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

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 localsurface 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 localsurface frame.

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