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Constraint implementation in wheeled apparatus rolling problems

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Abstract

The models obtained from equations of rolling of an apparatus with small slips of wheels with respect to the supporting plane are considered by passing to the limit of infinite values of rigidity of contact forces (zero values of slip speeds). The conditions under which these equations become the classical nonholonomic wheel no-slip model are discussed. It is shown that, for small angles of turn of the apparatus front wheels about the vertical axis, neglect of slips in the transverse direction is not correct; namely, the limit model is determined by the wheel no-slip conditions in the longitudinal direction and by the primary Dirac constraints arising owing to the degeneration of the Lagrangian of the system. The methods used to decrease the order of equations, where small slips of wheels are taken into account, can be useful for qualitative analysis of motion of wheeled systems and for solving the problems of estimation and control in real time.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    A. V. Vlakhova

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  1. A. V. Vlakhova
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Correspondence to A. V. Vlakhova.

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Original Russian Text © A.V. Vlakhova, 2013, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2013, No. 3, pp. 22–39.

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Vlakhova, A.V. Constraint implementation in wheeled apparatus rolling problems. Mech. Solids 48, 254–269 (2013). https://doi.org/10.3103/S0025654413030035

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