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I am training a reinforcement learning network in simulation for a robot which at the current stage learns Euler Angles to rotate the end-effector based on the actual state. The performance is overall not that satisfying. My network architecture is rather small and contains only two hidden layers. So, I would like to know what type of rotations can best be learned by neural networks? Euler Angles, Rotation matrices or Quaternions?

If someone could recommend a publication or paper for this topic, I would be very interested. Thank you for your help!

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Every three-dimensional parameterization of rotations has singularity. So even if you would implement the kinematics directly you would still run into trouble for some rotations when using Euler angles (or any other three-dimensional parameterization).

Quaternions, or more accurately unit quaternions, do not have such singularities. Though, do not have a unique parameterization (negating the quaternion would represent the same rotation). However, if you only consider the kinematics then unit quaternions already don't pose any issue in my opinion. So using a three by three rotation matrix would not really simplify the kinematics at the cost of higher over-parameterization. Additionally, unit quaternions are also easier than rotation matrices to "normalize", so ensuring that a four dimensional vector represents a unit quaternion vs that a three by three matrix represents a rotation matrix.

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The main problem is the continuity of the representation. This paper explains it.

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