Sigmoid vs Sinusoid acceleration control

You can calculate the desired acceleration/deceleration curve using expr. The smoothest acceleration/deceleration is exhibited by simple harmonic motion (like the swinging of a pendulum), which would be a sinusoidal curve rather than a sigmoid curve (and a sigmoid is theoretically asymptotic, i.e. never truly reaches its goal). You can calculate either with expr. Here’s an example comparing the two.