Masters Theses

Mir S. Azam

Date of Award

12-1994

Degree Type

Thesis

Degree Name

Master of Science

Major

Electrical Engineering

Major Professor

Mohan Trivedi

Committee Members

Marshall Pace, Igor Alexeff

Abstract

Surface interpolation using discrete and insufficient range data is the major em- phasis of this thesis. The underlying idea for the interpolation is to have a mobile robot make decisions while navigating in obstacle ridden environments. The inter- polation techniques chosen and developed are kept computationally simple. Two dimensional polynomials serve as the basis of this surface interpolation technique; developing a new surface interpolation algorithm involves using those polynomials on the sampled surface plane. Three different polynomials the Lagrange polynomial, the Piecewise Linear polynomial, and the Cubic Spline polynomial are used to interpolate surfaces. Ultrasonic range sensors are used to obtain the range data, and careful sensor placement is necessary to interpolate surfaces. The technique developed is thoroughly tested with both synthetic and real data. Experiments are performed on available hardware such as a mobile robot and also on developed hardware such as the sensory template built for this thesis. In order to be able to do the experiments, integration between the sensory subsystem and the robotic subsystem plays an important role. Graphical user interfaces are built in order to have both teleoperation and automatic navigation modes for the mobile robot, for the three dimensional approximation technique utilities, and for plotting surfaces in three dimensions. Finally, comparisons among the interpolation techniques are carried out based on the obtained results from the analyses.

Using the surface interpolation technique developed here for this thesis, the La- grange polynomial and the Piecewise Linear polynomial perform close to each other,each one's results staying within 2% of those of the other one. The Cubic Spline polynomial based approach, however, deviates considerably from Lagrange and Lin- ear algorithms based approaches by giving 5 or 6 times worse mean errors in some cases. Nevertheless, the three dimensional shapes of the original surfaces are pre- served by all the polynomials. The unique contributions of this thesis are the less computation demand for surface interpolation, an extensive set of experiments over at least five different synthetic surfaces and at least two different real surfaces, friendly graphical user interfaces, and the implementation of a polynomial based reactive obstacle negotiation algorithm on a mobile robot in completely unknown but obstacle cluttered environments.

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