Kinematic Comparison of Exponential and Cayley Maps in the Planar Motion Group

Year 2020, Volume: 13 Issue: 1, 107 - 115, 30.01.2020

İlhan Karakılıç Soner Erkuş

https://doi.org/10.36890/iejg.699429

Abstract

In this work, the exponential and the Cayley maps, from the Lie algebra $\mathfrak{se(2)}$ of the planar motion group $SE(2)$, to the group itself are studied. The comparison between these maps on $SE(2)$ is given by using the Rodrigues vector. A three joint mechanism is discussed as an application.

Keywords

Kinematics, Lie Group, planar motion group, exponential map, Cayley map, Rodrigues vector

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