# Pose Rotation Order

In the description of a Pose, it says the last 3 values are “an axis-angle”, but if you look at a Waypoint, it shows a Rotation Vector as RX, RY, RZ. I am used to working with compound Euler angles (Yaw, Pitch, Roll), but haven’t worked with a rotation vector before.

Is there a way to convert between RPY and a Rotation Vector, either through math or a built-in script function, or a way a pose can be defined directly using YPR? I can’t find any examples in the manual or an explanation any further than pointing to a wikipedia page.

You can use the URScript codes `rotvec2rpy(rotation_vector)` and `rpy2rotvec(rpy_vector)` to convert the rotation vectors to RPY and vice versa in URScript.
They are both explained in the script manual.

Below are some example formulas that can be used in URScript before the above functions were implemented (3.3.0.145), other methods might work just as fine.

For conversion from RPY to rotation vector:

``````  def rpy2rv(roll,pitch,yaw):

alpha = yaw
beta = pitch
gamma = roll

ca = cos(alpha)
cb = cos(beta)
cg = cos(gamma)
sa = sin(alpha)
sb = sin(beta)
sg = sin(gamma)

r11 = ca*cb
r12 = ca*sb*sg-sa*cg
r13 = ca*sb*cg+sa*sg
r21 = sa*cb
r22 = sa*sb*sg+ca*cg
r23 = sa*sb*cg-ca*sg
r31 = -sb
r32 = cb*sg
r33 = cb*cg

theta = acos((r11+r22+r33-1)/2)
sth = sin(theta)
kx = (r32-r23)/(2*sth)
ky = (r13-r31)/(2*sth)
kz = (r21-r12)/(2*sth)

rv = theta*kx
rv = theta*ky
rv = theta*kz

return rv

end
``````

For conversion from rotation vector to RPY:

``````  def rv2rpy(rx,ry,rz):

theta = sqrt(rx*rx + ry*ry + rz*rz)
kx = rx/theta
ky = ry/theta
kz = rz/theta
cth = cos(theta)
sth = sin(theta)
vth = 1-cos(theta)

r11 = kx*kx*vth + cth
r12 = kx*ky*vth - kz*sth
r13 = kx*kz*vth + ky*sth
r21 = kx*ky*vth + kz*sth
r22 = ky*ky*vth + cth
r23 = ky*kz*vth - kx*sth
r31 = kx*kz*vth - ky*sth
r32 = ky*kz*vth + kx*sth
r33 = kz*kz*vth + cth

beta = atan2(-r31,sqrt(r11*r11+r21*r21))

if beta > d2r(89.99):
beta = d2r(89.99)
alpha = 0
gamma = atan2(r12,r22)
elif beta < -d2r(89.99):
beta = -d2r(89.99)
alpha = 0
gamma = -atan2(r12,r22)
else:
cb = cos(beta)
alpha = atan2(r21/cb,r11/cb)
gamma = atan2(r32/cb,r33/cb)
end

rpy= gamma
rpy= beta
rpy= alpha

return rpy

end
``````