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Workspace Multiplicity and Fault Tolerance of Cooperating Robots

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Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

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Abstract

Cooperating robotic systems, especially in the context of fault-tolerance of complex robotic mechanisms, is an important question for theoretical and applied studies. In this paper, we focus on one measure of fault tolerance in robots, namely, the multiplicity of the configurations for reaching a particular point in the workspace, which is difficult to measure using traditional methods. As a particular example, we consider the case of a free-swinging failure of a robotic arm that is handled by having a cooperating functional robot grasp the link adjacent to the failed joint. We present an efficient method to compute the multiplicity measure of the workspace, based on the tools from numerical algebraic geometry, applied to the inverse kinematics problem re-cast in the form of a polynomial system. To emphasize the difference between our methods and more traditional approaches, we compute the measure of workspace based on the multiplicity of configurations, and optimize placement of synergistic robot arms and the optimal grasp point on each link of the broken robot based on this measure.

D.A. Brake—Partially supported by grants NSF-DMS-09087551 and NSF-IIS-0812437.

D.J. Bates—Partially supported by grants NSF DMS–0914674 and NSF DMS–1115668.

V. Putkaradze—Partially supported by grant NSF-DMS-09087551.

A.A. Maciejewski—Partially supported by grant NSF-IIS-0812437.

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Author information

Authors and Affiliations

  1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, USA

    Daniel A. Brake

  2. Department of Mathematics, Colorado State University, Fort Collins, USA

    Daniel J. Bates

  3. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada

    Vakhtang Putkaradze

  4. Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, USA

    Anthony A. Maciejewski

Authors
  1. Daniel A. Brake
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  2. Daniel J. Bates
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  3. Vakhtang Putkaradze
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  4. Anthony A. Maciejewski
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Correspondence to Daniel J. Bates .

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Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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Brake, D.A., Bates, D.J., Putkaradze, V., Maciejewski, A.A. (2016). Workspace Multiplicity and Fault Tolerance of Cooperating Robots. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_8

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