Yaskawa Pose Format¶

The pose format that is used by Yaskawa robots consists of a position $XYZ$ in millimeters and an orientation that is given by three angles in degrees, with $Rx$ rotating around $x$ -axis, $Ry$ rotating around $y$ -axis and $Rz$ rotating around $z$ -axis. The rotation order is $x$ - $y$ - $z$ and computed by $r_z(Rz) r_y(Ry) r_x(Rx)$ .

Conversion from Yaskawa Rx, Ry, Rz to quaternion¶

The conversion from the $Rx, Ry, Rz$ angles in degrees to a quaternion $q=(\begin{array}{cccc}x & y & z & w\end{array})$ can be done by first converting all angles to radians

$X_r = Rx \frac{\pi}{180} \text{,} \\ Y_r = Ry \frac{\pi}{180} \text{,} \\ Z_r = Rz \frac{\pi}{180} \text{,} \\$

and then calculating the quaternion with

$x = \cos{(Z_r/2)}\cos{(Y_r/2)}\sin{(X_r/2)} - \sin{(Z_r/2)}\sin{(Y_r/2)}\cos{(X_r/2)} \text{,} \\ y = \cos{(Z_r/2)}\sin{(Y_r/2)}\cos{(X_r/2)} + \sin{(Z_r/2)}\cos{(Y_r/2)}\sin{(X_r/2)} \text{,} \\ z = \sin{(Z_r/2)}\cos{(Y_r/2)}\cos{(X_r/2)} - \cos{(Z_r/2)}\sin{(Y_r/2)}\sin{(X_r/2)} \text{,} \\ w = \cos{(Z_r/2)}\cos{(Y_r/2)}\cos{(X_r/2)} + \sin{(Z_r/2)}\sin{(Y_r/2)}\sin{(X_r/2)} \text{.}$

Conversion from quaternion to Yaskawa Rx, Ry, Rz¶

The conversion from a quaternion $q=(\begin{array}{cccc}x & y & z & w\end{array})$ with $||q||=1$ to the $Rx, Ry, Rz$ angles in degrees can be done as follows.

$Rx &= \text{atan}_2{(2(wx + yz), 1 - 2(x^2 + y^2))} \frac{180}{\pi} \\ Ry &= \text{asin}{(2(wy - zx))} \frac{180}{\pi} \\ Rz &= \text{atan}_2{(2(wz + xy), 1 - 2(y^2 + z^2))} \frac{180}{\pi}$