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

Seyed Amir Tafrishi, Mikhail Mikhailovich Svinin, Motoji Yamamoto

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number104415
JournalMechanism and Machine Theory
Volume164
DOIs
Publication statusPublished - Oct 2021

All Science Journal Classification (ASJC) codes

  • Bioengineering
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications

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