Optimization techniques for satellites proximity maneuvers

The main topic of this dissertation is the control optimization problem for satellites Rendezvous and Docking. Saving resources is almost as important as the mission safeness and effectiveness. Three different numerical approaches are developed. The first two techniques deal with realtime and sub-optimal control, generating a reliable control sequence for a chaser spacecraft which eventually docks to a target. The first approach uses dynamic programming to quickly generate a sub-optimal control sequence on a predetermined path to be followed by one of the two vehicles involved into the docking operations. The second method presents a fast direct optimization technique, which was previously validated on real aircraft for trajectory optimization. The third approach aims to take into account the limitations of space qualified hardware, in particular thrusters. The new technique fuses the use of a set of low thrust on-off engines with impulsive-high-thrust engines. The hybrid method here developed combines and customizes different techniques. The relative motion in the above mentioned control strategies is represented by a linear dynamic model. As secondary topic of this dissertation, the use of a genetic algorithm optimizer to find possible conditions under which spacecraft relative motion can be periodic, or at least bounded, is presented. This analysis takes into account the J2 gravity perturbation and some drag effects. The importance of the obtained results directly apply to the problem of formation keeping, as natural dynamics can be exploited to reduce the amount of active control preventing the spacecrafts to drift apart along tim

Understanding the effect of key operational conditions on amino acid acidification for a knowledge-driven protein fermentation

Proteins are a relevant fraction of many organic waste streams which are potential feedstocks for resource recovery processes, such as mixed-culture fermentations. However, limited and contradictory information is available on the conversion of amino acids into volatile fatty acids, as literature has been mostly focusing on the sugar fraction. The present PhD thesis aims to provide knowledge about protein fermentation by identifying and understanding the most influential operational conditions affecting amino acids consumption. The results obtained are useful for process design and optimization as they help to define the operational strategies to steer proteins fermentation towards the desired outcome

Modeling and Estimation of a Continuous Flexible Structure using the Theory of Functional Connections

This talk presents a novel method for modeling and estimating the dynamics of a continuous structure based on a limited number of noisy measurements. The goal is reached using a Kalman filter in synergy with the recently developed mathematical framework known as the Theory of Functional Connections (TFC). The TFC allows to derive a functional expression capable of representing the entire space of the functions that satisfy a given set of linear and, in some cases, nonlinear constraints. The proposed approach exploits the possibilities offered by the TFC to derive an approximated dynamical model for the flexible system using the Lagrangian mechanics. The result is a representation of the structural dynamics using a finite number of states, in contrast to the infinite-dimensional model that would be obtained by application of the traditional continuum mechanics models that are based on sets of partial differential equations. The limited number of states enables the application of the well-known Kalman filter framework to improve the estimation of the displacements and displacement velocities. In addition, the continuous displacement field of the structure can be reconstructed with high fidelity. The theoretical development of the method is presented in relation to the case of a Euler-Bernoulli beam. Finally, the obtained model is used to carry out a simulation campaign aimed at assessing the accuracy, efficiency, and robustness of the proposed method

Optimization techniques for satellites proximity maneuvers

The main topic of this dissertation is the control optimization problem for satellites Rendezvous and Docking. Saving resources is almost as important as the mission safeness and effectiveness. Three different numerical approaches are developed. The first two techniques deal with realtime and sub-optimal control, generating a reliable control sequence for a chaser spacecraft which eventually docks to a target. The first approach uses dynamic programming to quickly generate a sub-optimal control sequence on a predetermined path to be followed by one of the two vehicles involved into the docking operations. The second method presents a fast direct optimization technique, which was previously validated on real aircraft for trajectory optimization. The third approach aims to take into account the limitations of space qualified hardware, in particular thrusters. The new technique fuses the use of a set of low thrust on-off engines with impulsive-high-thrust engines. The hybrid method here developed combines and customizes different techniques. The relative motion in the above mentioned control strategies is represented by a linear dynamic model. As secondary topic of this dissertation, the use of a genetic algorithm optimizer to find possible conditions under which spacecraft relative motion can be periodic, or at least bounded, is presented. This analysis takes into account the J2 gravity perturbation and some drag effects. The importance of the obtained results directly apply to the problem of formation keeping, as natural dynamics can be exploited to reduce the amount of active control preventing the spacecrafts to drift apart along tim

Spacecraft rendezvous by differential drag under uncertainties

At low Earth orbits, differentials in the drag forces between spacecraft can be used for controlling their relative motion in the orbital plane. Current methods for determining the drag force may result in errors due to inaccuracies in the density models and drag coefficients. In this work, a methodology for relative maneuvering of spacecraft based on differential drag, accounting for uncertainties in the drag model, is proposed. A dynamical model composed of the mean semimajor axis and the argument of latitude is used for describing long-range maneuvers. For this model, a linear quadratic regulator is implemented, accounting for the uncertainties in the drag force. The actuation is the pitch angle of the satellites, considering saturation. The control scheme guarantees asymptotic stability of the system up to a certain magnitude of the state vector, which is determined by the uncertainties. Numerical simulations show that the method exhibits consistent robustness to accomplish the maneuvers, even in the presence of realistic modeling of density fields, drag coefficients, the corotation of the atmosphere, and zonal harmonics up to J(8)

Using Machine Learning to Predict Hypervelocity Fragment Propagation of Space Debris Collisions

The future of spaceflight is threatened by the increasing amount of space debris, especially in the near-Earth environment. To continue operations, accurate characterization of hypervelocity fragment propagation following collisions and explosions is imperative. While large debris particles can be tracked by current methods, small particles are often missed. This paper presents a method to estimate fragment fly-out properties, such as fragment, velocity, and mass distributions, using machine learning. Previous work was performed on terrestrial data and associated simulations representing space debris collisions. The fragmentation of high-velocity fragmentation can be modeled by terrestrial fragmentation tests, such as static detonations. Recently, stereoscopic imaging techniques have become an addition to static arena testing. Collecting data with this method provides position vector and mass information faster and more accurately than previous manual-collection methods. Additionally, there is limited space debris data of similar accuracy on individual fragments. Therefore, this imaging technique was used as the primary collection method for the previous research data. Now, two-line element (TLE) sets for Iridium 33 are also used. Machine learning methodologies are leveraged to predict fragmentation fly-out from the collision event with Cosmos 2251. First, gaussian mixture models (GMMs) are used to model the probability distribution of the particles for a given desired characteristic at Julian dates following the event. Once this training data is generated, regression techniques can be used to predict these characteristics. K-nearest neighbor (K-NN) regressors are used to estimate the spatial distribution of the satellite fragments. Monte Carlo simulations are then used to validate the results, finding that this technique accurately estimates the total number of fragments expected to intersect a region of interest at a given time. Following this work, the same technique can be used to estimate the velocity and mass distributions of the debris. This information can then be used to estimate the kinetic energy of the particle and classify it to avoid future debris collisions

State Space Modeling and Estimation of Flexible Structure Using the Theory of Functional Connections

In this work, we present a novel method to model the dynamics of a continuous structure based on measurements taken at discrete points. The method is conceived to provide new instruments to address the problem of flexible dynamics modeling in a spacecraft, where an effective mathematical representation of the non-rigid behavior of the is of critical importance in the design of an effective and reliable attitude estimation and control system. Both the measurements and the model that describes the structure can be affected by uncertainty. The purpose of the developed method is to estimate the position and the velocity of any point of the physical domain relying on a limited number of measurements while filtering out the noise. To this aim, the well-assessed Kalman filter is used in synergy with the recently developed Theory of Functional Connections (TFC). This is a mathematical framework to perform functional interpolation with applications in many fields being currently discovered and investigated. Initially, an algorithm for the solution of the corresponding static problem was developed based on the TFC; the results of the tests were promising and the approach presented in this work constitutes an effort to extend the idea to the dynamic case. In the proposed method, the continuous structure is approximated by the TFC constrained expression, while the system state variables are defined as the coefficients used to represent the free function in a basis of orthogonal polynomials. This leads to a system that, despite being continuous and thus formed of an infinite number of material points, is modeled using a finite number of state variables allowing for the use of Kalman filter to deal with the uncertainties intrinsic in both the modeling and measurements. This is accomplished by exploiting the original structure model Differential Equation(s) to obtain a process model for the filter and using the constrained expression itself as the measurement model. Then the Kalman filter algorithm is applied and the a posteriori estimates of the state variables (that is the free function coefficients) can be used to build the TFC expression that approximates the instantaneous shape of the structure, thus enabling the evaluation of the displacement at any point of the domain. The power of the proposed method is twofold. First, an estimate of the displacements of all the points is obtained based on a limited number of noisy measurements. Second, the relation between discrete measurements and continuous displacement field always accounts for the real physics of the problem. In this paper, the theoretical developments of the proposed approach are shown along with the results of numerical simulations showing the effectiveness of the method in estimating the actual dynamics of a Euler-Bernoulli beam. The technique yielded good results both for the free response and in the case of a forcing input to the system

Solar Sailing Adaptive Control Using Integral Concurrent Learning for Solar Flux Estimation

In the interest of exploiting natural forces for propellant-less spacecraft missions, this investigation proposes an adaptive control strategy to account for unknown parameters in the dynamic modeling of a reflectivity-controlled solar sail spacecraft. A Lyapunov-based control law along with integral concurrent learning is suggested to accomplish and prove global exponential tracking of the estimated parameters and states of interest, without satisfying the common persistence of excitation condition, which in most nonlinear systems cannot be guaranteed a priori. This involves estimating the solar flux or irradiance from the Sun to account for uncertainty and variation over time in this value. To illustrate potential applications, two missions are considered: (1) a geostationary debris removal case and (2) an Earth-Mars interplanetary transfer orbit following a logarithmic spiral reference trajectory. The proposed formulation demonstrates the benefit of estimating the solar flux using integral concurrent learning. Results are compared to trajectories with no estimation to illustrate the need to account for the actual solar flux

Dual Quaternion Relative Dynamics for Gravity Recovery Missions

A dual quaternion modeling approach is compared to traditional modeling methods for formation flying spacecraft utilized for gravity recovery missions. A modeling method that has traditionally been used for gravity recovery missions is presented which models the motion of two formation flying spacecraft and a test mass. This is followed by the dual quaternion-based formulation for the equations of motion of the twelve degree-of-freedom coupled relative dynamics of formation flying spacecraft and a test mass. Lastly, utilizing data products from the Gravity Recovery and Climate Experiment Follow-On mission, a comparison of these two modeling methods is presented which proves the advantage of the proposed dual quaternion-based modeling approach

Drag De-Orbit Device: A New Standard Re-Entry Actuator for CubeSats

With the advent of CubeSats, research in Low Earth Orbit (LEO) becomes possible for universities and small research groups. Only a handful of launch sites can be used, due to geographical and political restrictions. As a result, common orbits in LEO are becoming crowded due to the additional launches made possible by low-cost access to space. CubeSat design principles require a maximum of a 25-year orbital lifetime in an effort to reduce the total number of spacecraft in orbit at any time. Additionally, since debris may survive re-entry, it is ideal to de-orbit spacecraft over unpopulated areas to prevent casualties. The Drag Deorbit Device (D3) is a self-contained targeted re-entry subsystem intended for CubeSats. By varying the cross-wind area, the atmospheric drag can be varied in such a way as to produce desired maneuvers. The D3 is intended to be used to remove spacecraft from orbit to reach a desired target interface point. Additionally, attitude stabilization is performed by the D3 prior to deployment and can replace a traditional ADACS on many missions.This paper presents the hardware used in the D3 and operation details. Four stepper-driven, repeatedly retractable booms are used to modify the cross-wind area of the D3 and attached spacecraft. Five magnetorquers (solenoids) over three axes are used to damp rotational velocity. This system is expected to be used to improve mission flexibility and allow additional launches by reducing the orbital lifetime of spacecraft.The D3 can be used to effect a re-entry to any target interface point, with the orbital inclination limiting the maximum latitude. In the chance that the main spacecraft fails, a timer will automatically deploy the booms fully, ensuring the spacecraft will at the minimum reenter the atmosphere in the minimum possible time, although not necessarily at the desired target interface point. Although this does not reduce the risk of casualties, the 25-year lifetime limit is still respected, allowing a reduction of the risk associated with a hardware failure