Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame

Year 2018, , 1787 - 1792, 01.12.2018

Vahide Bulut

https://doi.org/10.16984/saufenbilder.400272

Abstract

Controlling the relative motion between two contacting
rigid bodies is necessary when manipulation and locomotion tasks are
encountered in robotics. In this paper, we express the kinematics of
spin-rolling motion of rigid objects with point contact based on the
local-surface frame method. We give the relationship between the Darboux frame
and local-surface frame, and also between the Frenet-Serret frame and local-surface
frame. Additionally, we obtain velocity of the moving object according to the
local-surface frame curvatures of the respective contact curve and geometric
invariants. We can have proper information about trajectory planning if we take
the formulations of moving object into consideration according to the
local-surface frame.

Keywords

Frenet-Serret frame, Darboux frame, Local-Surface frame, kinematics, point contact

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