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A New Application of Discrete Morse Theory to Optimizing Safe Motion Planning Paths

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Algorithmic Foundations of Robotics XV (WAFR 2022)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 25))

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Abstract

We present a novel method for extracting geometric and topological features from a robot’s configuration space. To accomplish this, we define a discrete Morse function on the Vietoris-Rips simplicial complex to identify critical points on the surface of obstacles present. These critical points serve as waypoints for determining feasible bounds near an identified obstacle. This work builds on previous work that provides a method to approximate the number of samples required to generate pathways. Our results achieve near-optimal paths with a low computation time and reduced path distance in this work. We conduct experiments in different environments and with various robots, including the Kuka YouBot and PR2 robots in simulation, and demonstrate the performance gains compared to state-of-the-art methods.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University at Albany, State University of New York, Albany, NY, USA

    Aakriti Upadhyay & Chinwe Ekenna

  2. Department of Mathematics and Statistics, University at Albany, State University of New York, Albany, NY, USA

    Boris Goldfarb

  3. Baidu Research, Beijing, China

    Weifu Wang

Authors
  1. Aakriti Upadhyay
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  2. Boris Goldfarb
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  3. Weifu Wang
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  4. Chinwe Ekenna
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Corresponding author

Correspondence to Aakriti Upadhyay .

Editor information

Editors and Affiliations

  1. Center for Ubiquitous Computing, University of Oulu, Oulu, Finland

    Steven M. LaValle

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA

    Jason M. O’Kane

  3. Department of Aerospace Engineering, University of Maryland, College Park, MD, USA

    Michael Otte

  4. Gates Computer Science, Stanford University, Stanford, CA, USA

    Dorsa Sadigh

  5. Department of Computer Science, University of Maryland, College Park, MD, USA

    Pratap Tokekar

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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Upadhyay, A., Goldfarb, B., Wang, W., Ekenna, C. (2023). A New Application of Discrete Morse Theory to Optimizing Safe Motion Planning Paths. In: LaValle, S.M., O’Kane, J.M., Otte, M., Sadigh, D., Tokekar, P. (eds) Algorithmic Foundations of Robotics XV. WAFR 2022. Springer Proceedings in Advanced Robotics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-031-21090-7_2

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