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Controllabilty of a two-body crawling system on an inclined plane

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Abstract

A simple two-body model of a limbless crawler moving on an inclined rough plane is considered. The bodies are regarded as point masses. The system is controlled by the force of interaction of the bodies. Coulomb’s friction force acts between the underlying plane and each of the bodies. The controllability of the crawler is investigated. It is proved that if no constraints are imposed on the control force, then the system can be driven from any initial state of rest on the plane into an arbitrarily small neighborhood of any prescribed terminal state of rest, provided that at the initial time instant the bodies do not lie on the common line of maximum slope. A control strategy that alternates infinitely slow (quasistatic) and infinitely fast motions is defined. It is important that the plane is inclined; on the horizontal plane, the two-body crawler is uncontrollable.

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The manuscript has no associated data.

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Funding

This study was partially supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the Russian State Assignment under contract No. AAAA-A20-120011690138-6 and partially supported by Russian Foundation for Basic Research (Grant No. 20-01-00378).

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Vernadsky ave, Moscow, Russia, 119526

    Nikolay Bolotnik & Tatiana Figurina

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  1. Nikolay Bolotnik
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  2. Tatiana Figurina
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Correspondence to Nikolay Bolotnik.

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Bolotnik, N., Figurina, T. Controllabilty of a two-body crawling system on an inclined plane. Meccanica 58, 321–336 (2023). https://doi.org/10.1007/s11012-021-01466-5

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  • DOI: https://doi.org/10.1007/s11012-021-01466-5

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