Novel Mathematical Modeling and Motion Analysis of a Sphere Considering Slipping

Abstract

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.

Evaluation of the Roller Arrangements for the Ball-Dribbling Mechanisms Adopted by RoboCup Teams

“…As shown in Table 2, ||V||, j and r are values calculated from n 1 , n 2 = −0.91 (m/s) by Equations (11) and 14refer to Kimura et al [17]. 14refer to Kimura et al [17].…”

“…As shown in Table 2, ||V||, j and r are values calculated from n 1 , n 2 = −0.91 (m/s) by Equations (11) and 14refer to Kimura et al [17]. 14refer to Kimura et al [17]. ||V|| e , j e and r e are experimental values measured from In the evaluation case of a = 0°, n 1 e and n 2 e are close to n 1 m and n 2 m , respectively (see Figure 4).…”

“…In Section 2, we introduce a sphere kinematics model that allows for slipping. In Section 3, we validated the model introduced in Kimura et al [17] and theoretical formula of sphere slip velocity vector. In Section 4, we considered the distribution of slip velocity vector and the roller arrangement of a ball dribbling mechanism based on the results of a robotic experiment.…”

“…Other teams, namely the Turtles [10], Falcons, Musashi150 [15], NuBot [16], and Water, have adopted roller arrangements that allow for slip to occur (see Figure 1b) through a differential between roller and ball velocity. Based on analysis of sphere rotational motion in which slip is allowed, we developed a sphere kinematics model in which dual-constraint rollers allow for slipping [17].…”

“…In this study, we validated the model introduced in Kimura et al [17] and evaluated the roller arrangements used by the competition teams from the standpoint of sphere speed, efficiency, and sphere slip speed (ball-holding power). The remainder of this paper is organized as follows.…”