One major source of new space debris are spacecraft (S/C) that are not removed from orbit after t... more One major source of new space debris are spacecraft (S/C) that are not removed from orbit after the end of their operational lifetime. Many regulations (e.g. ISO 24113) require the removal of S/C at the end of operation - known as Post-Mission-Disposal (PMD) - with a compliance rate of 90% to ensure that S/C do not become a new source of space debris. An analysis performed by ESA shows that the success rate of PMD in 2013 was in the range of about 50%-60%. The goal of TeSeR (Technology for Self-Removal) is to take the first step towards the development of a costefficient, but highly reliable PMD module. This PMD module is to be attached to the S/C on ground and it shall ensure the PMD of the S/C at the end of the operational lifetime. This PMD module shall be scalable and flexible, thus, enabling the PMD of any future S/C in an Earth orbit. Ultimately, the gap between the required 90% PMD success rate and the current success rate can be closed. The technological enhancements and dev...
The problem of nonlinear filtering represents a crucial issue in celestial mechanics. In this pap... more The problem of nonlinear filtering represents a crucial issue in celestial mechanics. In this paper a high-order filter based on differential algebra is presented. The proposed filtering algorithm is based on nonlinear mapping of statistics and a linear update scheme, in which only the probability density function of the measurement errors are constrained to be Gaussian. No hypothesis on the state probability density function is made. The case of an Earth-orbiting spacecraft in a two-body problem frame is considered as an example to demonstrate the general feature and performance of the filter. A comparison with the extended and unscented Kalman filters is also included.
Nowadays Linear Fractional Transformations (LFT) and the Structured Singular Value (mu) are very ... more Nowadays Linear Fractional Transformations (LFT) and the Structured Singular Value (mu) are very well established concepts for respectively modeling uncertain systems and to perform robust analyses. Despite their ample use in academia and industry during the last 30 years, and the availability of consolidated software toolboxes, their introduction to a new industrial collaborator is not without angst. In this article, the steps followed to transfer this technology to the GNC group at ELV, in charge of the VEGA atmospheric launcher, are presented. The aim of the transfer was to introduce worst-case analysis tools into the VEGA verification and validation process as a complement to the standard LTI gain/phase margin analyses and the nonlinear simulation-based Monte Carlo campaigns. The successful transfer hinged on the reconciliation of the following two facets: (i) the physical behavior of the system with the LFT model capabilities, and (ii) the classical design experience from the VEGA GNC group with the results from the robust mu analyses.
The problem of nonlinear uncertainty propagation represents a crucial issue in celestial mechanic... more The problem of nonlinear uncertainty propagation represents a crucial issue in celestial mechanics. In this paper a method for nonlinear propagation of uncertainties based on differential algebra is presented. Working in the differential algebra framework enables a general approach to nonlinear uncertainty propagation that can provide high estimate accuracy with low computational burden. The nonlinear mapping of the statistics is here shown adopting the two-body problem as working framework, including coordinate system transformations. The general feature of the proposed method is also demonstrated by presenting long-term integrations in a complex dynamical framework, such as the n-body problem or the HANDE model.
The nonlinear filtering problem consists of estimating the state of a nonlinear stochastic system... more The nonlinear filtering problem consists of estimating the state of a nonlinear stochastic system from noisy observation data. Nonlinear filtering plays an important role in various space-related applications, such as vehicle navigation, orbit determination, target tracking, etc. However, estimation in nonlinear systems is extremely difficult. The optimal Bayesian solution to the problem requires the propagation of the full probability density function. However, for most nonlinear models and non-Gaussian noise problems, closed-form analytic expressions for the posterior distributions do not exist in general. Therefore, any practical estimator must use an approximation of some kind. Different types of approximations have been developed. In case of nonlinear filtering problems the most widely used filter is the Extended Kalman Filter (EKF). The EKF belongs to a class of filters called Gaussian filters that provide Gaussian approximation of the filtering and predictive distributions. Higher-order filters as well as all the EKF variations are also included into this class. These filters have been successfully applied to many problems, but in some cases, depending on the nature of the nonlinearities, they diverge or provide poor accuracy. On the other hand, another class of filters, i.e., sequential importance sampling filters, can provide higher accuracy in describing the posterior distribution, but are computationally intensive. In this paper, we introduce a new Gaussian filter based on Differential Algebra (DA) called the DA-based Gaussian Particle Filter (DAGPF). Essentially, the DAGPF solves the prediction problem through Monte Carlo simulation, which approximates the probability distribution by averaging a large set of random samples. Differential algebra can enhance and speed up the approach of classical Monte Carlo simulation by replacing thousands of integrations with fast polynomial evaluations. The statistics derived from the propagated samples is then used to obtain the information required for the measurement update step, which includes the predicted measurement, the covariance matrix between the state and the measurement, the covariance matrix of the measurement, and so on. As the EKF, the DAGPF approximates the posterior distribution by single Gaussians. The filter performance has been critically analysed by numerical simulations. The navigation problem of a spacecraft in LEO is considered as test case. The problem is modelled in the 2-body frame and both the case of linear and nonlinear measurement is considered. Comparisons are made with the EKF, the Unscented Kalman Filter (UKF), and Particle Filter (PF). The paper will show the theoretical approach and discuss the obtained results
In this article, the development of a proper Linear Fractional Transformation model for the robus... more In this article, the development of a proper Linear Fractional Transformation model for the robust analysis of the atmospheric controllers of the European VEGA launcher is presented. By proper it is meant a model that: (i) captures the key launcher's behavior during the ascent atmospheric phase, (ii) has a complexity in terms of number of parameters and repetitions that does not limit the applicability of robust analyses, (iii) can be easily updated with very different trajectory profiles, and (iv) arises from a methodology that is well connected with industrial practice and can be understood and used relatively easy. This last requirement is fundamental to transfer the LFT methodology into the VEGA program, which is critical if robust analysis is to be used within their verification and validation process. The potential of the proposed methodology and the validity of the developed LFT models for robust analysis have been successfully verified using simulation data from three of the four VEGA qualification flights.
This work presents the design of a robust control law, and the related control system architectur... more This work presents the design of a robust control law, and the related control system architecture, for the Vega launcher ballistic phase, taking into account the complete six degrees of freedom dynamics. To gain robustness a non-linear control approach has been preferred: more specifically the Lyapunov's second stability theorem has been exploited, being a very powerful tool to guarantee asymptotic stability of the controlled dynamics. The dynamics of Vega's actuators has also been taken into account. The system performance has been checked and analyzed by numerical simulations run on real mission data for different operational and configuration scenarios, and the effectiveness of the synthesized control highlighted: in particular scenarios including a wide range of composite's inertial configurations performing various typologies of maneuvers have been run. The robustness of the controlled dynamics has been validated by 100 cases Monte Carlo analysis campaign: the containment of the dispersion for the controlled variables -say the composite roll, yaw and pitch angles -confirmed the wide validity and generality of the proposed control law. This paper will show the theoretical approach and discuss the obtained results.
The paper investigates the problem of nonlinear filtering applied to spacecraft navigation. Diffe... more The paper investigates the problem of nonlinear filtering applied to spacecraft navigation. Differential algebraic (DA) techniques are proposed as a valuable tool to implement the higher-order numerical and analytic extended Kalman filters. Working in the DA framework allows us to consistently reduce the required computational effort without losing accuracy. The performance of the proposed filters is assessed on different orbit determination problems with realistic orbit uncertainties. The case of nonlinear measurements is also considered. Numerical simulations show the good performance of the filter in case of both complex dynamics and highly nonlinear measurement problems.
This work presents the design of a robust control law, and the related control system architectur... more This work presents the design of a robust control law, and the related control system architecture, for the Vega launcher ballistic phase, taking into account the complete six degrees of freedom dynamics. To gain robustness a non-linear control approach has been preferred: more specifically the Lyapunov's second stability theorem has been exploited, being a very powerful tool to guarantee asymptotic stability of the controlled dynamics. The dynamics of Vega's actuators has also been taken into account. The system performance has been checked and analyzed by numerical simulations run on real mission data for different operational and configuration scenarios, and the effectiveness of the synthesized control highlighted: in particular scenarios including a wide range of composite's inertial configurations performing various typologies of maneuvers have been run. The robustness of the controlled dynamics has been validated by 100 cases Monte Carlo analysis campaign: the containment of the dispersion for the controlled variables -say the composite roll, yaw and pitch angles -confirmed the wide validity and generality of the proposed control law. This paper will show the theoretical approach and discuss the obtained results.
One major source of new space debris are spacecraft (S/C) that are not removed from orbit after t... more One major source of new space debris are spacecraft (S/C) that are not removed from orbit after the end of their operational lifetime. Many regulations (e.g. ISO 24113) require the removal of S/C at the end of operation - known as Post-Mission-Disposal (PMD) - with a compliance rate of 90% to ensure that S/C do not become a new source of space debris. An analysis performed by ESA shows that the success rate of PMD in 2013 was in the range of about 50%-60%. The goal of TeSeR (Technology for Self-Removal) is to take the first step towards the development of a costefficient, but highly reliable PMD module. This PMD module is to be attached to the S/C on ground and it shall ensure the PMD of the S/C at the end of the operational lifetime. This PMD module shall be scalable and flexible, thus, enabling the PMD of any future S/C in an Earth orbit. Ultimately, the gap between the required 90% PMD success rate and the current success rate can be closed. The technological enhancements and dev...
The problem of nonlinear filtering represents a crucial issue in celestial mechanics. In this pap... more The problem of nonlinear filtering represents a crucial issue in celestial mechanics. In this paper a high-order filter based on differential algebra is presented. The proposed filtering algorithm is based on nonlinear mapping of statistics and a linear update scheme, in which only the probability density function of the measurement errors are constrained to be Gaussian. No hypothesis on the state probability density function is made. The case of an Earth-orbiting spacecraft in a two-body problem frame is considered as an example to demonstrate the general feature and performance of the filter. A comparison with the extended and unscented Kalman filters is also included.
Nowadays Linear Fractional Transformations (LFT) and the Structured Singular Value (mu) are very ... more Nowadays Linear Fractional Transformations (LFT) and the Structured Singular Value (mu) are very well established concepts for respectively modeling uncertain systems and to perform robust analyses. Despite their ample use in academia and industry during the last 30 years, and the availability of consolidated software toolboxes, their introduction to a new industrial collaborator is not without angst. In this article, the steps followed to transfer this technology to the GNC group at ELV, in charge of the VEGA atmospheric launcher, are presented. The aim of the transfer was to introduce worst-case analysis tools into the VEGA verification and validation process as a complement to the standard LTI gain/phase margin analyses and the nonlinear simulation-based Monte Carlo campaigns. The successful transfer hinged on the reconciliation of the following two facets: (i) the physical behavior of the system with the LFT model capabilities, and (ii) the classical design experience from the VEGA GNC group with the results from the robust mu analyses.
The problem of nonlinear uncertainty propagation represents a crucial issue in celestial mechanic... more The problem of nonlinear uncertainty propagation represents a crucial issue in celestial mechanics. In this paper a method for nonlinear propagation of uncertainties based on differential algebra is presented. Working in the differential algebra framework enables a general approach to nonlinear uncertainty propagation that can provide high estimate accuracy with low computational burden. The nonlinear mapping of the statistics is here shown adopting the two-body problem as working framework, including coordinate system transformations. The general feature of the proposed method is also demonstrated by presenting long-term integrations in a complex dynamical framework, such as the n-body problem or the HANDE model.
The nonlinear filtering problem consists of estimating the state of a nonlinear stochastic system... more The nonlinear filtering problem consists of estimating the state of a nonlinear stochastic system from noisy observation data. Nonlinear filtering plays an important role in various space-related applications, such as vehicle navigation, orbit determination, target tracking, etc. However, estimation in nonlinear systems is extremely difficult. The optimal Bayesian solution to the problem requires the propagation of the full probability density function. However, for most nonlinear models and non-Gaussian noise problems, closed-form analytic expressions for the posterior distributions do not exist in general. Therefore, any practical estimator must use an approximation of some kind. Different types of approximations have been developed. In case of nonlinear filtering problems the most widely used filter is the Extended Kalman Filter (EKF). The EKF belongs to a class of filters called Gaussian filters that provide Gaussian approximation of the filtering and predictive distributions. Higher-order filters as well as all the EKF variations are also included into this class. These filters have been successfully applied to many problems, but in some cases, depending on the nature of the nonlinearities, they diverge or provide poor accuracy. On the other hand, another class of filters, i.e., sequential importance sampling filters, can provide higher accuracy in describing the posterior distribution, but are computationally intensive. In this paper, we introduce a new Gaussian filter based on Differential Algebra (DA) called the DA-based Gaussian Particle Filter (DAGPF). Essentially, the DAGPF solves the prediction problem through Monte Carlo simulation, which approximates the probability distribution by averaging a large set of random samples. Differential algebra can enhance and speed up the approach of classical Monte Carlo simulation by replacing thousands of integrations with fast polynomial evaluations. The statistics derived from the propagated samples is then used to obtain the information required for the measurement update step, which includes the predicted measurement, the covariance matrix between the state and the measurement, the covariance matrix of the measurement, and so on. As the EKF, the DAGPF approximates the posterior distribution by single Gaussians. The filter performance has been critically analysed by numerical simulations. The navigation problem of a spacecraft in LEO is considered as test case. The problem is modelled in the 2-body frame and both the case of linear and nonlinear measurement is considered. Comparisons are made with the EKF, the Unscented Kalman Filter (UKF), and Particle Filter (PF). The paper will show the theoretical approach and discuss the obtained results
In this article, the development of a proper Linear Fractional Transformation model for the robus... more In this article, the development of a proper Linear Fractional Transformation model for the robust analysis of the atmospheric controllers of the European VEGA launcher is presented. By proper it is meant a model that: (i) captures the key launcher's behavior during the ascent atmospheric phase, (ii) has a complexity in terms of number of parameters and repetitions that does not limit the applicability of robust analyses, (iii) can be easily updated with very different trajectory profiles, and (iv) arises from a methodology that is well connected with industrial practice and can be understood and used relatively easy. This last requirement is fundamental to transfer the LFT methodology into the VEGA program, which is critical if robust analysis is to be used within their verification and validation process. The potential of the proposed methodology and the validity of the developed LFT models for robust analysis have been successfully verified using simulation data from three of the four VEGA qualification flights.
This work presents the design of a robust control law, and the related control system architectur... more This work presents the design of a robust control law, and the related control system architecture, for the Vega launcher ballistic phase, taking into account the complete six degrees of freedom dynamics. To gain robustness a non-linear control approach has been preferred: more specifically the Lyapunov's second stability theorem has been exploited, being a very powerful tool to guarantee asymptotic stability of the controlled dynamics. The dynamics of Vega's actuators has also been taken into account. The system performance has been checked and analyzed by numerical simulations run on real mission data for different operational and configuration scenarios, and the effectiveness of the synthesized control highlighted: in particular scenarios including a wide range of composite's inertial configurations performing various typologies of maneuvers have been run. The robustness of the controlled dynamics has been validated by 100 cases Monte Carlo analysis campaign: the containment of the dispersion for the controlled variables -say the composite roll, yaw and pitch angles -confirmed the wide validity and generality of the proposed control law. This paper will show the theoretical approach and discuss the obtained results.
The paper investigates the problem of nonlinear filtering applied to spacecraft navigation. Diffe... more The paper investigates the problem of nonlinear filtering applied to spacecraft navigation. Differential algebraic (DA) techniques are proposed as a valuable tool to implement the higher-order numerical and analytic extended Kalman filters. Working in the DA framework allows us to consistently reduce the required computational effort without losing accuracy. The performance of the proposed filters is assessed on different orbit determination problems with realistic orbit uncertainties. The case of nonlinear measurements is also considered. Numerical simulations show the good performance of the filter in case of both complex dynamics and highly nonlinear measurement problems.
This work presents the design of a robust control law, and the related control system architectur... more This work presents the design of a robust control law, and the related control system architecture, for the Vega launcher ballistic phase, taking into account the complete six degrees of freedom dynamics. To gain robustness a non-linear control approach has been preferred: more specifically the Lyapunov's second stability theorem has been exploited, being a very powerful tool to guarantee asymptotic stability of the controlled dynamics. The dynamics of Vega's actuators has also been taken into account. The system performance has been checked and analyzed by numerical simulations run on real mission data for different operational and configuration scenarios, and the effectiveness of the synthesized control highlighted: in particular scenarios including a wide range of composite's inertial configurations performing various typologies of maneuvers have been run. The robustness of the controlled dynamics has been validated by 100 cases Monte Carlo analysis campaign: the containment of the dispersion for the controlled variables -say the composite roll, yaw and pitch angles -confirmed the wide validity and generality of the proposed control law. This paper will show the theoretical approach and discuss the obtained results.
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Papers by Monica Valli