Abstract

Dynamic equations used for feed-forward control
of robotic mechanisms include interdependent
variables between the constituting links, since they are normally evaluated in relative polar coordinates and in the dimension of torque.
Accordingly, it will become highly complicated to derive inverse dynamics
of closed-loop link systems, continuously transforming systems, or of flexible
link systems. Consideration of dynamics is required to realize stable control of robotic
systems, and many researchers have tried to deal with the dynamics by improving
theories and methods against each system.

Isobe, on
the other hand, developed a completely new solution
scheme for inverse dynamics called the parallel solution scheme, which can be commonly applied in different types of link systems
such as open- or closed-loop mechanisms, or ones constituted with rigid or flexible link
members. The scheme is developed
using a finite element approach, handling the entire system as
a continuum. By taking advantage of natural
characteristics of the finite element method (FEM), i.e., the capability of expressing the behavior of each discrete
element as well as that of the entire continuous system, local information such
as nodal forces and displacements can be calculated in parallel. It evaluates the analyzed model in absolute Cartesian coordinates with the
equation of motion expressed in dimension of force. The inverse dynamics is calculated by using a matrix form relation to the nodal
forces obtained by the finite element calculation. The matrix-form equations are divided individually into terms of
force, transformation between coordinates, and length, which makes the scheme
potentially higher in applicability and expansibility.

The scheme can not only deal with
open- and closed-loop link systems independently, but it can also deal
seamlessly with those that gradually change their forms and dynamics. There is
also no need to revise the basic numerical algorithm of the scheme, regardless
of the stiffness of the constituting link member. Particularly, it is considered to be valid for link systems with elastic members,
since the calculation process of the scheme is based upon the finite element approach.

The main objective of this study is to verify the extensive ability
of the scheme as a unified scheme, by carrying out inverse
dynamics calculations on several types of rigid and
flexible manipulators, along with applications to feed-forward control of various types
of link systems and robotic mechanisms.

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