Although the kinematics and dynamics of spherical robots (SRs) on flat horizontal and inclined 2D surfaces are thoroughly\ninvestigated, their rolling behavior on generic 3D terrains has remained unexplored. This paper derives the kinematics equations\nof the most common SR configurations rolling over 3D surfaces. First, the kinematics equations for a geometrical sphere rolling\nover a 3D surface are derived along with the characterization of the modeling method. Next, a brief review of current mechanical\nconfigurations of SRs is presented as well as a novel classification for SRs based on their kinematics. Then, considering the\nmechanical constraints of each category, the kinematics equations for each group of SRs are derived. Afterward, a path-tracking\nmethod is utilized for a desired 3D trajectory. Finally, simulations are carried out to validate the developed models and the\neffectiveness of the proposed control scheme.
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