A Study on the Comparison between Minimum Jerk and Minimum Energy of Dynamic Systems

Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper proposes a simple yet very interesting relationship between the minimum jerk and minimum energy approaches in designing the time-dependent system yielding an alternative optimal solution, which gives concurrent minimal energy consumption and smoothness. Extremal solutions for the cost functions of jerk and energy are found using the dynamic optimization methods together with the numerical approximation. This is to allow us to simulate and compare visually and statistically the time history of control inputs employed by minimum energy and minimum jerk designs. By considering minimum jerk problem, both end points boundary conditions of the control input can be assigned to the problem