If I remember my uni engineering/calculus maths class correctly, the third derivative of position is used in planning these sort of curves.
The first derivative of postion (with respect to time) is velocity. The second derivative is acceleration (ie rate of change of velocity). And the third derivative is jerk (rate of change of acceleration).
And 'jerk' has to be kept below a certain threshold for humans to find movement comfortable.
The first derivative of postion (with respect to time) is velocity. The second derivative is acceleration (ie rate of change of velocity). And the third derivative is jerk (rate of change of acceleration).
And 'jerk' has to be kept below a certain threshold for humans to find movement comfortable.