Navigation in dynamic environments taking advantage of moving agents

Esta tese propõe uma forma diferente de navegação de robôs em ambientes dinâmicos, onde o robô tira partido do movimento de pedestres, com o objetivo de melhorar as suas capacidades de navegação. A ideia principal é que, ao invés de tratar as pessoas como obstáculos dinâmicos que devem ser evitados, elas devem ser tratadas como agentes especiais com conhecimento avançado em navegação em ambientes dinâmicos. Para se beneficiar do movimento de pedestres, este trabalho propõe que um robô os selecione e siga, de modo que possa mover-se por caminhos ótimos, desviar-se de obstáculos não detetados, melhorar a navegação em ambientes densamente populados e aumentar a sua aceitação por outros humanos. Para atingir estes objetivos, novos métodos são desenvolvidos na área da seleção de líderes, onde duas técnicas são exploradas. A primeira usa métodos de previsão de movimento, enquanto a segunda usa técnicas de aprendizagem por máquina, para avaliar a qualidade de candidatos a líder, onde o treino é feito com exemplos reais. Os métodos de seleção de líder são integrados com algoritmos de planeamento de movimento e experiências são realizadas para validar as técnicas propostas.

In search of reliable centimeter-level indoor positioning: a smartphone-based approach

This thesis describes the design and implementation of a reliable centimeter-level indoor positioning system fully compatible with a conventional smartphone. The proposed system takes advantage of the smartphone audio I/O and processing capabilities to perform acoustic ranging in the audio band using non-invasive audio signals and it has been developed having in mind applications that require high accuracy, such as augmented reality, virtual reality, gaming and audio guides. The system works in a distributed operation mode, i.e. each smartphone is able to obtain its own position using only acoustic signals. To support the positioning system, a Wireless Sensor Network (WSN) of synchronized acoustic beacons is used. To keep the infrastructure in sync we have developed an Automatic Time Synchronization and Syntonization (ATSS) protocol with a standard deviation of the sync offset error below 1.25 μs. Using an improved Time Difference of Arrival (TDoA) estimation approach (which takes advantage of the beacon signals’ periodicity) and by performing Non-Line-of-Sight (NLoS) mitigation, we were able to obtain very stable and accurate position estimates with an absolute mean error of less than 10 cm in 95% of the cases and a mean standard deviation of 2.2 cm for a position refresh period of 350 ms.

The Riemann sphere in GeoGebra

The stereographic projection is a bijective smooth map which allows us to think the sphere as the extended complex plane. Among its properties it should be emphasized the remarkable property of being angle conformal that is, it is an angle measure preserving map. Unfortunately, this projection map does not preserve areas. Besides being conformal it has also the property of projecting spherical circles in either circles or straight lines in the plane This type of projection maps seems to have been known since ancient times by Hipparchus (150 BC), being Ptolemy (AD 140) who, in his work entitled "The Planisphaerium", provided a detailed description of such a map. Nonetheless, it is worthwhile to mention that the property of the invariance of angle measure has only been established much later, in the seventeenth century, by Thomas Harriot. In fact, it was exactly in that century that the Jesuit François d’Aguilon introduced the terminology "stereographic projection" for this type of maps, which remained up to our days. Here, we shall show how we create in GeoGebra, the PRiemannz tool and its potential concerning the visualization and analysis of the properties of the stereographic projection, in addition to the viewing of the amazing relations between Möbius Transformations and stereographic projections.