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arXiv 2102.07923cs.ROmath.DG
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基于Darboux标架的平面自旋-滚动球体的参数化:欠驱动系统到全驱动模型的非线性变换

Darboux-Frame-Based Parametrization for a Spin-Rolling Sphere on a Plane: A Nonlinear Transformation of Underactuated System to Fully-Actuated Model

Tohoku University(东北大学);Ritsumeikan University(立命馆大学);Kyushu University(九州大学)

Seyed Amir Tafrishi, Mikhail Svinin, Motoji Yamamoto

摘要:

本文提出了一种新的运动学模型的基础上的达布框架的运动控制和规划。在这项工作中,我们证明了一个欠驱动模型的自旋滚动球在一个平面上的五个状态和三个输入可以转化为一个完全驱动的一个给定的达布框架变换。这种非线性状态转换建立了一个不同于传统状态空间的几何模型。首先建立了滚动球体接触点处的达布标架运动学模型。接下来,我们提出了一个虚拟的表面,被困在球体和接触平面之间。该虚拟表面用于生成用于控制球体和平面上的接触轨迹的基于弧长的输入。最后,我们讨论了这个新模型的可控性。在未来,我们将设计一个几何路径规划方法所提出的运动学模型。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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