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Iterative inverse kinematics for robot manipulators using quaternion algebra and conformal geometric algebra

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Abstract

This paper presents a set of generalized iterative algorithms to find the inverse position kinematics of n-degree-of-freedom kinematic chains with revolute joints. As a first approach, an iterative algorithm is developed using the gradient descent method in Quaternion Algebra to find both the inverse position and velocity kinematics solution in redundant systems closest to their initial configuration. Additionally, a generalized extension of this approach is developed employing screw rotors and Conformal Geometric Algebra, where efficient update rules are obtained to solve the problem of inverse position kinematics. Simulation experiments using different degree-of-freedom models as well as real-time experiments using a Geomagic Touch Haptic device are carried out to demonstrate the effectiveness of the proposed methods.

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Acknowledgements

The authors would like to thank CONACYT and CINVESTAV-IPN for the scholarship and the economic and technological support for the realization of this work.

Funding

This work was supported by CONACYT institute and CINVESTAV-IPN.

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Authors and Affiliations

  1. Cuerpo Académico de Electrónica y Control, Universidad Autónomia del Estado de Hidalgo, Mineral de la Reforma, Hidalgo, Mexico

    L. Lechuga-Gutierrez

  2. Departamento de Ingeniería Eléctrica y Ciencias de la Computación, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Zapopan, Jalisco, México

    E. Macias-Garcia, G. Martínez-Terán & E. Bayro-Corrochano

  3. Intel Labs, Zapopan, Jalisco, Mexico

    J. Zamora-Esquivel

Authors
  1. L. Lechuga-Gutierrez
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  2. E. Macias-Garcia
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  3. G. Martínez-Terán
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  4. J. Zamora-Esquivel
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  5. E. Bayro-Corrochano
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Contributions

All authors contributed to the study conception and design of this work. L. Lechuga-Gutierrez: Paper writing, main contributions in Sects. 2, 3 and 6. E. Macias-Garcia: Paper writing, document review, main contributions in Sects. 2, 4 and 5. G. Martínez-Terán: Main contributions in Sect. 6. J. Zamora-Esquivel: Document review, main contributions in Sects. 4 and 5. E. Bayro-Corrochano: Paper writing, document review, project supervision.

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Correspondence to E. Bayro-Corrochano.

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The authors have no conflicts of interest to declare that are relevant to the content of this article.

Code availability

The Conformal Geometric Algebra library developed in this work is available at: github.com/iqedgarmg/conformal_library while additional multimedia resources at: drive.google.com/drive/folders/11DfFiQ8wZsfY31VDIK2i-Mg0rnHeucCM.

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Lechuga-Gutierrez, L., Macias-Garcia, E., Martínez-Terán, G. et al. Iterative inverse kinematics for robot manipulators using quaternion algebra and conformal geometric algebra. Meccanica 57, 1413–1428 (2022). https://doi.org/10.1007/s11012-022-01512-w

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