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

被引：0

作者：

Tafrishi, Seyed Amir ^{[1
]}

Svinin, Mikhail ^{[3
]}

Yamamoto, Motoji ^{[2
]}

机构：

[1] Department of Robotics, Tohoku University, Sendai,Miyagi, Japan

[2] Department of Mechanical Engineering, Kyushu University, Kyushu, Japan

[3] Department of Information Science and Engineering, Ritsumeikan University, Kyoto, Japan

来源：

Mechanism and Machine Theory | 2021年 / 164卷

基金：

日本科学技术振兴机构; 日本学术振兴会;

关键词：

Kinematics - Mathematical transformations - Motion planning;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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. © 2021 Elsevier Ltd

引用