Soft Subdivision Motion Planning for Complex Planar Robots

Authors Bo Zhou, Yi-Jen Chiang, Chee Yap

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Author Details

Bo Zhou
  • Department of Computer Science and Engineering, New York University, Brooklyn, NY, USA
Yi-Jen Chiang
  • Department of Computer Science and Engineering, New York University, Brooklyn, NY, USA
Chee Yap
  • Department of Computer Science, New York University, New York, NY, USA

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Bo Zhou, Yi-Jen Chiang, and Chee Yap. Soft Subdivision Motion Planning for Complex Planar Robots. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 73:1-73:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


The design and implementation of theoretically-sound robot motion planning algorithms is challenging. Within the framework of resolution-exact algorithms, it is possible to exploit soft predicates for collision detection. The design of soft predicates is a balancing act between easily implementable predicates and their accuracy/effectivity. In this paper, we focus on the class of planar polygonal rigid robots with arbitrarily complex geometry. We exploit the remarkable decomposability property of soft collision-detection predicates of such robots. We introduce a general technique to produce such a decomposition. If the robot is an m-gon, the complexity of this approach scales linearly in m. This contrasts with the O(m^3) complexity known for exact planners. It follows that we can now routinely produce soft predicates for any rigid polygonal robot. This results in resolution-exact planners for such robots within the general Soft Subdivision Search (SSS) framework. This is a significant advancement in the theory of sound and complete planners for planar robots. We implemented such decomposed predicates in our open-source Core Library. The experiments show that our algorithms are effective, perform in real time on non-trivial environments, and can outperform many sampling-based methods.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Computing methodologies → Robotic planning
  • Computational Geometry
  • Algorithmic Motion Planning
  • Resolution-Exact Algorithms
  • Soft Predicates
  • Planar Robots with Complex Geometry


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