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Autonomous assembly of multiple flexible spacecraft using RRT* algorithm and input shaping technique

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Abstract

The on-orbit assembly is an appealing method to build large space structures. To improve the assembly efficiency, each module trends towards a flexible one. How to account for the nonlinear rigid-flexible dynamics is still an open problem during the assembly mission. This paper presents the dynamics modeling, path planning and controller design for the autonomous assembly of multiple flexible spacecraft. Both the one-by-one and simultaneous assembly scenarios are considered. The assumed modes method is adopted to describe the nonlinear dynamic behaviors of the spacecraft equipped with six flexible appendages. The input shaping technique is used to shape the trajectory planned by the RRT* algorithm to reduce the vibrations of flexible appendages caused by the trajectory tracking for each spacecraft. To avoid collisions among the spacecraft in the team and obstacles, a PD controller together with collision avoidance forces is proposed to drive the spacecraft to track their desired trajectories. Finally, some numerical results are presented to show the effectiveness of the developed path planning algorithm and controller design method. The main major finding of this paper is that the introduction of input shaping technique can reduce the vibration caused by the collision-free trajectory from the RRT* algorithm in assembly mission.

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Data Availability Statement

The datasets generated during and/or analyzed during the current study are proprietary and thus not publicly available, but any data appearing in the present work are available from the author upon reasonable request.

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Acknowledgements

The author owes a profound debt of gratitude to the editor and the reviewers for their insightful comments and constructive feedback throughout the development of this paper.

Funding

This work was supported by the National Natural Science Foundation of China under Grants No. 12102174 and 11832005, the Science and Technology on Space Intelligent Control Laboratory (Grant No. 2021-JCJQ-LB-010-17), the Fundamental Research Funds for the Central Universities (No. NP2022301), and the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and astronautics) (Grant No. MCMS-I-0122K01).

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  1. State Key Laboratory of Mechanics and Control of Aerospace Structures, Nanjing University of Aeronautics and Astronautics, 29 Yudao St., Nanjing, 210016, Jiangsu, People’s Republic of China

    Ti Chen, Yankai Wang, Hao Wen & Junjie Kang

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  1. Ti Chen
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Correspondence to Ti Chen.

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Appendices

Appendix

A Detailed Expressions of M\(_2\)

The nonzero elements of \(\varvec{M}_2 \in {\mathbb {R}}^{6\times 24}\) are as follows:

\(\varvec{M}_{2,(1,9)} = c_1\), \(\varvec{M}_{2,(1,10)} = c_2\), \(\varvec{M}_{2,(1,13)} = -c_1\), \(\varvec{M}_{2,(1,14)} = -c_2\), \(\varvec{M}_{2,(1,17)} = c_1\), \(\varvec{M}_{2,(1,18)} = c_2\), \(\varvec{M}_{2,(1,21)} = -c_1\), \(\varvec{M}_{2,(1,22)} = -c_2\), \(\varvec{M}_{2,(2,1)} = c_1\), \(\varvec{M}_{2,(2,2)} = c_2\), \(\varvec{M}_{2,(2,5)} = -c_1\), \(\varvec{M}_{2,(2,6)} = -c_2\), \(\varvec{M}_{2,(2,19)} = c_1\), \(\varvec{M}_{2,(2,20)} = c_2\), \(\varvec{M}_{2,(2,23)} = -c_1\), \(\varvec{M}_{2,(2,24)} = -c_2\), \(\varvec{M}_{2,(3,3)} = c_1\), \(\varvec{M}_{2,(3,4)} = c_2\), \(\varvec{M}_{2,(3,7)} = -c_1\), \(\varvec{M}_{2,(3,8)} =- c_2\), \(\varvec{M}_{2,(3,11)} = c_1\), \(\varvec{M}_{2,(3,12)} = c_2\), \(\varvec{M}_{2,(3,15)} = -c_1\), \(\varvec{M}_{2,(3,16)} =- c_2\), \(\varvec{M}_{2,(4,11)} = c_3\), \(\varvec{M}_{2,(4,12)} = c_4\), \(\varvec{M}_{2,(4,15)} = c_3\), \(\varvec{M}_{2,(4,16)} = c_4\), \(\varvec{M}_{2,(4,19)} = -c_3\), \(\varvec{M}_{2,(4,20)} = -c_4\), \(\varvec{M}_{2,(4,23)} = -c_3\), \(\varvec{M}_{2,(4,24)} = -c_4\), \(\varvec{M}_{2,(5,3)} = -c_3\), \(\varvec{M}_{2,(5,4)} = -c_4\), \(\varvec{M}_{2,(5,7)} = -c_3\), \(\varvec{M}_{2,(5,8)} = -c_4\), \(\varvec{M}_{2,(5,17)} = c_3\), \(\varvec{M}_{2,(5,18)} = c_4\), \(\varvec{M}_{2,(5,21)} = c_3\), \(\varvec{M}_{2,(5,22)} = c_4\), \(\varvec{M}_{2,(6,1)} = c_3\), \(\varvec{M}_{2,(6,2)} = c_4\), \(\varvec{M}_{2,(6,5)} = c_3\), \(\varvec{M}_{2,(6,6)} = c_4\), \(\varvec{M}_{2,(6,9)} = -c_3\), \(\varvec{M}_{2,(6,10)} = -c_4\), \(\varvec{M}_{2,(6,13)} = -c_3\), \(\varvec{M}_{2,(6,14)} = -c_4\), where \( c_1 = \rho \int _{0}^{l} \varPhi _1(x) dx\), \( c_2 = \rho \int _{0}^{l} \varPhi _1(x) dx\), \(c_3 = \rho r \int _{0}^{l} \varPhi _1(x) dx+ \rho \int _{0}^{l} x \varPhi _1(x) dx\) and \(c_4 = \rho r \int _{0}^{l} \varPhi _2(x) dx+ \rho \int _{0}^{l} x \varPhi _2(x) dx\).

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Chen, T., Wang, Y., Wen, H. et al. Autonomous assembly of multiple flexible spacecraft using RRT* algorithm and input shaping technique. Nonlinear Dyn 111, 11223–11241 (2023). https://doi.org/10.1007/s11071-023-08445-3

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