טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentBondarenko Alina
SubjectReconstruction of Moving Geometrical Shapes Based on
Measurements Obtained by a Moving Sensor
DepartmentDepartment of Mechanical Engineering
Supervisors Professor Yoram Halevi
Professor Emeritus Moshe Shpitalni


Abstract

Applications of reconstruction of moving geometrical shapes from the noisy measurements, obtained by a moving sensor can be found in the areas of robotics, kinematics, biomechanics, medical imaging, CAD/CAM and flight/vehicle simulator design. The measurements from the sensor represent points on the shape and can be translated into an implicit function that relates the position and the orientation of the shape to static parameters defining the shape. The work considers two types of available information, direct distance measuring, and measurements taken by a camera.

The suggested estimation algorithm is based on static parameters identification and dynamic variables (position, orientation and corresponding velocities) estimation simultaneously. Methods based on Kalman filter were selected as the estimation tool. In this work a new estimation algorithm for non-linear systems with non-additive measurement noise is introduced. Such a situation appears in shape estimation problems, because the noisy measurements are included in an implicit function that plays the role of measurement equation in the problem formulation.

An important issue in many engineering applications, is registration, or finding a transformation between two positions of a rigid body. We introduce an algorithm of finding the transformation, where in the first position the shape is extensively measured, and in the second a relatively small number of points is measured. Another problem, which has been addressed in this work, is geometrical evaluation of a cylindrical workpiece. An algorithm for minimum zone evaluation of rotating and imprecisely positioned workpiece has been developed. The method is based on estimation of the geometrical axis position and orientation at each instant, and enables separation of the spindle error using only a single probe.

This work presented a variety of problems dealing with identification and estimation of static or moving shapes, in several configurations. The estimation methods are based on Kalman filter extensions. An important issue in the development is appropriate representation of noise in systems with non-linear implicit measurements, which lead to significant improvement in the estimation results.