Darboux-frame-based parametrization for a spin-rolling sphere on a plane: A nonlinear transformation of underactuated system to fully-actuated model

Tafrishi, Seyed Amir ORCID: https://orcid.org/0000-0001-9829-3144, Svinin, Mikhail and Yamamoto, Motoji 2021. Darboux-frame-based parametrization for a spin-rolling sphere on a plane: A nonlinear transformation of underactuated system to fully-actuated model. Mechanism and Machine Theory 164 , 104415. 10.1016/j.mechmachtheory.2021.104415

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Abstract

This paper presents a new kinematic model based on the Darboux frame for motion control and planning. In this work, we show that an underactuated model of a spin-rolling sphere on a plane with five states and three inputs can be transformed into a fully-actuated one by a given Darboux frame transformation. This nonlinear state transformation establishes a geometric model that is different from conventional state-space ones. First, a kinematic model of the Darboux frame at the contact point of the rolling sphere is established. Next, we propose a virtual surface that is trapped between the sphere and the contact plane. This virtual surface is used for generating arc-length-based inputs for controlling the contact trajectories on the sphere and the plane. Finally, we discuss the controllability of this new model. In the future, we will design a geometric path planning method for the proposed kinematic model.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Publisher:	Elsevier
ISSN:	0094-114X
Date of Acceptance:	31 May 2021
Last Modified:	24 Jan 2023 02:08
URI:	https://orca.cardiff.ac.uk/id/eprint/155877

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