IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v191y2021i2d10.1007_s10957-021-01921-z.html
   My bibliography  Save this article

Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials

Author

Listed:
  • Calvin Kielas-Jensen

    (University of Iowa)

  • Venanzio Cichella

    (University of Iowa)

  • David Casbeer

    (Control Science Center of Excellence, Air Force Research Laboratory)

  • Satyanarayana Gupta Manyam

    (Infoscitex Corp., A DCS company)

  • Isaac Weintraub

    (Aerospace Systems Directorate, Air Force Research Laboratory)

Abstract

A framework for monitoring a target modeled as Dubins car using multiple UAVs is proposed. The UAVs are subject to minimum and maximum speed, maximum angular rate constraints, as well as inter-vehicle safety requirements and no-fly-zones. The problem is formulated as a continuous time nonlinear optimal control problem. This problem is first simplified by using a sequential approach, which significantly reduces its complexity. Then, by defining the desired trajectories to be tracked by the UAVs as Bernstein polynomials, it is transcribed into a nonlinear optimization problem. It is shown through numerical simulations that the present approach is computationally efficient, and thus it is well suited for trajectory planning/re-planning to monitor a target of unknown speed, heading direction and unexpected detours. Moreover, the proposed method guarantees satisfaction of feasibility and safety constraints for the whole planning time period, rather than only at discrete time points.

Suggested Citation

  • Calvin Kielas-Jensen & Venanzio Cichella & David Casbeer & Satyanarayana Gupta Manyam & Isaac Weintraub, 2021. "Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 899-916, December.
  • Handle: RePEc:spr:joptap:v:191:y:2021:i:2:d:10.1007_s10957-021-01921-z
    DOI: 10.1007/s10957-021-01921-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-021-01921-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-021-01921-z?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. Bruce A. Conway, 2012. "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 271-306, February.
    2. Scott Shorey Brown, 1980. "Optimal Search for a Moving Target in Discrete Time and Space," Operations Research, INFORMS, vol. 28(6), pages 1275-1289, December.
    3. Johannes O. Royset & Hiroyuki Sato, 2010. "Route optimization for multiple searchers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 701-717, December.
    4. Hoam Chung & Elijah Polak & Johannes O. Royset & Shankar Sastry, 2011. "On the optimal detection of an underwater intruder in a channel using unmanned underwater vehicles," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 804-820, December.
    Full references (including those not matched with items on IDEAS)

    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. Lawrence D. Stone & Alan R. Washburn, 1991. "Introduction special issue on search theory," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 465-468, August.
    2. Joseph B. Kadane, 2015. "Optimal discrete search with technological choice," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 317-336, June.
    3. Mauro Pontani, 2021. "Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 545-574, December.
    4. Michael P. Atkinson & Moshe Kress & Roberto Szechtman, 2017. "To catch an intruder: Part A—uncluttered scenario," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 29-40, February.
    5. Hohzaki, Ryusuke, 2006. "Search allocation game," European Journal of Operational Research, Elsevier, vol. 172(1), pages 101-119, July.
    6. Mauro Pontani & Bruce Conway, 2014. "Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 272-292, July.
    7. Bourque, François-Alex, 2019. "Solving the moving target search problem using indistinguishable searchers," European Journal of Operational Research, Elsevier, vol. 275(1), pages 45-52.
    8. Alan R. Washburn, 1998. "Branch and bound methods for a search problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 243-257, April.
    9. Joseph Kadane, 2015. "Optimal discrete search with technological choice," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 317-336, June.
    10. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    11. Brian Lunday & Hanif Sherali, 2012. "Network interdiction to minimize the maximum probability of evasion with synergy between applied resources," Annals of Operations Research, Springer, vol. 196(1), pages 411-442, July.
    12. Lyn C. Thomas & James N. Eagle, 1995. "Criteria and approximate methods for path‐constrained moving‐target search problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 27-38, February.
    13. J F J Vermeulen & M van den Brink, 2005. "The search for an alerted moving target," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 514-525, May.
    14. Klaus Werner Schmidt & Öncü Hazır, 2019. "Formulation and solution of an optimal control problem for industrial project control," Annals of Operations Research, Springer, vol. 280(1), pages 337-350, September.
    15. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    16. Joseph Foraker & Seungho Lee & Elijah Polak, 2016. "Validation of a strategy for harbor defense based on the use of a min‐max algorithm receding horizon control law," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 247-259, April.
    17. Claire Walton & Panos Lambrianides & Isaac Kaminer & Johannes Royset & Qi Gong, 2018. "Optimal motion planning in rapid‐fire combat situations with attacker uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(2), pages 101-119, March.
    18. David Ottesen & Ryan P. Russell, 2021. "Unconstrained Direct Optimization of Spacecraft Trajectories Using Many Embedded Lambert Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 634-674, December.
    19. Delavernhe, Florian & Jaillet, Patrick & Rossi, André & Sevaux, Marc, 2021. "Planning a multi-sensors search for a moving target considering traveling costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 469-482.
    20. Johannes O. Royset & Hiroyuki Sato, 2010. "Route optimization for multiple searchers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 701-717, 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:joptap:v:191:y:2021:i:2:d:10.1007_s10957-021-01921-z. 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.