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Although the kinematics and dynamics of spherical robots (SRs) on flathorizontal and inclined 2D surfaces are thoroughly investigated, their rollingbehavior on generic 3D terrains has remained unexplored. This paper derives thekinematics equations of the most common SRs configurations rolling over 3Dsurfaces. First, the kinematics equations for a geometrical sphere rolling overa 3D surface are derived along with the characterization of the modelingmethod. Next, a brief review of current SR mechanical configurations ispresented as well as a novel classification for spherical robots based on theirkinematics. Then, considering the mechanical constraints of each category, thekinematics equations for each group of spherical robots are presented.Afterwards, a path tracking method is utilized for a desired 3D trajectory.Finally, simulations are carried out to validate the developed models and theeffectiveness of the proposed control scheme.

Kinematics of Spherical Robots Rolling Over 3D Terrains