Evandro Marconi Rocco

Station Keeping of Constellations Using Multiobjective Strategies

The goal of the present paper is to study the problem of station keeping maneuvers of satellites that belong to a constellation. The objective is to perform those maneuvers with low fuel consumption and but also including a time constraint. This type of problem has several aspects to be considered, like fuel consumption, duration of the maneuvers. These aspects are applied to all the satellites of the constellation, so a strategy has to be found to consider the global optimization of those variables that can control the geometry of the constellation. So, this is a multiobjective problem. To find a solution, strategies are formulated that minimize the fuel consumption considering all the satellites and also considering the duration of the maneuver. Numerical examples are shown.

Minimum Fuel Low-Thrust Transfers for Satellites Using a Permanent Magnet Hall Thruster

Most of the satellite missions require orbital maneuvers to accomplish its goals. An orbital maneuver is an operation where the orbit of a satellite is changed, usually applying a type of propulsion. The maneuvers may have several purposes, such as the transfer of a satellite to its final orbit, the interception of another spacecraft, or the adjustment of the orbit to compensate the shifts caused by external forces. In this situation it is essential to minimize the fuel consumption to allow a greater number of maneuvers to be performed, and thus the lifetime of the satellite can be extended. There are several papers and studies which aim at the fuel minimization in maneuvers performed by space vehicles. In this context, this paper has two goals: (i) to develop an algorithm capable of finding optimal trajectories with continuous thrust that can fit different types of missions and constraints at the same time and (ii) to study the performance of two propulsion devices for orbital maneuvers under development at the Universidade de Brasilia, including a study of the effects of the errors in magnitude of these new devices.

Discrete Multiobjective Optimization Methodology applied to the Mixed Actuators Problem and Tested in a Hardware-in-the-loop Rendevzous Simulator

The spacecraft control problem using a set of actuators with conflicting characteristics is investigated in this paper. A novel approach, called actuator multiobjective command method, based on a discrete multiobjective optimization technique is proposed. The method is included in a coupled translational and attitude control system applied to the final approach rendezvous. Furthermore, all elements of the guidance, navigation and control loop have been developed and implemented in a simulation framework. A reaction control system, a set of reaction wheels, and a set of magnetic torqrods are the group of actuators used in this work. The discrete multiobjective problem is formulated with four objectives: torque error, fuel and electrical charge consumption, disturbance of coupling, and risk of utilization. The decision variable represent the command torque to the actuators. In addition, the hardware-in-the-loop rendezvous and docking simulation facility of the German Aerospace Center has been used to test the proposed method under realtime conditions. Results indicate that a mixed actuators methodology can achieve better performance with respect to those using the same type of actuators.

Orbital Disturbance Analysis due to the Lunar Gravitational Potential and Deviation Minimization through the Trajectory Control in Closed Loop

A study evaluating the influence due to the lunar gravitational potential, modeled by spherical harmonics, on the gravity acceleration is accomplished according to the model presented in Konopliv (2001). This model provides the components x, y and z for the gravity acceleration at each moment of time along the artificial satellite orbit and it enables to consider the spherical harmonic degree and order up to100. Through a comparison between the gravity acceleration from a central field and the gravity acceleration provided by Konoplivs model, it is obtained the disturbing velocity increment applied to the vehicle. Then, through the inverse problem, the Keplerian elements of perturbed orbit of the satellite are calculated allowing the orbital motion analysis. Transfer maneuvers and orbital correction of lunar satellites are simulated considering the disturbance due to non-uniform gravitational potential of the Moon, utilizing continuous thrust and trajectory control in closed loop. The simulations are performed using the Spacecraft Trajectory Simulator-STRS, Rocco (2008), which evaluate the behavior of the orbital elements, fuel consumption and thrust applied to the satellite over the time.

Multi-Objective Optimization Applied to Real-Time Command Problem of Spacecraft Thrusters

A novel approach to solve the real-time command problem of spacecraft thrusters, called the thruster multi-objective command method, is proposed in this paper. The reaction control system technology uses a set of thrusters in a special setup to simultaneously provide force and torque to the spacecraft. The thruster management function calculates all the candidate solutions that solve the thruster coupling problem. Then, a discrete multi-objective optimization method selects at every control cycle the best combination of thrusters and their firing time duration, which simultaneously optimizes a group of four objectives: the force error, the torque error, the propellant mass consumption, and the total number of pulses. The proposed method is included in a coupled translational and attitude control system applied to the final approach rendezvous scenario. Furthermore, all elements of the guidance, navigation, and control loop are accurately designed and implemented in a simulation framework. Results indicate...

Application of the Kalman Filter to Estimate the State of an Aerobraking Maneuver

This paper presents a study about the application of a Kalman filter to estimate the position and velocity of a spacecraft in an aerobraking maneuver around the Earth. The cis-lunar aerobraking of the Hiten spacecraft as well as an aerobraking in a LEO orbit are simulated in this paper. The simulator developed considers a reference trajectory and a trajectory perturbed by external disturbances combined with nonidealities of sensors and actuators. It is able to operate in closed loop controlling the trajectory at each instant of time using a PID controller and propulsive jets. A Kalman filter utilizes the sensor data to estimate the state of the spacecraft. The estimation algorithms and propagation equations used in this process are presented. The U.S. Standard Atmosphere is adopted as the atmospheric model. The main results are compared with the case where the Kalman filter is not used. Therefore, it was possible to perform an analysis of the Kalman filter importance applied to an aerobraking maneuver.

The Study of the Asymmetric Multiple Encounters Problem and Its Application to Obtain Jupiter Gravity Assisted Maneuvers

The Multiple Encounters Problem is described in the literature as the problem of finding trajectories for a spacecraft that leaves from a mother planet, describes a trajectory in the interplanetary space, and then goes back to the mother planet. The present paper extends the literature and the departure and arrival angles of the spacecraft are generalized to be nonsymmetrical. The solutions are shown in terms of the true () and eccentric anomaly (). The velocity variation () required for the transfer is also shown. Then, this study is generalized to consider the possibility that the spacecraft makes a close approach with the mother planet to change its energy in the return trip. The velocity () and energy variation () due to this passage are obtained. The topics studied here can be applied in missions that leave and come back to the Earth, with the goal of studying the interplanetary space, as well as for missions whose objective is to make an alteration in the energy of the space vehicle through a swing-by with the mother body.

Efeitos dos Termos Individuais do Potencial Gravitacional Lunar no Movimento de Satélites Artificiais ao Redor da Superfície da Lua

O presente trabalho analisa a influencia da nao homogeneidade do campo gravitacional lunar na orbita de um satelite artificial. O modelo baseia-se nos harmonicos esfericos, de acordo com o desenvolvimento apresentado por Konopliv. Este modelo nos permite considerar harmonicos esfericos ate grau e ordem 100. Simulacoes sao realizadas para que sejam feitas as seguintes analises: a contribuicao de cada termo do potencial gravitacional lunar, a variacao da perturbacao devido a inclinacao da orbita e a atuacao do sistema de controle. Manobras de transferencia e de correcao de satelites lunares sao simuladas considerando empuxo continuo e controle de trajetoria em malha fechada.

Estudo da execução de serviços em órbita de satélites usando um braço robótico cooperativo com o controle de atitude

Neste estudo e analisada a aplicacao de um sistema robotico em ambiente espacial, levando em consideracao as perturbacoes causadas a atitude, em virtude do acionamento dos mecanismos roboticos durante a realizacao de servicos em orbita. O trabalho realizado sugere ganhos consideraveis ao empregar-se modelos que contemplem a correcao dinâmica dos erros de posicionamento do referencial do braco robotico, que por sua vez, atua simultaneamente ao controle de atitude do satelite. Atividades roboticas de servicos em orbita tem se tornado comuns devido ao surgimento de novas tecnologias na area de rendezvous, docking e berthing. O braco robotico que serve de objeto de estudo neste trabalho consiste de um manipulador revoluto com tres juntas rotativas e tres graus de liberdade em configuracao Torcional-Rotacional-Rotacional (TRR) movendo-se no espaco. Configuracao tal que o confere aplicabilidade diversificada e notoria utilidade em atividades de servico em orbita. A analise dos erros de posicionamento ocasionados pelos movimentos de extensao e rotacao do aparato nos possibilita uma visao mais clara sobre as estrategias necessarias para o uso futuro deste tipo de tecnologia. Neste trabalho proponho o uso de um manipulador robotico servindo como ferramenta a contribuir com a efetivacao de servicos em ambiente espacial e sanando problemas de controle encontrados quando do uso de outros atuadores para tal finalidade. E, portanto, fundamental que se tenha boa ideia das perturbacoes causadas a atitude do satelite em decorrencia da atuacao do braco robotico acoplado. Neste sentido nos concentraremos na analise dos torques perturbadores visto que a base do robo nao pode ser considerada, para fins de posicionamento preciso, como sendo de um sistema inercial. A perda da missao pode ser ocasionada por falha prematura de equipamentos do satelite, por isso as agencias espaciais tem investido no desenvolvimento de servicos em orbita (OOS – On Orbit Service). OOS inclui diversas atividades de um veiculo espacial [1] como montagem, reparo, resgate, aprimoramento, reabastecimento, recuperacao e manutencao. Esses servicos podem estender a vida util dos satelites, melhorar a capacidade dos sistemas espaciais, reduzir custos de operacao, e ate mesmo contribuir para a mitigacao dos detritos espaciais. E imprescindivel o dominio das tecnicas de rendezvous e docking, bem como, do controle de atitude para executar servicos em orbita em missoes do tipo montagem de grandes unidades, reabastecimento de estacoes, troca de tripulacao entre veiculos, reparo de satelites, entre outras. Primeiramente, obtemos um modelo que represente, por meio de um algoritmo implementado, a forma como responde um manipulador robotico durante simulacao com parâmetros controlados. A configuracao de robo articulado (antropomorfico) ou revoluto assemelha-se a um braco humano. Observa-se que e possivel calcular a posicao cartesiana no espaco, bem como a orientacao do punho, com base no conhecimento dos ângulos das juntas. Este equacionamento e conhecido como cinematica direta. O calculo das posicoes angulares das juntas a partir da posicao no espaco do orgao terminal consiste, portanto, na cinematica inversa. O calculo da cinematica, tanto direta quanto inversa, requer o conhecimento do comprimento dos elos com precisao adequada, bem como os ângulos de torcao entre juntas, ou seja, necessitamos definir tais constantes em nosso modelo computacional e para tanto a chamada notacao de Denavit-Hartenberg permite obter o conjunto de equacoes que descreve a cinematica de uma junta com relacao a junta seguinte vide [2]. Assim podemos ter uma visao matematizada da estrutura do robo para inserirmos no algoritmo. A Fig. 1 e a Fig. 3 mostram o mecanismo do qual obtivemos as equacoes para solucao da cinematica inversa, ou seja, dada a posicao desejada para o orgao terminal encontram-se os ângulos das juntas capazes de levar a extremidade do robo a tal posicao. A modelagem do comportamento do satelite e obtida por meio do Satellite Attitude Simulator (SAS) desenvolvido em [3] e [4], onde o movimento de atitude e calculado a cada passo da simulacao. Na arquitetura do simulador Fig. 2, a atitude de referencia e comparada continuamente com a posicao angular atual do veiculo espacial. Um sinal de erro e gerado por meio da diferenca entre os estados atual e de referencia. O sinal de erro e entao enviado a um controlador proporcional integral derivativo (PID) cuja lei de controle e definida pela Eq. (1), onde Kp e o ganho proporcional, Ki o ganho integral, Kd o ganho derivativo e er(t) e o sinal de erro [...]

Avaliação dos desvios na trajetória originados pelo acoplamento entre o controle de atitude e de órbita em manobras orbitais com propulsão contínua

Existem basicamente dois tipos de manobras orbitais: as que proporcionam a correcao de orbita e as de transferencia de orbita. Essas manobras exigem um sistema de controle que devera ser constituido, dentre outras coisas, por subsistemas que atuem na orbita e atitude. O controle de atitude e orbita sao subsistemas que podem interagir. Todavia, considerando um caso ideal, pode-se afirmar que nao existe um acoplamento matematico entre atitude e orbita. Porem, na pratica, o acoplamento ocorre quando o controle de orbita depende do apontamento de um propulsor fixo no veiculo, que por sua vez depende da atitude. Assim, o controle de atitude deve seguir uma direcao de referencia fornecida pelo subsistema de controle de orbita. Mas os erros no controle de atitude, ou ate mesmo o tempo de resposta do sistema, afetarao o controle de orbita. Portanto, o estudo da interacao entre os sistemas de controle de atitude e de orbita faz-se necessario.