Symbolic manipulator laboratory : an efficient symbolic modeling package for the kinematic analysis and control of robot manipulators

A new program package, Symbolic Manipulator Laboratory (SML), for the automatic generation of both kinematic and static manipulator models in symbolic form is presented. Critical design parameters may be identified and optimized using symbolic models. The computer-aided development of these models yields equations with reduced numerical complexity. Important considerations have been placed on the closed form solutions simplification and on the user friendly operation. The main emphasis of this research is the development of a methodology which is implemented in a computer program capable of generating symbolic kinematic and static forces models of manipulators.

The trigonometric reductions are among the most significant results of this work and the most difficult to implement. Previously, only pattern matching has been used. In addition to pattern matching, a new method, based on exponential functions, has been developed and improved in SML. This new method drastically reduces the amount of time necessary to produce the model and to perform its numerical computation.

Mathematica (Wolfram 1988), a commercial program that allows symbolic manipulation, is used to implement the program package. SML is written such that the user can change any of the subroutines or create new ones easily. Further, the subroutines can be used independently or jointly, allowing the creation of the user's own work routine. To assist the user, an on-line help has been written to make this package user friendly.

SML can be used in an interactive mode or in a batch mode. In the first mode, each function of the package can be called separately. Then, each output can be analyzed and used as input for the following calls to functions. In the batch mode, a program to call the functions can be written easily by the user. Furthermore, the user can easily develop new routines and even create new functions that were not in the original package. Thus, the capability of the program can be extended, improving the user's efficiency and accuracy.

Some sample applications are presented. The kinematic and static models of three different 7-degree-of-freedom (DOF) manipulators are calculated symbolically. Finally, the design of a 5-DOF manipulator using SML is discussed.