Skip to main content
Erschienen in: International Journal of Machine Learning and Cybernetics 1/2013

01.02.2013 | Original Article

Optimal trajectory planning for the herding problem: a continuous time model

verfasst von: Samy A. Shedied

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 1/2013

Einloggen

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

search-config
loading …

Abstract

This paper presents an optimal trajectory planning solution to a special class of the pursuit-evasion game; the herding problem in continuous time. In this model, the pursuer’s objective is to herd the evader to a certain location in the Euclidian co-ordinate system over the shortest path. First, the problem is modeled as a constrained optimization problem. Then the optimal trajectory that the pursuer should follow is obtained as the solution for that problem. After that, the derived solution is applied to a non-holonomic realization of the problem.

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 "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!

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!

Weitere Produktempfehlungen anzeigen
Literatur
1.
Zurück zum Zitat Bassar T, Olsder GJ (1999) Dynamic non-cooperative game theory. SIAM, 2nd edn Bassar T, Olsder GJ (1999) Dynamic non-cooperative game theory. SIAM, 2nd edn
2.
Zurück zum Zitat Guibas L, Latombe J-C, LaValle S, Lin D, Motwani R (1985) A visibility-based pursuit-evasion problem. Int J Comput Geom Appl 4(2):74–123 Guibas L, Latombe J-C, LaValle S, Lin D, Motwani R (1985) A visibility-based pursuit-evasion problem. Int J Comput Geom Appl 4(2):74–123
3.
Zurück zum Zitat Stephens L, Merx M (1990) The effect of agent control strategy on the performance of a dai pursuit problem. In: Proceedings of the distributed AI workshop Stephens L, Merx M (1990) The effect of agent control strategy on the performance of a dai pursuit problem. In: Proceedings of the distributed AI workshop
5.
Zurück zum Zitat LaValle S, Hinrichsen J (1999) Visibility-based pursuit-evasion: an extension to curved environments. In: IEEE International Conference on Robotics, Automation, pp 1677–1682 LaValle S, Hinrichsen J (1999) Visibility-based pursuit-evasion: an extension to curved environments. In: IEEE International Conference on Robotics, Automation, pp 1677–1682
6.
Zurück zum Zitat Vidal R, Rashid S, Sharp C, Shakernia O, Kim J, Sastry S (2001) Pursuit-evasion games with unmanned ground and aerial vehicles. In: IEEE International Conference on Robotics, Automation, pp 2948–2955 Vidal R, Rashid S, Sharp C, Shakernia O, Kim J, Sastry S (2001) Pursuit-evasion games with unmanned ground and aerial vehicles. In: IEEE International Conference on Robotics, Automation, pp 2948–2955
7.
Zurück zum Zitat Kachroo P, Shedied SA, Bay JS, Vanlandingham H (2001) Dynamic programming solution for a class of pursuit evasion problems: the herding problem. In: IEEE transactions on systems, man and cybernetics, part C Kachroo P, Shedied SA, Bay JS, Vanlandingham H (2001) Dynamic programming solution for a class of pursuit evasion problems: the herding problem. In: IEEE transactions on systems, man and cybernetics, part C
8.
Zurück zum Zitat Zhong Z, Liu Z, Li C, Guan Y (2011) Event ontology reasoning based on event class influence factors. Int J Mach Learn Cyber 2 Zhong Z, Liu Z, Li C, Guan Y (2011) Event ontology reasoning based on event class influence factors. Int J Mach Learn Cyber 2
9.
Zurück zum Zitat Berkovitz LD, Flemming WH (1957) A variational approach to differential games. Annals of Mathematics Study 39, Princeton University Press, Princeton Berkovitz LD, Flemming WH (1957) A variational approach to differential games. Annals of Mathematics Study 39, Princeton University Press, Princeton
10.
Zurück zum Zitat Isaacs R (1965) Differential games: a mathematical theory with application to warfare and pursuit control and optimization. Dover Publications Inc., NY Isaacs R (1965) Differential games: a mathematical theory with application to warfare and pursuit control and optimization. Dover Publications Inc., NY
11.
Zurück zum Zitat Askari H, Zahiri SH (2011) Decision function estimation using intelligent gravitational search algorithm. Int J Mach Learn Cyber 2 Askari H, Zahiri SH (2011) Decision function estimation using intelligent gravitational search algorithm. Int J Mach Learn Cyber 2
12.
Zurück zum Zitat Biggio B, Fumera G, Roli F (2010) Multiple classifier systems for robust classifier design in adversarial environments. Int J Mach Learn Cyber 1(1–4):27–41CrossRef Biggio B, Fumera G, Roli F (2010) Multiple classifier systems for robust classifier design in adversarial environments. Int J Mach Learn Cyber 1(1–4):27–41CrossRef
13.
Zurück zum Zitat Sahin F, Bay JS (2001) Learning from experience using a decision-theoretic intelligent agent in multiagent systems. In: Proceedings of the 2001 IEEE mountain workshop on soft computing in industrial applications Sahin F, Bay JS (2001) Learning from experience using a decision-theoretic intelligent agent in multiagent systems. In: Proceedings of the 2001 IEEE mountain workshop on soft computing in industrial applications
14.
Zurück zum Zitat Sahin F, Bay JS (2002) Structural Bayesian network learning in a biological decision-theoretic intelligent agent and its application to a herding problem in the context of distributed multi-agent systems. In: IEEE international conference on systems, man, and cybernetics Sahin F, Bay JS (2002) Structural Bayesian network learning in a biological decision-theoretic intelligent agent and its application to a herding problem in the context of distributed multi-agent systems. In: IEEE international conference on systems, man, and cybernetics
15.
Zurück zum Zitat Kachroo P, Shedied SA, Vanlandingham H (2002) Pursuit evasion: the herding non-cooperative dynamic game. J Integr Design Process Sci 6(1) Kachroo P, Shedied SA, Vanlandingham H (2002) Pursuit evasion: the herding non-cooperative dynamic game. J Integr Design Process Sci 6(1)
16.
Zurück zum Zitat Hespanha J, Prandini M, Sastry S (2000) Probabilistic pursuit-evasion games: a one-step nash approach. In: Proceedings of 39th IEEE conference on decision and control, pp 2272–2277 Hespanha J, Prandini M, Sastry S (2000) Probabilistic pursuit-evasion games: a one-step nash approach. In: Proceedings of 39th IEEE conference on decision and control, pp 2272–2277
17.
Zurück zum Zitat Hespanha J, Kim J, Sastry S (1999) Multiple-agent probabilistic pursuit-evasion games. In: Proceedings of 38th IEEE conference on decision and control, pp 2432–2437 Hespanha J, Kim J, Sastry S (1999) Multiple-agent probabilistic pursuit-evasion games. In: Proceedings of 38th IEEE conference on decision and control, pp 2432–2437
18.
Zurück zum Zitat Vidal R, Shakernia O, Kim H, Shim D, Sastry S (2002) Probabilistic pursuit-evasion games: Theory, implementation, and experimental evaluation. IEEE transactions on robotics and automation, pp 662–669 Vidal R, Shakernia O, Kim H, Shim D, Sastry S (2002) Probabilistic pursuit-evasion games: Theory, implementation, and experimental evaluation. IEEE transactions on robotics and automation, pp 662–669
19.
Zurück zum Zitat Kachroo P, Shedied SA, Vanlandingham H (2002) Pursuit evasion: the herding non-cooperative dynamic game: the stochastic model. In: IEEE transactions on systems, man, and cybernetics, part c: applications and reviews, vol 32(1) Kachroo P, Shedied SA, Vanlandingham H (2002) Pursuit evasion: the herding non-cooperative dynamic game: the stochastic model. In: IEEE transactions on systems, man, and cybernetics, part c: applications and reviews, vol 32(1)
20.
Zurück zum Zitat Vidal R, Shakernia O, Jin Kim H, Hyunchul Shim D, Sastry S (2002) Probabilistic pursuit-evasion games: theory, implementation and experimental evaluation. In: IEEE transactions on robotics and automation Vidal R, Shakernia O, Jin Kim H, Hyunchul Shim D, Sastry S (2002) Probabilistic pursuit-evasion games: theory, implementation and experimental evaluation. In: IEEE transactions on robotics and automation
21.
Zurück zum Zitat George M (1969) Ewing calculus of variations with applications. Dover Publication Inc George M (1969) Ewing calculus of variations with applications. Dover Publication Inc
22.
Zurück zum Zitat Lewis FL, Syrmos VL (1995) Optimal control. Wiley, New York Lewis FL, Syrmos VL (1995) Optimal control. Wiley, New York
23.
Zurück zum Zitat Leitmann G (1981) The calculus of variations and optimal control: an introduction. Plenum Press, New York Leitmann G (1981) The calculus of variations and optimal control: an introduction. Plenum Press, New York
24.
Zurück zum Zitat Slotine JJE, Li W (1990) Applied nonlinear control. Prentice Hall Slotine JJE, Li W (1990) Applied nonlinear control. Prentice Hall
25.
Zurück zum Zitat Laumond J-P (1998) Robot motion planning and control. Springer Laumond J-P (1998) Robot motion planning and control. Springer
Metadaten
Titel
Optimal trajectory planning for the herding problem: a continuous time model
verfasst von
Samy A. Shedied
Publikationsdatum
01.02.2013
Verlag
Springer-Verlag
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 1/2013
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-012-0071-2

Weitere Artikel der Ausgabe 1/2013

International Journal of Machine Learning and Cybernetics 1/2013 Zur Ausgabe

Neuer Inhalt