 Euler Angles

The Euler angles are three angles that describe the orientation of a rigid body. There are twelve different conventions when talking about Euler angles. They can be grouped into Proper Euler angles, and Tait-Bryan angles where the latter represents rotations about three distinct axes. In CoppeliaSim, we use Tait-Bryan angles alpha, beta and gamma (or (a,b,g)) describing a rotation composed by three elemental rotations: [Euler angles convention in CoppeliaSim]

where Rz, Ry and Rx represent elemental rotations about axes Z, Y and X respectively (in that order), of the absolute reference frame.

For a rigid body, or scene object, you can obtain the same transformation if you rotate it in following order about its own reference frame: rotation of alpha about own x, followed by a rotation of beta about own y, followed by a rotation of gamma about own z.

Yaw-Pitch-Roll are also Tait-Bryan angles describing a rotation composed by three elemental rotations: [Yaw-Pitch-Roll rotations]

where Rx, Ry and Rz represent elemental rotations about axes X, Y and Z respectively (in that order), of the absolute reference frame.

To convert between alpha-beta-gamma angles and yaw-pitch-roll angles, you can use sim.yawPitchRollToAlphaBetaGamma or sim.alphaBetaGammaToYawPitchRoll functions.