Computer generation of geometrical error equations applicable for improvement of robots' positioning accuracy

Abstract

A symbolic manipulation software package has been developed to automatically generate geometrical error model equations applicable for robot's error compensation and calibration. The software package named AREEM (Automatic Robot Error Equation Modeler) utilizes MACSYMA, a LISP-based artificial intelligence language, to output scalar algebraic equations representing the positioning error correction in world coordinates for N degree-of-freedom robots. The motivation of this work is trifold: (1) to demonstrate the feasibility of utilizing a well-established algebraic manipulation code for robot error compensation, simulation and modeling purposes; (2) to provide a base for investigating the performance and accuracy of numerous robot geometrical error compensation models; (3) to represent output results in a concise form eliminating completely the manual derivation process. When such computer generated outputs are fed to a simulation program, saving in computational time for error estimation is realized. At present, AREEM incorporates three kinematic error models based on the Denavit-Hartenberg representation (DH) and a non-DH representation. The AREEM program is user-friendly, interactively menu-driven, and has been tested on numerous robots. The worst case takes 174.80 seconds to generate error model equations in world coordinates for the PUMA 600 robot, which is insignificant compared to the time required for accurate manual derivation.