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Collision Avoidance Problem of Ellipsoid Motion

Author

Listed:
  • Shujun Guo

    (School of Business, Qingdao University, Qingdao 266071, China)

  • Lujing Jing

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Zhaopeng Dai

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Yang Yu

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Zhiqing Dang

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Zhihang You

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Ang Su

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Hongwei Gao

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
    College of Science, Jiamusi University, Jiamusi 154007, China)

  • Jinqiu Guan

    (College of Science, Jiamusi University, Jiamusi 154007, China)

  • Yujun Song

    (College of Science, Jiamusi University, Jiamusi 154007, China)

Abstract

This paper studies the problem of target control and how a virtual ellipsoid can avoid the static obstacle. During the motion to the target set, the virtual ellipsoid can achieve a motion under collision avoidance by keeping the distance between the ellipsoid and obstacle. We present solutions to this problem in the class of closed-loop (feedback) controls based on Hamilton–Jacobi–Bellman (HJB) equation. Simulation results verify the validity and effectiveness of our algorithm.

Suggested Citation

  • Shujun Guo & Lujing Jing & Zhaopeng Dai & Yang Yu & Zhiqing Dang & Zhihang You & Ang Su & Hongwei Gao & Jinqiu Guan & Yujun Song, 2022. "Collision Avoidance Problem of Ellipsoid Motion," Mathematics, MDPI, vol. 10(19), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3478-:d:923369
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    References listed on IDEAS

    as
    1. A. B. Kurzhanski & I. M. Mitchell & P. Varaiya, 2006. "Optimization Techniques for State-Constrained Control and Obstacle Problems," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 499-521, March.
    2. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
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