Abstract
A coordinate-free formulation of nonholonomic constraint equations for wheeled vehicles is presented. The no-slip condition for the contact point of the wheel with the ground is translated to a pure geometric formula. Based on this general geometric interpretation, explicit formulas for nonholonomic constraints are derived. The final calculations of the constraint equations are realized in Maxima, a computer algebra system. The general no-slip condition formulation is validated via the direct derivation of nonholonomic constraint equations for well-known robotic systems. The presented approach provides a systematic procedure to calculate the nonholonomic constraint equations for wheel components. The final equations are suitable for symbolic calculations and computer aimed modeling of mechanical systems.
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Acknowledgements
This work was supported by the Polish National Science Center (NCN) under the Grant No.: 2011/01/N/ST8/01894.
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Cesar, S.S.P., Jarzȩbowska, E. (2014). Coordinate-Free Formulation of Nonholonomic Constraints for Wheeled Robots. In: Awrejcewicz, J. (eds) Applied Non-Linear Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 93. Springer, Cham. https://doi.org/10.1007/978-3-319-08266-0_33
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DOI: https://doi.org/10.1007/978-3-319-08266-0_33
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