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 Svinin,
Motoji Yamamoto
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 system as a spin-rolling sphere on a plane with three inputs and five states can be transformed into a fully-actuated model by the given Darboux-frame transformation. This nonlinear state transformation is a geometric model that is different from conventional state-space models. First, a kinematic model of the Darboux frame at the contact point of a rotating object i… Show more
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