Helio Kk - Academia.edu (original) (raw)
Papers by Helio Kk
Optical System Alignment and Tolerancing II, 2008
High image quality and complex, refractive optical systems, as those used in remote sensing appli... more High image quality and complex, refractive optical systems, as those used in remote sensing applications, are, in general, very difficult to be manufactured with the required performance. This can be charged to the high sensitivity of such systems to the fabrication tolerances, mainly concerning the relative alignment of the optical components with respect to each other. When the system does not achieve the expected quality, the puzzle is to identify where the problems lies. This is even worsened when the number of optical elements becomes high. Due to these facts, some misalignment characterization and estimation techniques based on Bayesian estimators and wavefront measurements have been proposed in the literature. This paper is the result of a deep study and investigation of these techniques, with emphasis on an application to an intentionally simple system for the sake of illustration that highlights conceptual issues that could be extended to more realistic, complex optical systems. With this purpose, the sensitivity of the wavefront Zernike coefficients to the misalignment parameters, its use in a parameter estimator design that includes nonlinear terms, the study of the system observability, and a statistical analysis of the estimator performance considering the observation noise are addressed in details. Numerical simulation results for the simple system are shown. We also present insights on how to apply the technique to the alignment of a 11-lens optical system used in the Brazilian remote sensing camera MUX, that will fly on-board the upcoming Sino-Brazilian satellites CBERS 3&4.
This paper presents some approaches to the design and some experimental results for a reaction wh... more This paper presents some approaches to the design and some experimental results for a reaction wheel (RW) current and speed control loops. Reaction wheels are largely employed in satellite attitude control due to its large range of torque capability, small power consumption and high reliability. However, to achieve such performance the RW design shall deal with several restrictions, such as to support the space environment hazards (radiation, vacuum, high and fast temperature variation), and launch requirements (vibration, noise and choke). In this work some experimental results of an air-bearing table attitude control equipped with a Fiber Optics Gyro (FOG), a reaction wheel and a small fan will be presented. The RW is controlled by speed reference, and a second speed mode control similar to the first one was implemented in an external computer. Both were then compared by means of the airbearing attitude control performance during the wheel zero-speed crossing. The results showed that the controllers have similar performance, as expected, and the maximum attitude error remained below 0.08 degrees, which attends the attitude requirements of Earth pointing satellites. 11 th International Conference on Vibration Problems Z. Dimitrovová et al. (eds.
Anais do 2º Congresso Aeroespacial Brasileiro, 2019
Resumo. A proposta deste trabalhoé estudar o comportamento do Filtro de Kalman Unscented (FKU) ut... more Resumo. A proposta deste trabalhoé estudar o comportamento do Filtro de Kalman Unscented (FKU) utilizando os parâmetros modificados de Rodrigues (PMR), quando dados reais de sensores que estãoà bordo do satélite CBERS-2B (China Brazil Earth Resources Satellite) alimentam o estimador.
An artificial satellite subject to the attraction of the Earth is disturbed due to nonspherical d... more An artificial satellite subject to the attraction of the Earth is disturbed due to nonspherical distribution and non-symmetrical Earth mass. This uneven distribution of mass is expressed by the so-called spherical harmonic coefficients of the Earth potential. For a faster computation, the acceleration derived from the potential is obtained by a series expansion in terms of these harmonics, the fully normalized Legendre polynomials and their derivatives, and several recursions associated with the longitude, geocentric latitude and altitude of the center of mass of the satellite. This paper analyzes the detailed aspects of disturbances in artificial satellites, related with the modeling of the Earth's gravitational potential as well as numerical implementation of a recursive algorithm to calculate the acceleration of the geopotential based on the Clenshaw summation. In general, one uses recursive equations of high degree and order to calculate the Legendre polynomials in order to obtain faster processing and numerical accuracy. However, the recursions can yield numerical errors at each step of the recursion so that higher orders and degrees of harmonics, the accumulated error may be quite pronounced. The computational implementation of the algorithm is carried out by a PC computer. With the implementation of this algorithm it is possible to calculate the geopotential acceleration for different orbits and different situations. Such approach aims at mitigating the numerical problems arising from usage of extended series expansion when computing recursively the Legendre polynomials. Once the favorable numerical properties are proven, the algorithm can be used in the solution of practical problems of orbital space mechanics and for the Brazilian Space Mission.
This paper presents some approaches to the design and some experimental results for a reaction wh... more This paper presents some approaches to the design and some experimental results for a reaction wheel (RW) current and speed control loops. Reaction wheels are largely employed in satellite attitude control due to its large range of torque capability, small power consumption and high reliability. However, to achieve such performance the RW design shall deal with several restrictions, such as to support the space environment hazards (radiation, vacuum, high and fast temperature variation), and launch requirements (vibration, noise and choke). In this work some experimental results of an air-bearing table attitude control equipped with a Fiber Optics Gyro (FOG), a reaction wheel and a small fan will be presented. The RW is controlled by speed reference, and a second speed mode control similar to the first one was implemented in an external computer. Both were then compared by means of the airbearing attitude control performance during the wheel zero-speed crossing. The results showed t...
This work is applied to the dynamics of rotational motion of artificial satellites, that is, its ... more This work is applied to the dynamics of rotational motion of artificial satellites, that is, its orientation (attitude) with respect to an inertial reference system. The attitude determination involves approaches of nonlinear estimation techniques, which knowledge is essential to the safety and control of the satellite and payload. Here one focuses on determining the attitude of a real satellite: CBERS-2 (China Brazil Earth Resources Satellite). This satellite was launched in 2003 and were controlled and operated in turns by China (Xi'an Control Center) and Brazil (Satellite Control Center). Its orbit is near polar sun-synchronous with an altitude of 778km, crossing Equator at 10:30am in descending direction, frozen perigee at 90 degrees, and providing global coverage of the world every 26 days. The attitude dynamical model is described by nonlinear equations involving the Euler angles. The attitude sensors available are two DSS (Digital Sun Sensor), two IRES (Infra-Red Earth Sensor), and one triad of mechanical gyros. The two IRES give direct measurements of roll and pitch angles with a certain level of error. The two DSS are nonlinear functions of roll, pitch, and yaw attitude angles. The gyros furnish the angular measurements in the body frame reference system. Gyros are very important sensors, as they provide direct incremental angles or angular velocities. They can sense instantaneous variations of nominal velocities. An important feature is that it allows the replacement of complex models (different torques acting on the space environment) by using their measurements to turn the dynamical equations into simple kinematic equations. However gyros present several sources of error of which the drift is the most troublesome. Such drifts yield along time an accumulation of errors which must be accounted for in the attitude determination process. Herein one proposes to estimate the attitude and the drift of the gyros using the Least Squares Method. Results show that one can reach accuracies in attitude determination within the prescribed requirements, besides providing estimates of the gyro drifts which can be further used to enhance the gyro error model.
CONASAT is being designed to gather environmental data like rain volume, temperature, humidity, a... more CONASAT is being designed to gather environmental data like rain volume, temperature, humidity, air pollution, ocean streams, environmental hazards, etc. collected and transmitted to satellite by remote platforms on ground, and to retransmit them to the mission center. At least two identical satellites shall be launched, and, together with their antecessors SCD1 and SCD2 (Data Collecting Satellites 1 and 2, from Brazil) launched in 1993 and 1998, respectively, and still operating, they will provide large temporal resolution for environmental monitoring. In order to keep the costs low, CONASAT shall be based on CubeSat technologies. However, the large power required by onboard data transponder implied an arrangement of 8 CubeSat units in a single cubic one, with 230 mm size. All internal subsystems shall be duplicated in cold redundancy, in order to assure the reliability. In addition, in order to fulfill the power requirements, the attitude shall be Earth pointed, since the payload ...
This work describes the attitude determination and the gyros drift estimation using the Regulariz... more This work describes the attitude determination and the gyros drift estimation using the Regularized Particle Filter (RPF) with Roughening and Unscented Kalman Filter (UKF) for nonlinear systems. The Particle Filter has some similarities with the Unscented Kalman Filter which transforms a set of points (cloud) through known nonlinear equations and combines the results to estimate the moments (mean and covariance) of the state. However, in the Particle Filter the points (particles cloud) are chosen randomly, whereas in the Unscented Kalman Filter the points are carefully picked up based on a very specific criterion. In this way, the number of points (particles) used in a Particle Filter generally needs to be much greater than the number of points (sigma-points) in an Unscented Kalman Filter. The application of the Regularized Particle Filter in this work uses simulated measurements of a real satellite CBERS-2 (China Brazil Earth Resources Satellite 2) which was at a polar sun-synchron...
Nowadays, satellites with rigid and flexible components are increasingly being extended to advanc... more Nowadays, satellites with rigid and flexible components are increasingly being extended to advanced applications, where solar panels, communication antennas, telescopic structures and robotics arms must achieve better pointing accuracy requirements. On the other hand, the guaranty of the controller performance depends not only on its good design but also on the knowledge of all states to be fed-back in order to improve the overall control system efficiency. As a result, control system design methods that include parameters identification and/or states estimation need more investigation to know their capability and limitations. In this paper, a Kalman filter methodology is used to recover the unmeasured states (elastic displacement and its rates) considering that only the states associated with rigid motion are measured (angle and angular velocity). In order to investigate the robustness of the filter, the Kalman filter methology is tested with a satellite model compose of one, two and three flexible modes. One observes that the fidelity of the estimation process increase with the inclusion of more modes in the satellite model, which in turn not affect the performance of the Kalman filter procedure.
Acta Astronautica, 2003
ABSTRACT A simplified and compact algorithm with low computational cost providing an accuracy aro... more ABSTRACT A simplified and compact algorithm with low computational cost providing an accuracy around tens of meters for artificial satellite orbit determination in real-time and on-board is developed in this work. The state estimation method is the extended Kalman filter. The Cowell's method is used to propagate the state vector, through a simple Runge–Kutta numerical integrator of fourth order with fixed step size. The modeled forces are due to the geopotential up to 50th order and degree of JGM-2 model. To time-update the state error covariance matrix, it is considered a simplified force model. In other words, in computing the state transition matrix, the effect of J2 (Earth flattening) is analytically considered, which unloads dramatically the processing time. In the measurement model, the single frequency GPS pseudorange is used, considering the effects of the ionospheric delay, clock offsets of the GPS and user satellites, and relativistic effects. To validate this model, real live data are used from Topex/Poseidon satellite and the results are compared with the Topex/Poseidon Precision Orbit Ephemeris (POE) generated by NASA/JPL, for several test cases. It is concluded that this compact algorithm enables accuracies of tens of meters with such simplified force model, analytical approach for computing the transition matrix, and a cheap GPS receiver providing single frequency pseudorange measurements.
Advances in Space Research, 2005
An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the in... more An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the influence of the residual magnetic torques. Assuming an inclined dipole model for the EarthÕs magnetic field, an analytical averaging method is applied to obtain the mean residual torque every orbital period. The orbit mean anomaly is utilized to compute the average components of residual torque in the spacecraft body frame reference system. The theory is developed for time variations in the orbital elements, and non-circular orbits, giving rise to many curvature integrals. It is observed that the residual magnetic torque does not have component along the spin axis. The inclusion of this torque on the rotational motion differential equations of a spin stabilized spacecraft yields conditions to derive an analytical solution. The solution shows that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spin axis of the spacecraft.
The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artifi... more The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite China Brazil Earth Resources Satellite. The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.
Optical System Alignment and Tolerancing II, 2008
High image quality and complex, refractive optical systems, as those used in remote sensing appli... more High image quality and complex, refractive optical systems, as those used in remote sensing applications, are, in general, very difficult to be manufactured with the required performance. This can be charged to the high sensitivity of such systems to the fabrication tolerances, mainly concerning the relative alignment of the optical components with respect to each other. When the system does not achieve the expected quality, the puzzle is to identify where the problems lies. This is even worsened when the number of optical elements becomes high. Due to these facts, some misalignment characterization and estimation techniques based on Bayesian estimators and wavefront measurements have been proposed in the literature. This paper is the result of a deep study and investigation of these techniques, with emphasis on an application to an intentionally simple system for the sake of illustration that highlights conceptual issues that could be extended to more realistic, complex optical systems. With this purpose, the sensitivity of the wavefront Zernike coefficients to the misalignment parameters, its use in a parameter estimator design that includes nonlinear terms, the study of the system observability, and a statistical analysis of the estimator performance considering the observation noise are addressed in details. Numerical simulation results for the simple system are shown. We also present insights on how to apply the technique to the alignment of a 11-lens optical system used in the Brazilian remote sensing camera MUX, that will fly on-board the upcoming Sino-Brazilian satellites CBERS 3&4.
This paper presents some approaches to the design and some experimental results for a reaction wh... more This paper presents some approaches to the design and some experimental results for a reaction wheel (RW) current and speed control loops. Reaction wheels are largely employed in satellite attitude control due to its large range of torque capability, small power consumption and high reliability. However, to achieve such performance the RW design shall deal with several restrictions, such as to support the space environment hazards (radiation, vacuum, high and fast temperature variation), and launch requirements (vibration, noise and choke). In this work some experimental results of an air-bearing table attitude control equipped with a Fiber Optics Gyro (FOG), a reaction wheel and a small fan will be presented. The RW is controlled by speed reference, and a second speed mode control similar to the first one was implemented in an external computer. Both were then compared by means of the airbearing attitude control performance during the wheel zero-speed crossing. The results showed that the controllers have similar performance, as expected, and the maximum attitude error remained below 0.08 degrees, which attends the attitude requirements of Earth pointing satellites. 11 th International Conference on Vibration Problems Z. Dimitrovová et al. (eds.
Anais do 2º Congresso Aeroespacial Brasileiro, 2019
Resumo. A proposta deste trabalhoé estudar o comportamento do Filtro de Kalman Unscented (FKU) ut... more Resumo. A proposta deste trabalhoé estudar o comportamento do Filtro de Kalman Unscented (FKU) utilizando os parâmetros modificados de Rodrigues (PMR), quando dados reais de sensores que estãoà bordo do satélite CBERS-2B (China Brazil Earth Resources Satellite) alimentam o estimador.
An artificial satellite subject to the attraction of the Earth is disturbed due to nonspherical d... more An artificial satellite subject to the attraction of the Earth is disturbed due to nonspherical distribution and non-symmetrical Earth mass. This uneven distribution of mass is expressed by the so-called spherical harmonic coefficients of the Earth potential. For a faster computation, the acceleration derived from the potential is obtained by a series expansion in terms of these harmonics, the fully normalized Legendre polynomials and their derivatives, and several recursions associated with the longitude, geocentric latitude and altitude of the center of mass of the satellite. This paper analyzes the detailed aspects of disturbances in artificial satellites, related with the modeling of the Earth's gravitational potential as well as numerical implementation of a recursive algorithm to calculate the acceleration of the geopotential based on the Clenshaw summation. In general, one uses recursive equations of high degree and order to calculate the Legendre polynomials in order to obtain faster processing and numerical accuracy. However, the recursions can yield numerical errors at each step of the recursion so that higher orders and degrees of harmonics, the accumulated error may be quite pronounced. The computational implementation of the algorithm is carried out by a PC computer. With the implementation of this algorithm it is possible to calculate the geopotential acceleration for different orbits and different situations. Such approach aims at mitigating the numerical problems arising from usage of extended series expansion when computing recursively the Legendre polynomials. Once the favorable numerical properties are proven, the algorithm can be used in the solution of practical problems of orbital space mechanics and for the Brazilian Space Mission.
This paper presents some approaches to the design and some experimental results for a reaction wh... more This paper presents some approaches to the design and some experimental results for a reaction wheel (RW) current and speed control loops. Reaction wheels are largely employed in satellite attitude control due to its large range of torque capability, small power consumption and high reliability. However, to achieve such performance the RW design shall deal with several restrictions, such as to support the space environment hazards (radiation, vacuum, high and fast temperature variation), and launch requirements (vibration, noise and choke). In this work some experimental results of an air-bearing table attitude control equipped with a Fiber Optics Gyro (FOG), a reaction wheel and a small fan will be presented. The RW is controlled by speed reference, and a second speed mode control similar to the first one was implemented in an external computer. Both were then compared by means of the airbearing attitude control performance during the wheel zero-speed crossing. The results showed t...
This work is applied to the dynamics of rotational motion of artificial satellites, that is, its ... more This work is applied to the dynamics of rotational motion of artificial satellites, that is, its orientation (attitude) with respect to an inertial reference system. The attitude determination involves approaches of nonlinear estimation techniques, which knowledge is essential to the safety and control of the satellite and payload. Here one focuses on determining the attitude of a real satellite: CBERS-2 (China Brazil Earth Resources Satellite). This satellite was launched in 2003 and were controlled and operated in turns by China (Xi'an Control Center) and Brazil (Satellite Control Center). Its orbit is near polar sun-synchronous with an altitude of 778km, crossing Equator at 10:30am in descending direction, frozen perigee at 90 degrees, and providing global coverage of the world every 26 days. The attitude dynamical model is described by nonlinear equations involving the Euler angles. The attitude sensors available are two DSS (Digital Sun Sensor), two IRES (Infra-Red Earth Sensor), and one triad of mechanical gyros. The two IRES give direct measurements of roll and pitch angles with a certain level of error. The two DSS are nonlinear functions of roll, pitch, and yaw attitude angles. The gyros furnish the angular measurements in the body frame reference system. Gyros are very important sensors, as they provide direct incremental angles or angular velocities. They can sense instantaneous variations of nominal velocities. An important feature is that it allows the replacement of complex models (different torques acting on the space environment) by using their measurements to turn the dynamical equations into simple kinematic equations. However gyros present several sources of error of which the drift is the most troublesome. Such drifts yield along time an accumulation of errors which must be accounted for in the attitude determination process. Herein one proposes to estimate the attitude and the drift of the gyros using the Least Squares Method. Results show that one can reach accuracies in attitude determination within the prescribed requirements, besides providing estimates of the gyro drifts which can be further used to enhance the gyro error model.
CONASAT is being designed to gather environmental data like rain volume, temperature, humidity, a... more CONASAT is being designed to gather environmental data like rain volume, temperature, humidity, air pollution, ocean streams, environmental hazards, etc. collected and transmitted to satellite by remote platforms on ground, and to retransmit them to the mission center. At least two identical satellites shall be launched, and, together with their antecessors SCD1 and SCD2 (Data Collecting Satellites 1 and 2, from Brazil) launched in 1993 and 1998, respectively, and still operating, they will provide large temporal resolution for environmental monitoring. In order to keep the costs low, CONASAT shall be based on CubeSat technologies. However, the large power required by onboard data transponder implied an arrangement of 8 CubeSat units in a single cubic one, with 230 mm size. All internal subsystems shall be duplicated in cold redundancy, in order to assure the reliability. In addition, in order to fulfill the power requirements, the attitude shall be Earth pointed, since the payload ...
This work describes the attitude determination and the gyros drift estimation using the Regulariz... more This work describes the attitude determination and the gyros drift estimation using the Regularized Particle Filter (RPF) with Roughening and Unscented Kalman Filter (UKF) for nonlinear systems. The Particle Filter has some similarities with the Unscented Kalman Filter which transforms a set of points (cloud) through known nonlinear equations and combines the results to estimate the moments (mean and covariance) of the state. However, in the Particle Filter the points (particles cloud) are chosen randomly, whereas in the Unscented Kalman Filter the points are carefully picked up based on a very specific criterion. In this way, the number of points (particles) used in a Particle Filter generally needs to be much greater than the number of points (sigma-points) in an Unscented Kalman Filter. The application of the Regularized Particle Filter in this work uses simulated measurements of a real satellite CBERS-2 (China Brazil Earth Resources Satellite 2) which was at a polar sun-synchron...
Nowadays, satellites with rigid and flexible components are increasingly being extended to advanc... more Nowadays, satellites with rigid and flexible components are increasingly being extended to advanced applications, where solar panels, communication antennas, telescopic structures and robotics arms must achieve better pointing accuracy requirements. On the other hand, the guaranty of the controller performance depends not only on its good design but also on the knowledge of all states to be fed-back in order to improve the overall control system efficiency. As a result, control system design methods that include parameters identification and/or states estimation need more investigation to know their capability and limitations. In this paper, a Kalman filter methodology is used to recover the unmeasured states (elastic displacement and its rates) considering that only the states associated with rigid motion are measured (angle and angular velocity). In order to investigate the robustness of the filter, the Kalman filter methology is tested with a satellite model compose of one, two and three flexible modes. One observes that the fidelity of the estimation process increase with the inclusion of more modes in the satellite model, which in turn not affect the performance of the Kalman filter procedure.
Acta Astronautica, 2003
ABSTRACT A simplified and compact algorithm with low computational cost providing an accuracy aro... more ABSTRACT A simplified and compact algorithm with low computational cost providing an accuracy around tens of meters for artificial satellite orbit determination in real-time and on-board is developed in this work. The state estimation method is the extended Kalman filter. The Cowell's method is used to propagate the state vector, through a simple Runge–Kutta numerical integrator of fourth order with fixed step size. The modeled forces are due to the geopotential up to 50th order and degree of JGM-2 model. To time-update the state error covariance matrix, it is considered a simplified force model. In other words, in computing the state transition matrix, the effect of J2 (Earth flattening) is analytically considered, which unloads dramatically the processing time. In the measurement model, the single frequency GPS pseudorange is used, considering the effects of the ionospheric delay, clock offsets of the GPS and user satellites, and relativistic effects. To validate this model, real live data are used from Topex/Poseidon satellite and the results are compared with the Topex/Poseidon Precision Orbit Ephemeris (POE) generated by NASA/JPL, for several test cases. It is concluded that this compact algorithm enables accuracies of tens of meters with such simplified force model, analytical approach for computing the transition matrix, and a cheap GPS receiver providing single frequency pseudorange measurements.
Advances in Space Research, 2005
An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the in... more An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the influence of the residual magnetic torques. Assuming an inclined dipole model for the EarthÕs magnetic field, an analytical averaging method is applied to obtain the mean residual torque every orbital period. The orbit mean anomaly is utilized to compute the average components of residual torque in the spacecraft body frame reference system. The theory is developed for time variations in the orbital elements, and non-circular orbits, giving rise to many curvature integrals. It is observed that the residual magnetic torque does not have component along the spin axis. The inclusion of this torque on the rotational motion differential equations of a spin stabilized spacecraft yields conditions to derive an analytical solution. The solution shows that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spin axis of the spacecraft.
The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artifi... more The aim of this work is to test an algorithm to estimate, in real time, the attitude of an artificial satellite using real data supplied by attitude sensors that are on board of the CBERS-2 satellite China Brazil Earth Resources Satellite. The real-time estimator used in this work for attitude determination is the Unscented Kalman Filter. This filter is a new alternative to the extended Kalman filter usually applied to the estimation and control problems of attitude and orbit. This algorithm is capable of carrying out estimation of the states of nonlinear systems, without the necessity of linearization of the nonlinear functions present in the model. This estimation is possible due to a transformation that generates a set of vectors that, suffering a nonlinear transformation, preserves the same mean and covariance of the random variables before the transformation. The performance will be evaluated and analyzed through the comparison between the Unscented Kalman filter and the extended Kalman filter results, by using real onboard data.