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Modeling of spherical robots rolling on generic surfaces

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Abstract

In this paper, the motion of a spherical robot rolling on a generic surface is considered. The motion equations are derived in matrix form using a Lagrangian approach, and quaternions are used to parametrize attitude. Focus is placed on a general formulation of the problem that facilitates the integration of the holonomic and nonholonomic constraints into the motion equations in a straightforward manner. The motion equations capture the nonholonomic nature of rolling without slipping, the contact requirement between the spherical rover and the generic surface, an additional constraint associated with an energy-harvesting pendulum, and the quaternion unit-length constraints. Numerical simulations involving Martian tumbleweed rovers are performed on complex three-dimensional surfaces resembling Martian craters and wave fields.

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Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, Montreal, Canada

    François Robert Hogan

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, USA

    James Richard Forbes

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  1. François Robert Hogan
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  2. James Richard Forbes
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Correspondence to François Robert Hogan.

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Hogan, F.R., Forbes, J.R. Modeling of spherical robots rolling on generic surfaces. Multibody Syst Dyn 35, 91–109 (2015). https://doi.org/10.1007/s11044-014-9438-3

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  • DOI: https://doi.org/10.1007/s11044-014-9438-3

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