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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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
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