Doctoral Dissertations

Date of Award

12-1997

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Electrical Engineering

Major Professor

M. A. Abidi

Committee Members

Rajiv Dubey, Walter Green, Michael Roberts, Ross Whitaker

Abstract

Determination of relative three-dimensional (3-D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry. A solution to this problem that uses two-dimensional (2-D), intensity images from a single camera is desirable for real-time applications. Where the object geometry is unknown, the estimation of structure is also required. A single camera is advantageous because a standard video camera is low in cost, setup and calibration are simple, physical space requirements are small, reliability is high, and low-cost hardware is available for digitizing and processing the images. A difficulty in performing this measurement is the process of projecting 3-D object features to 2-D images, a nonlinear transformation. Noise is present in the form of perturbations to the assumed process dynamics, imperfections in system modeling, and errors in the feature locations extracted from the 2-D images. This dissertation presents solutions to the remote measurement problem for a dynamic system given a sequence of 2-D intensity images of an object where feature positions of the object are known relative to a base reference frame and where the feature positions are unknown relative to a base reference frame. The 3-D transformation is modeled as a nonlinear stochastic system with the state estimate providing six degree-of-freedom motion and position values. The stochastic model uses the iterated extended Kalman filter as an estimator and as a screw representation of the 3-D transformation based on dual quaternions. Dual quaternions provide a means to represent both rotation and translation in a unified notation. The method has been implemented and tested with both simulated and actual experimental data. Simulation results are provided along with comparisons to a point-based method using rotation and translation to show the relative advantages of the proposed method. Experimental test results using a camera mounted on the end effector of a robot arm to demonstrate relative motion and position control are also presented.

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