To elaborate: Since a quadrotor can only generate thrust in one direction, any smooth trajectory through space specifies a unique pitch/roll attitude at each moment in time. The attitude at time t is determined by the trajectory's acceleration at time t, along with gravity.
Therefore, angular velocity is determined by jerk - the rate at which this thrust vector is changing.
The angular velocity cannot be changed instantaneously, because the quadrotor can only exert a finite torque about its rotational axes. So we need to design trajectories that do not attempt to change the angular velocity -- and hence, the jerk -- too quickly.
Therefore, we should try to minimize something like the maximum norm of the snap along the trajectory.
In practice we often minimize the integral of the squared norm of the snap, because it can be posed as a convex quadratic optimization problem with respect to the control points of a spline.
Therefore, angular velocity is determined by jerk - the rate at which this thrust vector is changing.
The angular velocity cannot be changed instantaneously, because the quadrotor can only exert a finite torque about its rotational axes. So we need to design trajectories that do not attempt to change the angular velocity -- and hence, the jerk -- too quickly.
Therefore, we should try to minimize something like the maximum norm of the snap along the trajectory.
In practice we often minimize the integral of the squared norm of the snap, because it can be posed as a convex quadratic optimization problem with respect to the control points of a spline.