pytransform3d.rotations.quaternion_gradient

pytransform3d.rotations.quaternion_gradient(Q, dt=1.0)

Time-derivatives of a sequence of quaternions.

Note that this function does not provide the exact same functionality for quaternions as NumPy’s gradient function for positions. Gradients are always computed as central differences except the first and last gradient. We additionally accept a parameter dt that defines the time interval between each quaternion. Note that this means that we expect this to be constant for the whole sequence.

Parameters:

Qarray-like, shape (n_steps, 4)

Quaternions to represent rotations: (w, x, y, z)

dtfloat, optional (default: 1)

Time interval between steps. If you have non-constant dt, you can pass 1 and manually divide angular velocities by their corresponding time interval afterwards.

Returns:

Aarray-like, shape (n_steps, 3)

Angular velocities in a compact axis-angle representation. Each angular velocity represents the rotational offset after one unit of time. Angular velocities are given in global frame and will be left-multiplied during integration to the initial or previous orientation respectively.