Theoretical study demonstrates linear formulation of 3D rotational motion in physical systems, highlighting exact representations for robotics and computer vision without singularities.
Rotation motion in a three-dimensional physical world refers to an angular displacement of an object around a specific axis in R³. It is typically formulated as a non-linear and non-convex process due to the nonlinearity and nonconvexity of SO(3). However, this paper proposes a new perspective that the 3D rotation motion can be expressed by the linear equation without dropping any constraints and increasing any singularities. Moreover, two frequent cases, i.e., ∠(Rx,y)=0(π) and ∠(Rx,y)=π/2, in computer vision and robotics that can be expressed linearly are deeply discussed in this paper.
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Yinlong Liu (2024) studied this question.
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