notesum.ai

Published at December 5

eess.IV

cs.RO

Released Date: December 5, 2024

Authors: Joan Badia Torres¹, Eric Carmona, Abhijit Makhal, Omid Heidari, Alba Perez Gracia

Aff.: ¹Polytechnic University of Catalonia, Institute of Robotics and Industrial Informatics, Barcelona, Spain

$t_{\omega_{U}}$
$\epsilon_{2}$	$\omega=0$	$\omega=\frac{\pi}{2}$
$\epsilon_{2}<2$	$\begin{Bmatrix}0\\ 1\\ 0\end{Bmatrix}$	$\begin{Bmatrix}-1\\ 0\\ 0\end{Bmatrix}$
$\epsilon_{2}=2$	$\begin{Bmatrix}\frac{-a_{1}}{\sqrt{a_{1}^{2}+a_{2}^{2}}}\\ \frac{a_{2}}{\sqrt{a_{1}^{2}+a_{2}^{2}}}\\ 0\end{Bmatrix}$	$\begin{Bmatrix}\frac{-a_{1}}{\sqrt{a_{1}^{2}+a_{2}^{2}}}\\ \frac{a_{2}}{\sqrt{a_{1}^{2}+a_{2}^{2}}}\\ 0\end{Bmatrix}$
$\epsilon_{2}>2$	$\begin{Bmatrix}-1\\ 0\\ 0\end{Bmatrix}$	$\begin{Bmatrix}0\\ 1\\ 0\end{Bmatrix}$
$t_{\eta_{U}}$
$\epsilon_{1}$	$\eta=0$	$\eta=\frac{\pi}{2}$
$\epsilon_{1}<2$	$\begin{Bmatrix}0\\ 0\\ 1\end{Bmatrix}$	$\begin{Bmatrix}\frac{-a_{1}\cos^{\epsilon_{2}}{\omega}}{a_{\omega}}\\ \frac{-a_{2}\sin^{\epsilon_{2}}{\omega}}{a_{\omega}}\\ 0\end{Bmatrix}$
$\epsilon_{1}=2$	$\begin{Bmatrix}\frac{-a_{1}\cos^{\epsilon_{2}}{\omega}}{\sqrt{a_{3}^{2}+a_{% \omega}^{2}}}\\ \frac{-a_{2}\sin^{\epsilon_{2}}{\omega}}{\sqrt{a_{3}^{2}+a_{\omega}^{2}}}\\ \frac{a_{3}}{\sqrt{a_{3}^{2}+a_{\omega}^{2}}}\end{Bmatrix}$	$\begin{Bmatrix}\frac{-a_{1}\cos^{\epsilon_{2}}{\omega}}{\sqrt{a_{3}^{2}+a_{% \omega}^{2}}}\\ \frac{-a_{2}\sin^{\epsilon_{2}}{\omega}}{\sqrt{a_{3}^{2}+a_{\omega}^{2}}}\\ \frac{a_{3}}{\sqrt{a_{3}^{2}+a_{\omega}^{2}}}\end{Bmatrix}$
$\epsilon_{1}>2$	$\begin{Bmatrix}\frac{-a_{1}\cos^{\epsilon_{2}}{\omega}}{a_{\omega}}\\ \frac{-a_{2}\sin^{\epsilon_{2}}{\omega}}{a_{\omega}}\\ 0\end{Bmatrix}$	$\begin{Bmatrix}0\\ 0\\ 1\end{Bmatrix}$