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

\[\begin{split}X_r = Rx \frac{\pi}{180} \text{,} \\ Y_r = Ry \frac{\pi}{180} \text{,} \\ Z_r = Rz \frac{\pi}{180} \text{,} \\\end{split}\]

and then calculating the quaternion with

\[\begin{split}x = \cos{(Z_r/2)}\cos{(Y_r/2)}\sin{(X_r/2)} - \sin{(Z_r/2)}\sin{(Y_r/2)}\cos{(X_r/2)} \text{,} \\ y = \cos{(Z_r/2)}\sin{(Y_r/2)}\cos{(X_r/2)} + \sin{(Z_r/2)}\cos{(Y_r/2)}\sin{(X_r/2)} \text{,} \\ z = \sin{(Z_r/2)}\cos{(Y_r/2)}\cos{(X_r/2)} - \cos{(Z_r/2)}\sin{(Y_r/2)}\sin{(X_r/2)} \text{,} \\ w = \cos{(Z_r/2)}\cos{(Y_r/2)}\cos{(X_r/2)} + \sin{(Z_r/2)}\sin{(Y_r/2)}\sin{(X_r/2)} \text{.}\end{split}\]

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.

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