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Influences of space perturbations on robotic assembly process of ultra-large structures

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Abstract

The space assembly of two flexible beams by a dual-arm space robot is a typical assembly scenario to construct ultra-large space structure. Yet, previous studies mainly focused on the assembly of small structures, neglecting the influences of space perturbations. Two models are developed in this research to investigate the effects of space perturbations on the space assembly process of ultra-large space structures. Firstly, a theoretical modelling method is proposed based on quasi-static hypothesis and linear structural mechanics. The theoretical model can be utilized for analytically estimating the transverse and axial distributed forces of the flexible beams, structural vibrations, and the control moments of the space robot. An orbit–attitude–structure coupled simulation model is then established to validate the theoretical model and study the dynamic behaviours more accurately, using absolute nodal coordinate formulation and natural coordinate formulation. Finally, the effects of the attitude angle, orbital radius, and lengths of beams on the dynamic responses during assembly are investigated. Theoretical and simulation results show that the control moments and structural vibration amplitude increase dramatically with the length of the beams. The effects of Coriolis force and gravity gradient must be considered for ultra-large space structures during assembly, otherwise the control moments and structural vibrations would be substantially underestimated. The results are instructive to the assembly strategy design as well as modular component design of ultra-large space structures.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (12202508, 12232015), Young Elite Scientists Sponsorship Program by China Association for Science and Technology (2021QNRC001), and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (No. 22qntd0703).

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  1. School of Aeronautics and Astronautics, Sun Yat-Sen University, Shenzhen, 518107, People’s Republic of China

    Guang Yang, Lerong Zhang, Shi Yu, Shichang Meng, Qisheng Wang & Qingjun Li

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  1. Guang Yang
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Correspondence to Qingjun Li.

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National Natural Science Foundation of China, 12202508, Qingjun Li, 12232015, Qingjun Li, Young Elite Scientists Sponsorship Program by China Association for Science and Technology, 2021QNRC001, Qingjun Li, Fundamental Research Funds for the Central Universities, Sun Yat-sen University, No. 22qntd0703, Qingjun Li.

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Appendix

Appendix

The quasi-static vibration of Beam KI \(v_{{{\text{KI}}}}\) is obtained by integrating Eq. (24) with the boundary conditions in Eq. (25)

$$ \begin{gathered} v_{{{\text{KI}}}} = - \frac{3}{2}\frac{\rho A}{{EI}}\omega_{0}^{2} \left( {\frac{1}{120}x_{{{\text{KQ}}}}^{5} - \frac{{L_{{{\text{KI}}}}^{2} }}{12}x_{{{\text{KQ}}}}^{3} + \frac{{L_{{{\text{KI}}}}^{3} }}{6}x_{{{\text{KQ}}}}^{2} } \right)\sin \left( {2\alpha } \right) \\ - \frac{3}{2}\frac{\rho A}{{EI}}\omega_{0}^{2} \left( {\frac{1}{24}x_{{{\text{KQ}}}}^{4} - \frac{{L_{{{\text{KI}}}} }}{6}x_{{{\text{KQ}}}}^{3} + \frac{{L_{{{\text{KI}}}}^{2} }}{4}x_{{{\text{KQ}}}}^{2} } \right)\left( {x_{{{\text{SP}}}} + x_{{{\text{PK}}}} } \right)\sin \left( {2\alpha } \right) \\ - 2\frac{\rho A}{{EI}}\omega_{0} \dot{x}_{{{\text{PK}}}} \left( {\frac{1}{24}x_{{{\text{KQ}}}}^{4} - \frac{{L_{{{\text{KI}}}} }}{6}x_{{{\text{KQ}}}}^{3} + \frac{{L_{{{\text{KI}}}}^{2} }}{4}x_{{{\text{KQ}}}}^{2} } \right) \\ \end{gathered} $$
(A1)

Similarly, the quasi-static vibration of Beam MN \(v_{{{\text{MN}}}}\) is

$$ \begin{gathered} v_{{{\text{MN}}}} = - \frac{3}{2}\frac{\rho A}{{EI}}\omega_{0}^{2} \left( {\frac{1}{120}x_{{{\text{QM}}}}^{5} - \frac{{L_{{{\text{MN}}}}^{2} }}{12}x_{{{\text{QM}}}}^{3} + \frac{{L_{{{\text{MN}}}}^{3} }}{6}x_{{{\text{QM}}}}^{2} } \right)\sin \left( {2\alpha } \right) \\ - \frac{3}{2}\frac{\rho A}{{EI}}\omega_{0}^{2} \left( {\frac{1}{24}x_{{{\text{QM}}}}^{4} - \frac{{L_{{{\text{MN}}}} }}{6}x_{{{\text{QM}}}}^{3} + \frac{{L_{{{\text{MN}}}}^{2} }}{4}x_{{{\text{QM}}}}^{2} } \right)\left( {x_{{{\text{PS}}}} + x_{{{\text{MP}}}} } \right)\sin \left( {2\alpha } \right) \\ - 2\frac{\rho A}{{EI}}\omega_{0} \dot{x}_{{{\text{MP}}}} \left( {\frac{1}{24}x_{{{\text{QM}}}}^{4} - \frac{{L_{{{\text{MN}}}} }}{6}x_{{{\text{QM}}}}^{3} + \frac{{L_{{{\text{MN}}}}^{2} }}{4}x_{{{\text{QM}}}}^{2} } \right) \\ \end{gathered} $$
(A2)

The results of Eqs. (28)–(33) are

$$ M_{{{\text{KI}}}} = - L_{{{\text{KI}}}}^{2} \rho A\omega_{0} {\kern 1pt} \left[ {\dot{x}_{{{\text{PK}}}} + \frac{1}{2}L_{{{\text{KI}}}} \omega_{0} \sin \left( {2{\kern 1pt} \alpha } \right) + \frac{{3{\kern 1pt} }}{4}\omega_{0} \left( {x_{{{\text{SP}}}} + x_{{{\text{PK}}}} } \right)\sin \left( {2{\kern 1pt} \alpha } \right)} \right] $$
(A3)
$$ F_{{x,{\text{KI}}}} = \frac{{\rho AL_{{{\text{KI}}}} }}{2}\left[ {3{\kern 1pt} L_{{{\text{KI}}}} \omega_{0}^{2} \cos^{2} \left( \alpha \right) + 6{\kern 1pt} \omega_{0}^{2} \left( {x_{{{\text{SP}}}} + x_{{{\text{PK}}}} } \right)\cos^{2} \left( \alpha \right) - 2{\kern 1pt} \ddot{x}_{{{\text{PK}}}} } \right] $$
(A4)
$$ F_{{y,{\text{KI}}}} = - \frac{{\rho AL_{{{\text{KI}}}} \omega_{0} }}{4}\left[ {8\dot{x}_{{{\text{PK}}}} + 3{\kern 1pt} L_{{{\text{KI}}}} \omega_{0} \sin \left( {2{\kern 1pt} \alpha } \right) + 6\omega_{0} \left( {x_{{{\text{SP}}}} + x_{{{\text{PK}}}} } \right)\sin \left( {2{\kern 1pt} \alpha } \right)} \right] $$
(A5)
$$ M_{{{\text{MN}}}} = - L_{{{\text{MN}}}}^{2} \rho A\omega_{0} {\kern 1pt} \left[ {\dot{x}_{{{\text{MP}}}} + \frac{1}{2}L_{{{\text{MN}}}} \omega_{0} \sin \left( {2{\kern 1pt} \alpha } \right) + \frac{{3{\kern 1pt} }}{4}\omega_{0} \left( {x_{{{\text{MP}}}} + x_{{{\text{PS}}}} } \right)\sin \left( {2{\kern 1pt} \alpha } \right)} \right] $$
(A6)
$$ F_{{x{\text{,MN}}}} = \frac{{\rho AL_{{{\text{MN}}}} }}{2}\left[ {3{\kern 1pt} L_{{{\text{MN}}}} \omega_{0}^{2} \cos^{2} \left( \alpha \right) + 6{\kern 1pt} \omega_{0}^{2} \left( {x_{{{\text{MP}}}} + x_{{{\text{PS}}}} } \right)\cos^{2} \left( \alpha \right) - 2{\kern 1pt} \ddot{x}_{{{\text{MP}}}} } \right] $$
(A7)
$$ F_{{y{\text{,MN}}}} = - \frac{{\rho AL_{{{\text{MN}}}} \omega_{0} }}{4}\left[ {8\dot{x}_{{{\text{MP}}}} + 3{\kern 1pt} L_{{{\text{MN}}}} \omega_{0} \sin \left( {2{\kern 1pt} \alpha } \right) + 6\omega_{0} \left( {x_{{{\text{MP}}}} + x_{{{\text{PS}}}} } \right)\sin \left( {2{\kern 1pt} \alpha } \right)} \right] $$
(A8)

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Yang, G., Zhang, L., Yu, S. et al. Influences of space perturbations on robotic assembly process of ultra-large structures. Nonlinear Dyn 111, 10025–10048 (2023). https://doi.org/10.1007/s11071-023-08395-w

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