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.
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.
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.