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Quaternions are the angular part of a non-moving pose. Angular velocity is a measurement of how fast an object is rotating about a certain point.

If you're looking for prediction, I suggest using forward Euler.

theta_t = theta_t-1 + omega_theta * dtheta/dt

Where theta is an angle and omega is the angular velocity.

You'll likely want to convert between quaternion and euler notation, in which ros has the following functions

import tf
quat = tf.transformations.quaternion_from_euler(roll, pitch, yaw)
(roll, pitch, yaw) = tf.transformations.euler_from_quaternion(quat)