Analysis and Application of in Indirect MinimumJerk Method for Higher order Differential Equation in Dynamics Optimization Systems

Authors: V. Tawiwat, T. Amornthep, P. Pnop

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 considers the indirect minimum Jerk method for higher order differential equation in dynamics optimization proposes a simple yet very interesting indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of indirect jerks are found using the dynamic optimization methods together with the numerical approximation. This case considers the linear equation of a simple system, for instance, mass, spring and damping. The simple system uses two mass connected together by springs. The boundary initial is defined the fix end time and end point. The higher differential order is solved by Galerkin-s methods weight residual. As the result, the 6th higher differential order shows the faster solving time.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077006

References:

[1] C. A. Brebbia, The Boundary Element Method for Engineers. Pentech Press,1978.
[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] C.A.J, Fletcher Computational Gaelerkin Method, Springer Verlag, 1974.