Comparison between Minimum Direct and Indirect Jerks of Linear 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 direct and indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of direct and indirect jerks 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 direct and indirect jerk
designs. By considering minimum indirect jerk problem, the
numerical solution becomes much easier and yields to the similar
results as minimum direct jerk problem.
[1] S. K. Agrawal and B.C. Fabien, Optimization of Dynamic Systems.
Boston: Kluwer Academic Publishers, 1999.
[2] H. G. Bock, "Numerical Solution of Nonlinear Multipoint Boundary
Value Problems with Application to Optimal Control," ZAMM, pp. 58,
1978.
[3] J. J. Craig, Introduction to Robotic: Mechanics and Control. Addision-
Wesley Publishing Company, 1986.
[4] W. S. Mark, Robot Dynamics and Control. University of Illinois at
Urbana-Champaign, 1989.
[5] T. R. 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.
[1] S. K. Agrawal and B.C. Fabien, Optimization of Dynamic Systems.
Boston: Kluwer Academic Publishers, 1999.
[2] H. G. Bock, "Numerical Solution of Nonlinear Multipoint Boundary
Value Problems with Application to Optimal Control," ZAMM, pp. 58,
1978.
[3] J. J. Craig, Introduction to Robotic: Mechanics and Control. Addision-
Wesley Publishing Company, 1986.
[4] W. S. Mark, Robot Dynamics and Control. University of Illinois at
Urbana-Champaign, 1989.
[5] T. R. 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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:61232", author = "Tawiwat Veeraklaew and Nathasit Phathana-im and Songkit Heama", title = "Comparison between Minimum Direct and Indirect Jerks of Linear Dynamic Systems", 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
relationship between the minimum direct and indirect jerks
approaches in designing the time-dependent system yielding an
alternative optimal solution. Extremal solutions for the cost functions
of direct and indirect jerks 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 direct and indirect jerk
designs. By considering minimum indirect jerk problem, the
numerical solution becomes much easier and yields to the similar
results as minimum direct jerk problem.", keywords = "Optimization, Dynamic, Linear Systems, Jerks.", volume = "2", number = "1", pages = "62-5", }