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Abstract(s)
No mundo atual do controlo de tráfego aéreo uma das maiores preocupações é a minimização dos atrasos existentes em diversos aeroportos, certas vezes provocados por alterações repentinas nas trajetórias devido à existência de alguma zona interdita à navegação aérea/obstáculos estáticos. Esta dissertação teve como objetivo a investigação de diversos métodos para gerar uma trajetória que conseguisse prever e evitar a colisão de uma aeronave com um obstáculo estático tendo em conta sempre o objetivo principal de reduzir o tempo total de uma trajetória com 5 waypoints.
Numa primeira fase estudaram-se apenas teoricamente quatro métodos de geração de trajetória: por curvas de Bézier, por Splines Cúbicas, por B-Splines, e pelo método de Overhauser. Nesta fase concluiu-se que nem as curvas de Bézier, nem as B-Splines provocariam resultados satisfatórios, pois o primeiro método tem um controlo global, tornando difícil controlar as distâncias de passagem de determinados pontos, e o segundo método é demasiado pesado.
Apenas com o método de Overhauser e das Splines Cúbicas aproximou-se a trajetória inicialmente interpolada, onde se confirmou que ambos os métodos cumpriam com requisitos de passagem a uma distância máxima dos waypoints intermédios.
Num segundo teste de simulação numérica a estes dois métodos, o software MATLAB® apresentou dificuldades em cumprir com condições extra, que implicavam o respeito pelas velocidades mínimas e máximas da aeronave utilizada para o estudo, na minimização do comprimento total do método da spline cúbica. Por esta razão o estudo prosseguiu apenas com o método de Overhauser.
Na simulação final, concluiu-se que o método de Overhauser é capaz de evitar colisão com um obstáculo, no máximo dois, dependendo, ainda assim, do tamanho dos obstáculos a evitar, uma vez que este método usa apenas polinómios de grau 2, o que o torna algo limitado. Observou-se também uma redução no comprimento total da trajetória de 7,83% face ao comprimento total obtido para a trajetória interpoladora, e uma redução na ordem dos 43% comparativamente ao tempo inicial. Estudos futuros poderão apurar diferentes estratégias para utilização do método da Spline Cúbica na prevenção de colisão, o que certamente oferece uma solução mais satisfatória, uma vez que é um método com mais coeficientes, logo, melhor flexibilidade.
In today's world of air traffic control a major concern is the minimization of existing delays at various airports, sometimes caused by sudden changes in trajectory due to the existence of any protected zone to air navigation/statical obstacles. This work aimed to investigate several trajectory generation methods that can predict and prevent the collision of an aircraft with a statical obstacle, always taking into account the main goal of reducing the total time of a trajectory with five waypoints. Initially four methods trajectory generation were compared theoretically: Bezier curves, Cubic Splines, B-splines, and the Overhauser method. On this stage it was concluded that neither the Bezier curves nor B-splines would lead to satisfactory results because the first method has overall control, making it difficult to control the distance pass certain points, and the second method is too heavy. The trajectory initially interpolated was then approached with the Overhauser method and Cubic Splines Method, which has confirmed that both methods met with maximum distance requirements on intermediate waypoints. On a second numerical simulation test with these two methods, the MATLAB software presented difficulties to comply with additional conditions, which implied compliance for the minimum and maximum speeds of the aircraft used for the study, to minimize the total length of the Cubic Spline Method. For this reason, the study continued only with the Overhauser method. In the final simulation, it was concluded that the Overhauser method is able to avoid collision with an obstacle, at most two, depending yet the size of the obstacles to be avoided, since this method uses only polynomials of degree 2, which makes it somewhat limited. There was also a 7.83% reduction in the total length of the trajectory over the total length obtained for the interpolating path, and a reduction of around 43% compared to the initial time. Future studies will determine different strategies for using the cubic spline method for collision avoidance, which certainly gives a more satisfactory solution, since it is a method with more coefficients thus better flexibility.
In today's world of air traffic control a major concern is the minimization of existing delays at various airports, sometimes caused by sudden changes in trajectory due to the existence of any protected zone to air navigation/statical obstacles. This work aimed to investigate several trajectory generation methods that can predict and prevent the collision of an aircraft with a statical obstacle, always taking into account the main goal of reducing the total time of a trajectory with five waypoints. Initially four methods trajectory generation were compared theoretically: Bezier curves, Cubic Splines, B-splines, and the Overhauser method. On this stage it was concluded that neither the Bezier curves nor B-splines would lead to satisfactory results because the first method has overall control, making it difficult to control the distance pass certain points, and the second method is too heavy. The trajectory initially interpolated was then approached with the Overhauser method and Cubic Splines Method, which has confirmed that both methods met with maximum distance requirements on intermediate waypoints. On a second numerical simulation test with these two methods, the MATLAB software presented difficulties to comply with additional conditions, which implied compliance for the minimum and maximum speeds of the aircraft used for the study, to minimize the total length of the Cubic Spline Method. For this reason, the study continued only with the Overhauser method. In the final simulation, it was concluded that the Overhauser method is able to avoid collision with an obstacle, at most two, depending yet the size of the obstacles to be avoided, since this method uses only polynomials of degree 2, which makes it somewhat limited. There was also a 7.83% reduction in the total length of the trajectory over the total length obtained for the interpolating path, and a reduction of around 43% compared to the initial time. Future studies will determine different strategies for using the cubic spline method for collision avoidance, which certainly gives a more satisfactory solution, since it is a method with more coefficients thus better flexibility.
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Keywords
B-Splines Bézier Minimização do Comprimento de Trajetória Minimização do Tempo Overhauser Prevenção de Colisão Splines Cúbicas Trajetória 4d