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| Author(s): |
Matias de Jong van Lier
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2021-06-24 |
| Examining board members: |
Denise de Mattos;
Alice Kimie Miwa Libardi;
Thiago de Melo;
Pedro Luiz Queiroz Pergher
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| Advisor: | Denise de Mattos |
| Abstract | |
In recent years, a new field integrating robotics and topology was born, referred to by many as Topological Robotics, in which the main strategy is to use algebraic topological tools to get some insight into robotics problems. One of those problems is called the robot motion planning problem and is the main motivation for this work. We present an in-depth study of Topological Complexity, discussing how it relates to the Motion Planning Problem, and the main methods for computing it for CW complexes and Smooth Manifolds, spaces of great interest in robotics. The concept of Lusternik- Schnirelmann category is introduced due to its connection with Topological complexity, both being particular cases of the more general concept of the Schwarz Genus of a fibration. (AU) | |
| FAPESP's process: | 18/23410-3 - Topological complexity and Lusternik-Schnirelmann category |
| Grantee: | Matias de Jong van Lier |
| Support Opportunities: | Scholarships in Brazil - Master |