Forward Kinematic of a Sphere Considering Slipping and Motion Analysis in Three Rollers

Abstract

Compared to mobile robots equipped with multiple rollers, spherical robots can move in all directions and are superior in durability and in their ability to climb steps. Slippage between balls and rollers is a significant problem in friction drives. However, previously established roller-driven ball kinematics model considers sliding on only two constraining rollers. In this research, we developed it, proposed a motion model of sphere with three-constraint rollers, and developed a mathematical model that simulates the angular velocity vector of the sphere and the slip vector at each contact point. And we considered the existence of an angular velocity vector of sphere adapted three constraint rollers from the viewpoint of forward kinematics and succeed demonstration of the trajectory of the endpoint of the angular velocity vector and slip velocity vector of sphere.