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Rods and Rings: Soft Subdivision Planner for R^3 x S^2

Authors Ching-Hsiang Hsu, Yi-Jen Chiang, Chee Yap

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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Computing methodologies → Robotic planning
Keywords
  • Algorithmic Motion Planning
  • Subdivision Methods
  • Resolution-Exact Algorithms
  • Soft Predicates
  • Spatial Rod Robots
  • Spatial Ring Robots

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Abstract

We consider path planning for a rigid spatial robot moving amidst polyhedral obstacles. Our robot is either a rod or a ring. Being axially-symmetric, their configuration space is R^3 x S^2 with 5 degrees of freedom (DOF). Correct, complete and practical path planning for such robots is a long standing challenge in robotics. While the rod is one of the most widely studied spatial robots in path planning, the ring seems to be new, and a rare example of a non-simply-connected robot. This work provides rigorous and complete algorithms for these robots with theoretical guarantees. We implemented the algorithms in our open-source Core Library. Experiments show that they are practical, achieving near real-time performance. We compared our planner to state-of-the-art sampling planners in OMPL [Sucan et al., 2012].
Our subdivision path planner is based on the twin foundations of epsilon-exactness and soft predicates. Correct implementation is relatively easy. The technical innovations include subdivision atlases for S^2, introduction of Sigma_2 representations for footprints, and extensions of our feature-based technique for "opening up the blackbox of collision detection".

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Ching-Hsiang Hsu, Yi-Jen Chiang, and Chee Yap. Rods and Rings: Soft Subdivision Planner for R^3 x S^2. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.SoCG.2019.43

Author Details

Ching-Hsiang Hsu
  • Department of Computer Science, Courant Institute, New York University, New York, NY, USA
Yi-Jen Chiang
  • Department of Computer Science and Engineering, Tandon School of Engineering, New York University, Brooklyn, NY, USA
Chee Yap
  • Department of Computer Science, Courant Institute, New York University, New York, NY, USA

Funding

Supported in part by NSF Grants #CCF-1423228 and #CCF-1563942.
  • Hsu, Ching-Hsiang: Supported by NSF Grant #CCF-1423228.
  • Yap, Chee: Supported in part by NSF Grants #CCF-1423228 and #CCF-1563942.

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