IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v5y2015i3p297-317.html
   My bibliography  Save this article

On the Suicidal Pedestrian Differential Game

Author

Listed:
  • Ioannis Exarchos
  • Panagiotis Tsiotras
  • Meir Pachter

Abstract

We consider the following differential game of pursuit and evasion involving two participating players: an evader, which has limited maneuverability, and an agile pursuer. The agents move on the Euclidean plane with different but constant speeds. Whereas the pursuer can change the orientation of its velocity vector arbitrarily fast, that is, he is a “pedestrian” á la Isaacs, the evader cannot make turns having a radius smaller than a specified minimum turning radius. This problem can be seen as a reversed Homicidal Chauffeur game, hence the name “Suicidal Pedestrian Differential Game.” The aim of this paper is to derive the optimal strategies of the two players and characterize the initial conditions that lead to capture if the pursuer acts optimally, and areas that guarantee evasion regardless of the pursuer’s strategy. Both proximity-capture and point-capture are considered. After applying the optimal strategy for the evader, it is shown that the case of point-capture reduces to a special version of Zermelo’s Navigation Problem (ZNP) for the pursuer. Therefore, the well-known ZNP solution can be used to validate the results obtained through the differential game framework, as well as to characterize the time-optimal trajectories. The results are directly applicable to collision avoidance in maritime and Air Traffic Control applications. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Ioannis Exarchos & Panagiotis Tsiotras & Meir Pachter, 2015. "On the Suicidal Pedestrian Differential Game," Dynamic Games and Applications, Springer, vol. 5(3), pages 297-317, September.
  • Handle: RePEc:spr:dyngam:v:5:y:2015:i:3:p:297-317
    DOI: 10.1007/s13235-014-0130-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-014-0130-2
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s13235-014-0130-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. V. S. Patsko & V. L. Turova, 2001. "Level Sets Of The Value Function In Differential Games With The Homicidal Chauffeur Dynamics," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 67-112.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ritwik Bera & Venkata Ramana Makkapati & Mangal Kothari, 2017. "A Comprehensive Differential Game Theoretic Solution to a Game of Two Cars," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 818-836, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Valerii Patsko & Varvara Turova, 2020. "Antony Merz and His Works," Dynamic Games and Applications, Springer, vol. 10(1), pages 157-182, March.
    2. Sergey S. Kumkov & Stéphane Ménec & Valerii S. Patsko, 2017. "Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications," Dynamic Games and Applications, Springer, vol. 7(4), pages 609-633, December.
    3. Touffik Bouremani & Yacine Slimani, 2024. "Study of a Warfare Differential Game via Dynamic Programming Approach," Dynamic Games and Applications, Springer, vol. 14(4), pages 733-750, September.
    4. Sourabh Bhattacharya & Tamer Başar & Naira Hovakimyan, 2016. "A Visibility-Based Pursuit-Evasion Game with a Circular Obstacle," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 1071-1082, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:dyngam:v:5:y:2015:i:3:p:297-317. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.