Combining Minimum Energy and Minimum Direct Jerk of Linear Dynamic Systems

Authors: V. Tawiwat, P. Jumnong

Abstract:

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 when combining the minimum energy and jerk of indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of the minimum energy, the minimum jerk and combining them together 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 state inputs employed by combining minimum energy and jerk designs. The numerical solution of minimum direct jerk and energy problem are exactly the same solution; however, the solutions from problem of minimum energy yield the similar solution especially in term of tendency.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334245

References:

[1] S. K. Agrawal and B.C. Fabien, Optimization of Dynamic Systems. Boston: Kluwer Academic Publishers, 1999.
[2] HG. Bock, "Numerical Solution of Nonlinear Multipoint Boundary Value Problems with Application to Optimal Control," ZAMM, pp. 58, 1978.
[3] JJ. Craig, Introduction to Robotic: Mechanics and Control. Addision- Wesley Publishing Company, 1986.
[4] WS. Mark, Robot Dynamics and Control. University of Illinois at Urbana-Champaign, 1989.
[5] TR. Kane and DA. Levinson, Dynamics: Theory and Applications. McGraw-Hill Inc, 1985.
[6] T. Veeraklaew, Extensions of Optimization Theory and New Computational Approaches for Higher-order Dynamic systems
[Dissertation]. The University of Delaware, 2000.
[7] T. Veeraklaew, N. Phatthana-im and S. Heama, Comparison between Minimum Direct and Indirect Jerks of Linear Dynamic Systems. Proceeding of world academy of science and Technology, Vol. 27, Feb 2008.