Naren Vira

Use of symbolic computation in robotics education

An application of symbolic computation in robotics education is described. A software package is presented which combines generality, user interaction, and user-friendliness with the systematic usage of symbolic computation and artificial intelligence techniques. The software utilizes MACSYMA, a LISP-based symbolic algebra language, to automatically generate closed-form expressions representing forward and inverse kinematics solutions, the Jacobian transformation matrices, robot pose error-compensation models equations, and Lagrange dynamics formulation for N degree-of-freedom, open chain robotic manipulators. The goal of such a package is to aid faculty and students in the robotics course by removing burdensome tasks of mathematical manipulations. The software package has been successfully tested for its accuracy using commercially available robots. >

Precision measurements and control of an automated two-dimensional grid plate testing machine

Abstract The article describes current development of an automated two-dimensional precision grid plate testing system applicable to measure an array of grid marks or points premarked on a grid plate at sub-micron level accuracy. The grid plates are commonly being used as referencing devices to check sizes of small manufactured parts such as semiconductor geometry and integrated circuits. The grid plates discussed in this paper are generally glass plates with some type of symmetric marks placed on the glass surface. The primary goal of this research work is to use off-the-shelf type of equipment like laser interferometer, precision stage, machine vision system and micro-computer, and integrate them to build a low-cost, practical system usable for the grid plate calibration services. The initial assessment indicates that the present system can measure locations of grid points with an accuracy of 0.5 μm. This accuracy is comparable to much more expensive measurement systems available in the market place. There are many additional refinements and improvements to the system are under way to enhance its present capability and meet our original design goal of 0.05 μm accuracy.

Higher order approximation of the generalized kinematic error compensation model for robots

Abstract This article presents a higher-order approximation of the “generalized” kinematic error compensation model to enhance position accuracy and repeatability of robotic manipulators. The “generalized” model originally proposed by Driels and Pathre is successfully extended to include non-linear coupling effects among all error parameters. A pertubration technique is used in which second-order error terms are retained for improvement to the Denavit-Hartenberg A and T matrices. The model is called “generalized” in a sense that it incorporates ten error parameters (all six possible errors and four link parameter errors) per manipulators joint axis. The second-order terms in the model become important when considering large robot structure size or when input kinematic errors increase in their magnitudes. The formulation of the generalized Jacobian matrix is also presented including second-order error terms in the analysis.

Application of microcomputer in submicron level measurements and control of a positioning device

This article demonstrates an application of a microcomputer in the area of automated manufacturing, in particular to the measurement and control of a positioning device with the accuracy level of less than 1 μm. The positioning device is generally used for calibration or testing purposes to check the dimensional accuracy of manufactured parts. Here, however, it is utilized for calibration of artifacts like scales, grid plates, calipers, etc. The artifacts are widely used in industry as a referencing device to determine whether the manufactured product meets dimensional quality requirements whilst maintaining high reliability and speeding up quality control operations. The critical challenge here is to develop an automated two-dimensional precision grid plate testing system which measures an array of grid points premarked on a grid plate. The grid plates discussed in this paper are generally glass plates with some type of symmetric marks placed on the glass surface. The goal is to use off-the-shelf type of equipment such as laser interferometer, precision positioning stage, computer controlled machine vision system and a host microcomputer, and integrate them to build a low-cost, practical system usable for the grid plate calibration services. This requires the development of compatible hardware and software protocols. The initial assessment of the test setup indicates that the present system can measure locations of grid points with an accuracy of 0.5 μm. Further improvements to the system are also suggested.

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 robots 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.

Why symbolic computation in robotics

Abstract This article is organized to demosttrate various applications of symbolic computation in robot manipulator design and analysis. Four major areas—kinematics, dynamics, trajectory planning and control, and pose error modeling—are extensively surveyed. A concept of an intermediate symbolic manipulator module is also described to automate and couple the processes of an interactive robot geometry design and numerical simulation.

Robots' end point sensing: hardware and software techniques

Abstract This article describes a contact measurement technique to assess positioning performance of an industrial robot. A survey of some important robot testing methods and error compensation models that are presently available in the literature is also presented.

Interactive approach to reconstruction and visualisation of three-dimensional colour images

The paper describes an interactive approach to first reconstruct and then visualise three-dimensional image models created from a pair of two-dimensional digital colour images. The method integrates an interactive output data manipulation capability of JView, Java based API engineered by US Air Force with newly developed more accurate procedure of recreating texture mapped 3D-models using a stereo triangulation technique. Though several procedures have been proposed in literature on how to generate 3D models by recovering image depth, they are limited in predicting an accurate pixel matching between image correspondences. Furthermore, majority of papers lack depicting reconstructed 3D-image geometry to show how well their techniques have been able to recover scene depth at every pixel. We have employed a region-based block matching methodology for colour image analysis. The reconstructed image models can be viewed and manoeuvered on a computer screen by mouse buttons. This interactive viewing capability is an aid to visualisation process and facilitates algorithm designers to test their codes.

Application of symbolic computation in robot pose error modelling

This paper presents an application of symbolic computation in geometrical error modelling and simulation of an industrial robotic manipulator. A program named SCRPE (Symbolic Computation of Robot Pose Errors) has been developed to automatically generate error model equations for the end-eflector of N degree-of-freedom robots. The SCRPE utilizes symbolic manipulation capability of MACSYMA (a Lisp-base artificial intelligence language). The prime reasons of this work are to provide a base for comparison, performance assessment and accuracy judgment of numerous error calibration and compensation models available in the literature; and 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. As an example, the mathematical error model considered here is based on small perturbation in link parameters defined in accordance with a classical Denavit-Hartenberg notation. The time required to compute first and second order terms of the model are compared for numerous robots. The worst case scenario takes 290 seconds for a PUMA 600 series robot, which is insignificant compared to the time required for accurate manual derivation. The SCRPE program is user-friendly, interactively menu-driven and has been developed on VAX 750 Digital computer under the VMS operating system. Interested readers can obtain the program copy by contacting the first author.

Industrial robot training: A comprehensive short course

Abstract In this article a brief description of a short robotic training course is presented. The course often falls under the continuing education program and has two main objectives: (1) to give trainees an in-depth exposure to fundamentals and hands-on-experience with operation and programming of an industrial robot; (2) to provide trainees with an overview of the variety of existing applications of robots suitable for automated manufacturing environment and of general procedures for service, maintenance, and troubleshooting. The course offering is limited to a two-week period in order to be cost-effective as well as to represent one of the quickest methods to prepare personnel and practicing engineers for the rapidly expanding industry of robots and automation.