I have a sensor with 6 degree of freedom 3 axiz x,y,z and 3 angles yaw, pitch and roll. 3 axis distance is simple using distance formula but how to calculate 3 angular distances? Can anyone here please help me ???
+2
A:
Yaw, pitch, and roll represent a set of Euler angles that specify a rotation from one coordinate system, XYZ, into another, X'Y'Z' . This transformation can also be expressed as a single rotation about an arbitrary axis. If I understand your question correctly, you want to know what this single rotation angle is.
It is possible to convert a set of Euler angles into a four-element structure called a quaternion.
q4 = cos(yaw/2) cos(pitch/2) cos(roll/2) + sin(yaw/2) sin(pitch/2) sin(roll/2)
q1 = cos(yaw/2) cos(pitch/2) sin(roll/2) - sin(yaw/2) sin(pitch/2) cos(roll/2)
q2 = cos(yaw/2) sin(pitch/2) cos(roll/2) + sin(yaw/2) cos(pitch/2) sin(roll/2)
q3 = sin(yaw/2) cos(pitch/2) cos(roll/2) - cos(yaw/2) sin(pitch/2) sin(roll/2)
(Source: http://www.resonancepub.com/quaterni.htm)
Once you have the quaternion, the rotation axis and rotation angle are easily calculated from the quaternion components. Using the above author's notation,
q = [q4 q1 q2 q2]
q4 = cos(theta/2)
q1 = sin(theta/2)A
q2 = sin(theta/2)B
q3 = sin(theta/2)C
where [A B C] is a vector in the XYZ system specifying the rotation axis, and theta is the rotation angle you're looking for.
So theta = 2*acos(q4)
Jim Lewis
2009-08-10 06:25:33