Symbolically Automated Direct Kinematic Equations Solver for Robotic Manipulators

Abstract

SUMMARY Solving the direct kinematic problem in a symbolic form requires a laborious process of successive multiplications of the link homogeneous transformation matrices and involves a series of algebraic and trigonometric simplifications. The manual production of such solutions is tedious and error-prone. Due to the efficiency of the Prolog language in symbolic processing, a rule–based Prolog program is developed to automate the creation of the following processes: Link transformation matrices; forward kinematic solutions; and the Jacobian matrix. This paper presents the backward recursive formulation techniques, the trigonometric identity rules, and some heuristic rules for implementing the System. A verification of the System has been demonstrated in case of several industrial robots.