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Revisiting the Minimum Constraint Removal Problem in Mobile Robotics

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Intelligent Autonomous Systems 18 (IAS 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 795))

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Abstract

The minimum constraint removal problem seeks to find the minimum number of constraints, i.e., obstacles, that need to be removed to connect a start to a goal location with a collision-free path. This problem is NP-hard and has been studied in robotics, wireless sensing, and computational geometry. This work contributes to the existing literature by presenting and discussing two results. The first result shows that the minimum constraint removal is NP-hard for simply connected obstacles where each obstacle intersects a constant number of other obstacles. The second result demonstrates that for n simply connected obstacles in the plane, instances of the minimum constraint removal problem with minimum removable obstacles lower than \((n+1)/3\) can be solved in polynomial time. This result is also empirically validated using several instances of randomly sampled axis-parallel rectangles.

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Notes

  1. 1.

    MCR with disjoint and simply connected obstacles is in P [14].

  2. 2.

    In the following, we will omit the subscript P because the reference to a specific path P will be implicit.

  3. 3.

    Exact MCR using best-first search for non-overlap** and simply connected obstacles could still generate \(O(|E|2^n)\) states. However, for such sub-classes, a greedy search (running in O(|E|n)) generates an optimal solution [14].

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Authors and Affiliations

  1. Department of Informatics, Bioengineering, Robotics, and Systems Engineering, University of Genoa, Via All’Opera Pia 13, 16145, Genoa, Italy

    Antony Thomas, Fulvio Mastrogiovanni & Marco Baglietto

Authors
  1. Antony Thomas
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  2. Fulvio Mastrogiovanni
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  3. Marco Baglietto
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Corresponding author

Correspondence to Antony Thomas .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Kyung Hee University, Yongin-si, Korea (Republic of)

    Soon-Geul Lee

  2. Department of Interdisciplinary Engineering, Daegu Gyeongbuk Institute of Science and DGIST R4-708, Daegu, Korea (Republic of)

    **ung An

  3. School of Information Science, Human Information Science Research Area, Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Nak Young Chong

  4. DHBW Karlsruhe, Cooperative State University Baden-Wuerttemberg Karlsruhe, Karlsruhe, Germany

    Marcus Strand

  5. Department of Mechanical and Aerospace Engineering, New York University, New York, NY, USA

    Joo H. Kim

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Thomas, A., Mastrogiovanni, F., Baglietto, M. (2024). Revisiting the Minimum Constraint Removal Problem in Mobile Robotics. In: Lee, SG., An, J., Chong, N.Y., Strand, M., Kim, J.H. (eds) Intelligent Autonomous Systems 18. IAS 2023. Lecture Notes in Networks and Systems, vol 795. Springer, Cham. https://doi.org/10.1007/978-3-031-44851-5_3

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