Algorithms to estimate contours: two applications of analytical tools in differential geometry and topology

Author

Mohammad Abirul IslamFollow

Publication Date

Spring 5-14-2025

Abstract

We develop distributed robotics algorithms with analytical tools needed to define and analyze angle turned and distance traversed by robots executing geometric algorithms. We then use these analytical tools to obtain information, via sensor measurements, about an a priori unknown surface. Our contributions are threefold. First, we develop the Sketch Algorithm, which estimates the boundary of any unknown contour and is asymptotically optimal in terms of distance traversed and angle turned. Second, we present experimental field work that validates the Sketch Algorithm. Finally, we propose an approach to find multiple sources of a surface with potential applications to approximate that surface via contours whose total rotations are bounded by a constant.

Language

English

Keywords

Computational Geometry, Differential Geometry, Computational Topology, Robotics, Volcanology

Document Type

Dissertation

Degree Name

Computer Science

Level of Degree

Doctoral

Department Name

Department of Computer Science

First Committee Member (Chair)

Jared Saia

Second Committee Member

Melanie Moses

Third Committee Member

Maria Cristina Pereyra

Fourth Committee Member

Maxwell Young

Recommended Citation

Islam, Mohammad Abirul. "Algorithms to estimate contours: two applications of analytical tools in differential geometry and topology." (2025). https://digitalrepository.unm.edu/cs_etds/131