A Closed-Form Solution to Asymmetric Motion Profile Allowing Acceleration Manipulation

Abstract

In this paper, we propose a new complete closed-form formula for asymmetric motion profiles of long, medium, and short distances, which enables easy manipulation of jerks in arrival time for effectively reducing the acceleration and thus the overshoot. The design parameter named <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">jerk ratio</i> is newly introduced to scale down the jerks during the deceleration period so that the velocity profile is in an asymmetric S-curve. Owing to the jerk ratio, the motion formulas are remarkably simplified in analytic forms for short, medium, and long distances. The effectiveness of the proposed approach will be illustrated with the sledge movement control in an optical data storage system by experiments.