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The distance between convex sets with Minkowski sum structure: application to collision detection

Author

Listed:
  • Xiangfeng Wang

    (East China Normal University)

  • Junping Zhang

    (University of Electronic Science and Technology of China)

  • Wenxing Zhang

    (University of Electronic Science and Technology of China)

Abstract

The distance between sets is a long-standing computational geometry problem. In robotics, the distance between convex sets with Minkowski sum structure plays a fundamental role in collision detection. However, it is typically nontrivial to be computed, even if the projection onto each component set admits explicit formula. In this paper, we explore the problem of calculating the distance between convex sets arising from robotics. Upon the recent progress in convex optimization community, the proposed model can be efficiently solved by the recent hot-investigated first-order methods, e.g., alternating direction method of multipliers or primal-dual hybrid gradient method. Preliminary numerical results demonstrate that those first-order methods are fairly efficient in solving distance problems in robotics.

Suggested Citation

  • Xiangfeng Wang & Junping Zhang & Wenxing Zhang, 2020. "The distance between convex sets with Minkowski sum structure: application to collision detection," Computational Optimization and Applications, Springer, vol. 77(2), pages 465-490, November.
    • Handle: RePEc:spr:coopap:v:77:y:2020:i:2:d:10.1007_s10589-020-00211-0
    DOI: 10.1007/s10589-020-00211-0
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    References listed on IDEAS

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    Cited by:

    1. James Chok & Geoffrey M. Vasil, 2023. "Convex optimization over a probability simplex," Papers 2305.09046, arXiv.org.

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