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Local Geometric Control of a Certain Mechanism with the Growth Vector (4,7)

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Abstract

We study local control of a mechanism with the growth vector (4,7). We study controllability and extremal trajectories of the nilpotent approximation as an example of the control theory on a Lie group. We provide solutions to the system and show examples of local extremal trajectories.

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Acknowledgments

Access to computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum provided under the program “Projects of Large Research, Development, and Innovations Infrastructures” (CESNET LM2015042) is greatly appreciated.

The algebraic computations are partially calculated in CAS Maple package DifferentialGeometry [3].

We would like to thank Sebastiano Nicolussi Golo and Wojciech Kryński for helpful discussions and Pawel Nurowski for initial motivation. We thank the anonymous reviewers whose comments have greatly improved this manuscript.

Funding

The first author is supported by the grant of the Czech Science Foundation no. 17-21360S, “Advances in Snake-like Robot Control,” and by a Grant No. FSI-S-17-4464. The second author is partially supported by the grant of the Czech Science Foundation no. 17-01171S, “Invariant differential operators and their applications in geometric modelling and control theory,” and by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, 616 69, Brno, Czech Republic

    Jaroslav Hrdina

  2. Institute of Mathematics, Faculty of Science, University of South Bohemia, Branišovská 1760, 370 05, České Budějovice, Czech Republic

    Lenka Zalabová

  3. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37, Brno, Czech Republic

    Lenka Zalabová

Authors
  1. Jaroslav Hrdina
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  2. Lenka Zalabová
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Correspondence to Jaroslav Hrdina.

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Hrdina, J., Zalabová, L. Local Geometric Control of a Certain Mechanism with the Growth Vector (4,7). J Dyn Control Syst 26, 199–216 (2020). https://doi.org/10.1007/s10883-019-09460-7

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  • DOI: https://doi.org/10.1007/s10883-019-09460-7

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