Many mobile robots that use spherical locomotion employ friction-drive systems because such systems offer omnidirectional locomotion and are more capable of climbing steps than omni-wheel systems. One notable issue associated with friction-drive systems is slipping between the sphere and the roller. However, previously established sphere kinematics models do not consider slipping. This study proposes a mathematical model that allows for slipping and can be broadly applied to a variety of mobile robots in a range of situations.

Many types of spherical robots use friction-drive systems for locomotion because such systems enable omnidirectional movement and are more capable of climbing steps than mobile robots equipped with multiple omni-wheels. Slipping between spheres and rollers is a remarkable issue with friction-driven mechanisms. However, the previously established sphere kinematic models do not consider slipping, and kinematic models consider slipping in only two constraint rollers. In this study, we propose a mathematical model that allows for slipping on three constraint rollers and simulate the angular velocity vector of the sphere and slip speed at each contact point.

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