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A Visibility-Based Approach to Computing Nondeterministic Bouncing Strategies

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Algorithmic Foundations of Robotics XIII (WAFR 2018)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 14))

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Abstract

Inspired by motion patterns of some commercially available mobile robots, we investigate the power of robots that move forward in straight lines until colliding with an environment boundary, at which point they can rotate in place and move forward again; we visualize this as the robot “bouncing” off boundaries. Different boundary interaction rules can be defined for such robots, such as one that orients the robot relative to its heading prior to collision, or relative to the normal of the boundary. We introduce a new data structure, the bounce visibility graph, which is generated from a polygonal environment definition. The bounce visibility graph can be queried to determine the feasibility of path-based tasks such as navigation and patrolling, assuming we have unavoidable nondeterminism in our actuation. If the task is feasible, then this approach synthesizes a strategy (a sequence of nondeterministic rotations). We also show how to compute stable cyclic trajectories and use these to limit uncertainty in the robot’s position (Software implementation at https://github.com/alexandroid000/bounce_viz).

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Acknowledgement

This work was supported by NSF grants 1035345 and 1328018, and CONACyT post-doctoral fellowship 277028.

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Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Alexandra Q. Nilles, Yingying Ren, Israel Becerra & Steven M. LaValle

  2. Faculty of Information Technology and Electrical Engineering, University of Oulu, Oulu, Finland

    Steven M. LaValle

Authors
  1. Alexandra Q. Nilles
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  2. Yingying Ren
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  3. Israel Becerra
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  4. Steven M. LaValle
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Corresponding author

Correspondence to Alexandra Q. Nilles .

Editor information

Editors and Affiliations

  1. Departamento de Sistemas Digitales, Instituto Tecnológico Autónomo de México, México, Mexico

    Marco Morales

  2. Department of Computer Science, University of New Mexico, Albuquerque, NM, USA

    Lydia Tapia

  3. Universidad Politécnica de Yucatán, Yucatán, Mexico

    Gildardo Sánchez-Ante

  4. Georgia Tech, Atlanta, GA, USA

    Seth Hutchinson

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Nilles, A.Q., Ren, Y., Becerra, I., LaValle, S.M. (2020). A Visibility-Based Approach to Computing Nondeterministic Bouncing Strategies. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-44051-0_6

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