FANUC XYZ-WPR format¶

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

Conversion from FANUC-WPR to quaternion¶

The conversion from the $WPR$ 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

$W_r = W \frac{\pi}{180} \text{,} \\ P_r = P \frac{\pi}{180} \text{,} \\ R_r = R \frac{\pi}{180} \text{,} \\$

and then calculating the quaternion with

$x = \cos{(R_r/2)}\cos{(P_r/2)}\sin{(W_r/2)} - \sin{(R_r/2)}\sin{(P_r/2)}\cos{(W_r/2)} \text{,} \\ y = \cos{(R_r/2)}\sin{(P_r/2)}\cos{(W_r/2)} + \sin{(R_r/2)}\cos{(P_r/2)}\sin{(W_r/2)} \text{,} \\ z = \sin{(R_r/2)}\cos{(P_r/2)}\cos{(W_r/2)} - \cos{(R_r/2)}\sin{(P_r/2)}\sin{(W_r/2)} \text{,} \\ w = \cos{(R_r/2)}\cos{(P_r/2)}\cos{(W_r/2)} + \sin{(R_r/2)}\sin{(P_r/2)}\sin{(W_r/2)} \text{.}$

Conversion from quaternion to FANUC-WPR¶

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

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