Development of a Unified Feed-Forward Control System for Robotic Mechanisms using Finite Element Approach


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.

PDF file