences, 13(10), 420–428.CrossRef Raafat, R. M., Chater, N., & Frith, C. (2009). Herding in humans. Trends in Cognitive Sciences, 13(10), 420–428.CrossRef
Zurück zum Zitat Robinson, G. E. (1987). Modulation of alarm pheromone perception in the honey bee: Evidence for division of labor based on hormonally regulated response thresholds. Journal of Comparative Physiology A, 160(5), 613–619.CrossRef Robinson, G. E. (1987). Modulation of alarm pheromone perception in the honey bee: Evidence for division of labor based on hormonally regulated response thresholds. Journal of Comparative Physiology A, 160(5), 613–619.CrossRef
Zurück zum Zitat Seeley, T. D. (1989). Social foraging in honey bees: How nectar foragers assess their colony’s nutritional status. Behavioral Ecology and Sociobiology, 24(3), 181–199.CrossRef Seeley, T. D. (1989). Social foraging in honey bees: How nectar foragers assess their colony’s nutritional status. Behavioral Ecology and Sociobiology, 24(3), 181–199.CrossRef
Zurück zum Zitat Shehory, O., & Kraus, S. (1998). Methods for task allocation via agent coalition formation. Artificial Intelligence, 101(1), 165–200.MathSciNetCrossRefMATH Shehory, O., & Kraus, S. (1998). Methods for task allocation via agent coalition formation. Artificial Intelligence, 101(1), 165–200.MathSciNetCrossRefMATH
Zurück zum Zitat Suzuki, S., Adachi, R., Dunne, S., Bossaerts, P., & O’Doherty, J. P. (2015). Neural mechanisms underlying human consensus decision-making. Neuron, 86(2), 591–602.CrossRef Suzuki, S., Adachi, R., Dunne, S., Bossaerts, P., & O’Doherty, J. P. (2015). Neural mechanisms underlying human consensus decision-making. Neuron, 86(2), 591–602.CrossRef
Zurück zum Zitat Theraulaz, G., Bonabeau, E., & Deneubourg, J.-L. (1998). Response threshold reinforcements and division of labour in insect societies. Proceedings of the Royal Society of London Series B: Biological Sciences, 265(1393), 327–332.CrossRefMATH Theraulaz, G., Bonabeau, E., & Deneubourg, J.-L. (1998). Response threshold reinforcements and division of labour in insect societies. Proceedings of the Royal Society of London Series B: Biological Sciences, 265(1393), 327–332.CrossRefMATH
Zurück zum Zitat Tumer, K., & Wolpert, D. (2004). A survey of collectives. In Collectives and the design of complex systems (pp. 1–42). Springer. Tumer, K., & Wolpert, D. (2004). A survey of collectives. In Collectives and the design of complex systems (pp. 1–42). Springer.
Zurück zum Zitat Vig, L., & Adams, J. A. (2007). Coalition formation: From software agents to robots. Journal of Intelligent and Robotic Systems, 50(1), 85–118.CrossRef Vig, L., & Adams, J. A. (2007). Coalition formation: From software agents to robots. Journal of Intelligent and Robotic Systems, 50(1), 85–118.CrossRef
Zurück zum Zitat Yoshida, W., Seymour, B., Friston, K. J., & Dolan, R. J. (2010). Neural mechanisms of belief inference during cooperative games. Journal of Neuroscience, 30(32), 10744–10751.CrossRef Yoshida, W., Seymour, B., Friston, K. J., & Dolan, R. J. (2010). Neural mechanisms of belief inference during cooperative games. Journal of Neuroscience, 30(32), 10744–10751.CrossRef
Metadaten
Titel
Modeling multi-robot task allocation with limited information as global game
verfasst von
Anshul Kanakia
Behrouz Touri
Nikolaus Correll
Publikationsdatum
28.04.2016
Verlag
Springer US
Erschienen in
Swarm Intelligence / Ausgabe 2/2016
Print ISSN: 1935-3812
Elektronische ISSN: 1935-3820
DOI
https://doi.org/10.1007/s11721-016-0123-4