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Pose-Estimation Methods for Planar Underactuated Cable-Driven Parallel Robots

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Cable-Driven Parallel Robots (CableCon 2023)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 132))

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Abstract

Planar underactuated cable-driven parallel robots (UACDPRs) employ less than three cables to control the pose of the end-effector (EE). Consequently, the EE pose cannot be calculated only from cable-length geometrical constraint equations. In order to solve the direct kinematic problem, redundant measurements may be acquired, and the EE pose calculated by optimizing the resulting system of nonlinear equations. For the optimal pose estimation of planar UACDPRs, this paper presents three sensor fusion algorithms based on nonlinear weighted least squares equations, differing for the algorithm termination conditions. Additionally, different redundant measurement sets are experimentally compared.

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Notes

  1. 1.

    The proof is omitted for brevity sake, but is based on basic matrix product and derivative properties. See the appendix of [10] for similar calculations.

  2. 2.

    Computing the second-order vector derivative of a vector results in a 3rd-order tensor; any computation between a 3-rd order tensor, matrices, and vectors is not straightforward, but an example of how to perform them can be found in the appendix of [10].

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Acknowledgments

The authors acknowledge the support of the Italian Ministry of University and Research (MUR) through the PRIN 2020 grant “Extending Robotic Manipulation Capabilities by Cooperative Mobile and Flexible Multi-Robot Systems (Co-MiR)” (No. 2020CMEFPK).

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Authors and Affiliations

  1. University of Bologna, Bologna, Italy

    Sara Gabaldo, Edoardo Idà & Marco Carricato

Authors
  1. Sara Gabaldo
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  2. Edoardo Idà
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  3. Marco Carricato
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Corresponding author

Correspondence to Edoardo Idà .

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Editors and Affiliations

  1. École Centrale Nantes, CNRS, LS2N, Nantes Université, Nantes, France

    Stéphane Caro

  2. University of Stuttgart, Stuttgart, Germany

    Andreas Pott

  3. Chair of Mechatronics, University of Duisburg-Essen, Duisburg, Germany

    Tobias Bruckmann

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Gabaldo, S., Idà, E., Carricato, M. (2023). Pose-Estimation Methods for Planar Underactuated Cable-Driven Parallel Robots. In: Caro, S., Pott, A., Bruckmann, T. (eds) Cable-Driven Parallel Robots. CableCon 2023. Mechanisms and Machine Science, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-031-32322-5_1

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