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Singularity-Free Inverse Kinematics with Joint Prioritization for Manipulators

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Abstract

This paper presents a Jacobian-based solution for inverse kinematics of serial rigid link robots while providing an intuitive way to control joint priorities with virtual inertia parameters. We improve the Transposed Jacobian by pre-multiplying it with the Joint Space Inertia Matrix, resulting in an algorithm that we named JTi-IK, which has shown equivalent convergence performance in iterations when compared to the Damped Least Squares method in our experiments. Pre- or post-multiplication of the Transposed Jacobian by a matrix is a concept pursued by the most basic methods. In our approach, we explore the matrices related to dynamics as an implementation of this concept in a way that only positive-definite matrices are inverted, so there are no singularities. After simplifications on the Joint Space Inertia Matrix, we reach the Virtual Inertia Matrix, which allows modifications on virtual weight distributions as control parameters for prioritization of different joints, affecting body posture without extra algorithm steps. In this paper, we also discuss the stabilizing effects of pre-multiplication matrices that appear in most Jacobian-derived methods. As it is also based on the Jacobian, our method inherits its generality, being valid for any serial manipulator structure. When evaluating JTi-IK for a planar robot, we reach the same results obtained in our previous paper. This is a very interesting result, since the methods are derived in distinct ways.

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Authors and Affiliations

  1. Department of Electrical Engineering, Federal University of Sergipe, São Cristóvão, Brazil

    Raphael C. O. Jesus, Lucas Molina, Elyson A. N. Carvalho & Eduardo O. Freire

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  1. Raphael C. O. Jesus
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  2. Lucas Molina
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  3. Elyson A. N. Carvalho
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  4. Eduardo O. Freire
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This work was supported by CNPq and was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

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Jesus, R.C.O., Molina, L., Carvalho, E.A.N. et al. Singularity-Free Inverse Kinematics with Joint Prioritization for Manipulators. J Control Autom Electr Syst 33, 1022–1031 (2022). https://doi.org/10.1007/s40313-021-00860-4

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  • DOI: https://doi.org/10.1007/s40313-021-00860-4

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