Troposphere Calibration Techniques for Deep Space Probe Tracking

Ground-based Earth troposphere calibration systems play an important role in planetary exploration, especially to carry out radio science experiments aimed at the estimation of planetary gravity fields. In these experiments, the main observable is the spacecraft (S/C) range rate, measured from the Doppler shift of an electromagnetic wave transmitted from ground, received by the spacecraft and coherently retransmitted back to ground. If the solar corona and interplanetary plasma noise is already removed from Doppler data, the Earth troposphere remains one of the main error sources in tracking observables. Current Earth media calibration systems at NASA’s Deep Space Network (DSN) stations are based upon a combination of weather data and multidirectional, dual frequency GPS measurements acquired at each station complex. In order to support Cassini’s cruise radio science experiments, a new generation of media calibration systems were developed, driven by the need to achieve the goal of an end-to-end Allan deviation of the radio link in the order of 3×〖10〗^(-15) at 1000 s integration time. The future ESA’s Bepi Colombo mission to Mercury carries scientific instrumentation for radio science experiments (a Ka-band transponder and a three-axis accelerometer) which, in combination with the S/C telecommunication system (a X/X/Ka transponder) will provide the most advanced tracking system ever flown on an interplanetary probe. Current error budget for MORE (Mercury Orbiter Radioscience Experiment) allows the residual uncalibrated troposphere to contribute with a value of 8×〖10〗^(-15) to the two-way Allan deviation at 1000 s integration time. The current standard ESA/ESTRACK calibration system is based on a combination of surface meteorological measurements and mathematical algorithms, capable to reconstruct the Earth troposphere path delay, leaving an uncalibrated component of about 1-2% of the total delay. In order to satisfy the stringent MORE requirements, the short time-scale variations of the Earth troposphere water vapor content must be calibrated at ESA deep space antennas (DSA) with more precise and stable instruments (microwave radiometers). In parallel to this high performance instruments, ESA ground stations should be upgraded to media calibration systems at least capable to calibrate both troposphere path delay components (dry and wet) at sub-centimetre level, in order to reduce S/C navigation uncertainties. The natural choice is to provide a continuous troposphere calibration by processing GNSS data acquired at each complex by dual frequency receivers already installed for station location purposes. The work presented here outlines the troposphere calibration technique to support both Deep Space probe navigation and radio science experiments. After an introduction to deep space tracking techniques, observables and error sources, in Chapter 2 the troposphere path delay is widely investigated, reporting the estimation techniques and the state of the art of the ESA and NASA troposphere calibrations. Chapter 3 deals with an analysis of the status and the performances of the NASA Advanced Media Calibration (AMC) system referred to the Cassini data analysis. Chapter 4 describes the current release of a developed GNSS software (S/W) to estimate the troposphere calibration to be used for ESA S/C navigation purposes. During the development phase of the S/W a test campaign has been undertaken in order to evaluate the S/W performances. A description of the campaign and the main results are reported in Chapter 5. Chapter 6 presents a preliminary analysis of microwave radiometers to be used to support radio science experiments. The analysis has been carried out considering radiometric measurements of the ESA/ESTEC instruments installed in Cabauw (NL) and compared with the requirements of MORE. Finally, Chapter 7 summarizes the results obtained and defines some key technical aspects to be evaluated and taken into account for the development phase of future instrumentation.

Technologies for Ambient intelligence: from Smart Objects to Sensor Networks

n the last few years, the vision of our connected and intelligent information society has evolved to embrace novel technological and research trends. The diffusion of ubiquitous mobile connectivity and advanced handheld portable devices, amplified the importance of the Internet as the communication backbone for the fruition of services and data. The diffusion of mobile and pervasive computing devices, featuring advanced sensing technologies and processing capabilities, triggered the adoption of innovative interaction paradigms: touch responsive surfaces, tangible interfaces and gesture or voice recognition are finally entering our homes and workplaces. We are experiencing the proliferation of smart objects and sensor networks, embedded in our daily living and interconnected through the Internet. This ubiquitous network of always available interconnected devices is enabling new applications and services, ranging from enhancements to home and office environments, to remote healthcare assistance and the birth of a smart environment. This work will present some evolutions in the hardware and software development of embedded systems and sensor networks. Different hardware solutions will be introduced, ranging from smart objects for interaction to advanced inertial sensor nodes for motion tracking, focusing on system-level design. They will be accompanied by the study of innovative data processing algorithms developed and optimized to run on-board of the embedded devices. Gesture recognition, orientation estimation and data reconstruction techniques for sensor networks will be introduced and implemented, with the goal to maximize the tradeoff between performance and energy efficiency. Experimental results will provide an evaluation of the accuracy of the presented methods and validate the efficiency of the proposed embedded systems.

Context detection and abstraction in smart environments

Context-aware computing is currently considered the most promising approach to overcome information overload and to speed up access to relevant information and services. Context-awareness may be derived from many sources, including user profile and preferences, network information, sensor analysis; usually context-awareness relies on the ability of computing devices to interact with the physical world, i.e. with the natural and artificial objects hosted within the "environment”. Ideally, context-aware applications should not be intrusive and should be able to react according to user’s context, with minimum user effort. Context is an application dependent multidimensional space and the location is an important part of it since the very beginning. Location can be used to guide applications, in providing information or functions that are most appropriate for a specific position. Hence location systems play a crucial role. There are several technologies and systems for computing location to a vary degree of accuracy and tailored for specific space model, i.e. indoors or outdoors, structured spaces or unstructured spaces. The research challenge faced by this thesis is related to pedestrian positioning in heterogeneous environments. Particularly, the focus will be on pedestrian identification, localization, orientation and activity recognition. This research was mainly carried out within the “mobile and ambient systems” workgroup of EPOCH, a 6FP NoE on the application of ICT to Cultural Heritage. Therefore applications in Cultural Heritage sites were the main target of the context-aware services discussed. Cultural Heritage sites are considered significant test-beds in Context-aware computing for many reasons. For example building a smart environment in museums or in protected sites is a challenging task, because localization and tracking are usually based on technologies that are difficult to hide or harmonize within the environment. Therefore it is expected that the experience made with this research may be useful also in domains other than Cultural Heritage. This work presents three different approaches to the pedestrian identification, positioning and tracking: Pedestrian navigation by means of a wearable inertial sensing platform assisted by the vision based tracking system for initial settings an real-time calibration; Pedestrian navigation by means of a wearable inertial sensing platform augmented with GPS measurements; Pedestrian identification and tracking, combining the vision based tracking system with WiFi localization. The proposed localization systems have been mainly used to enhance Cultural Heritage applications in providing information and services depending on the user’s actual context, in particular depending on the user’s location.

Smart Sensors For Interoperable Smart Environment

Smart Environments are currently considered a key factor to connect the physical world with the information world. A Smart Environment can be defined as the combination of a physical environment, an infrastructure for data management (called Smart Space), a collection of embedded systems gathering heterogeneous data from the environment and a connectivity solution to convey these data to the Smart Space. With this vision, any application which takes advantages from the environment could be devised, without the need to directly access to it, since all information are stored in the Smart Space in a interoperable format. Moreover, according to this vision, for each entity populating the physical environment, i.e. users, objects, devices, environments, the following questions can be arise: “Who?”, i.e. which are the entities that should be identified? “Where?” i.e. where are such entities located in physical space? and “What?” i.e. which attributes and properties of the entities should be stored in the Smart Space in machine understandable format, in the sense that its meaning has to be explicitly defined and all the data should be linked together in order to be automatically retrieved by interoperable applications. Starting from this the location detection is a necessary step in the creation of Smart Environments. If the addressed entity is a user and the environment a generic environment, a meaningful way to assign the position, is through a Pedestrian Tracking System. In this work two solution for these type of system are proposed and compared. One of the two solution has been studied and developed in all its aspects during the doctoral period. The work also investigates the problem to create and manage the Smart Environment. The proposed solution is to create, by means of natural interactions, links between objects and between objects and their environment, through the use of specific devices, i.e. Smart Objects

Visual scanning in sports actions: comparison between soccer goalkeepers and judo fighters

Visual search and oculomotor behaviour are believed to be very relevant for athlete performance, especially for sports requiring refined visuo-motor coordination skills. Modern coaches believe that a correct visuo-motor strategy may be part of advanced training programs. In this thesis two experiments are reported in which gaze behaviour of expert and novice athletes were investigated while they were doing a real sport specific task. The experiments concern two different sports: judo and soccer. In each experiment, number of fixations, fixation locations and mean fixation duration (ms) were considered. An observational analysis was done at the end of the paper to see perceptual differences between near and far space. Purpose: The aim of the judo study was to delineate differences in gaze behaviour characteristics between a population of athletes and one of non athletes. Aspects specifically investigated were: search rate, search order and viewing time across different conditions in a real-world task. The second study was aimed at identifying gaze behaviour in varsity soccer goalkeepers while facing a penalty kick executed with instep and inside foot. Then an attempt has been done to compare the gaze strategies of expert judoka and soccer goalkeepers in order to delineate possible differences related to the different conditions of reacting to events occurring in near (peripersonal) or far (extrapersonal) space. Judo Methods: A sample of 9 judoka (black belt) and 11 near judoka (white belt) were studied. Eye movements were recorded at 500Hz using a video based eye tracker (EyeLink II). Each subject participated in 40 sessions for about 40 minutes. Gaze behaviour was considered as average number of locations fixated per trial, the average number of fixations per trial, and mean fixation duration. Soccer Methods: Seven (n = 7) intermediate level male volunteered for the experiment. The kickers and goalkeepers, had at least varsity level soccer experience. The vision-in-action (VIA) system (Vickers 1996; Vickers 2007) was used to collect the coupled gaze and motor behaviours of the goalkeepers. This system integrated input from a mobile eye tracking system (Applied Sciences Laboratories) with an external video of the goalkeeper’s saving actions. The goalkeepers took 30 penalty kicks on a synthetic pitch in accordance with FIFA (2008) laws. Judo Results: Results indicate that experts group differed significantly from near expert for fixations duration, and number of fixations per trial. The expert judokas used a less exhaustive search strategy involving fewer fixations of longer duration than their novice counterparts and focused on central regions of the body. The results showed that in defence and attack situation expert group did a greater number of transitions with respect to their novice counterpart. Soccer Results: We found significant main effect for the number of locations fixated across outcome (goal/save) but not for foot contact (instep/inside). Participants spent more time fixating the areas in instep than inside kick and in goal than in save situation. Mean and standard error in search strategy as a result of foot contact and outcome indicate that the most gaze behaviour start and finish on ball interest areas. Conclusions: Expert goalkeepers tend to spend more time in inside-save than instep-save penalty, differences that was opposite in scored penalty kick. Judo results show that differences in visual behaviour related to the level of expertise appear mainly when the test presentation is continuous, last for a relatively long period of time and present a high level of uncertainty with regard to the chronology and the nature of events. Expert judoist performers “anchor” the fovea on central regions of the scene (lapel and face) while using peripheral vision to monitor opponents’ limb movements. The differences between judo and soccer gaze strategies are discussed on the light of physiological and neuropsychological differences between near and far space perception.

Preventing worker’s musculoskeletal disorders with wearable inertial sensors: ergonomics and modelling of physical human-robot interactions

The most widespread work-related diseases are musculoskeletal disorders (MSD) caused by awkward postures and excessive effort to upper limb muscles during work operations. The use of wearable IMU sensors could monitor the workers constantly to prevent hazardous actions, thus diminishing work injuries. In this thesis, procedures are developed and tested for ergonomic analyses in a working environment, based on a commercial motion capture system (MoCap) made of 17 Inertial Measurement Units (IMUs). An IMU is usually made of a tri-axial gyroscope, a tri-axial accelerometer, and a tri-axial magnetometer that, through sensor fusion algorithms, estimates its attitude. Effective strategies for preventing MSD rely on various aspects: firstly, the accuracy of the IMU, depending on the chosen sensor and its calibration; secondly, the correct identification of the pose of each sensor on the worker’s body; thirdly, the chosen multibody model, which must consider both the accuracy and the computational burden, to provide results in real-time; finally, the model scaling law, which defines the possibility of a fast and accurate personalization of the multibody model geometry. Moreover, the MSD can be diminished using collaborative robots (cobots) as assisted devices for complex or heavy operations to relieve the worker's effort during repetitive tasks. All these aspects are considered to test and show the efficiency and usability of inertial MoCap systems for assessing ergonomics evaluation in real-time and implementing safety control strategies in collaborative robotics. Validation is performed with several experimental tests, both to test the proposed procedures and to compare the results of real-time multibody models developed in this thesis with the results from commercial software. As an additional result, the positive effects of using cobots as assisted devices for reducing human effort in repetitive industrial tasks are also shown, to demonstrate the potential of wearable electronics in on-field ergonomics analyses for industrial applications.

Motion control and real-time systems: an approach to trajectory rebuilding in non-deterministic networks

Motion control is a sub-field of automation, in which the position and/or velocity of machines are controlled using some type of device. In motion control the position, velocity, force, pressure, etc., profiles are designed in such a way that the different mechanical parts work as an harmonious whole in which a perfect synchronization must be achieved. The real-time exchange of information in the distributed system that is nowadays an industrial plant plays an important role in order to achieve always better performance, better effectiveness and better safety. The network for connecting field devices such as sensors, actuators, field controllers such as PLCs, regulators, drive controller etc., and man-machine interfaces is commonly called fieldbus. Since the motion transmission is now task of the communication system, and not more of kinematic chains as in the past, the communication protocol must assure that the desired profiles, and their properties, are correctly transmitted to the axes then reproduced or else the synchronization among the different parts is lost with all the resulting consequences. In this thesis, the problem of trajectory reconstruction in the case of an event-triggered communication system is faced. The most important feature that a real-time communication system must have is the preservation of the following temporal and spatial properties: absolute temporal consistency, relative temporal consistency, spatial consistency. Starting from the basic system composed by one master and one slave and passing through systems made up by many slaves and one master or many masters and one slave, the problems in the profile reconstruction and temporal properties preservation, and subsequently the synchronization of different profiles in network adopting an event-triggered communication system, have been shown. These networks are characterized by the fact that a common knowledge of the global time is not available. Therefore they are non-deterministic networks. Each topology is analyzed and the proposed solution based on phase-locked loops adopted for the basic master-slave case has been improved to face with the other configurations.

A dynamical system approach to data assimilation in chaotic models

The Assimilation in the Unstable Subspace (AUS) was introduced by Trevisan and Uboldi in 2004, and developed by Trevisan, Uboldi and Carrassi, to minimize the analysis and forecast errors by exploiting the flow-dependent instabilities of the forecast-analysis cycle system, which may be thought of as a system forced by observations. In the AUS scheme the assimilation is obtained by confining the analysis increment in the unstable subspace of the forecast-analysis cycle system so that it will have the same structure of the dominant instabilities of the system. The unstable subspace is estimated by Breeding on the Data Assimilation System (BDAS). AUS- BDAS has already been tested in realistic models and observational configurations, including a Quasi-Geostrophicmodel and a high dimensional, primitive equation ocean model; the experiments include both fixed and“adaptive”observations. In these contexts, the AUS-BDAS approach greatly reduces the analysis error, with reasonable computational costs for data assimilation with respect, for example, to a prohibitive full Extended Kalman Filter. This is a follow-up study in which we revisit the AUS-BDAS approach in the more basic, highly nonlinear Lorenz 1963 convective model. We run observation system simulation experiments in a perfect model setting, and with two types of model error as well: random and systematic. In the different configurations examined, and in a perfect model setting, AUS once again shows better efficiency than other advanced data assimilation schemes. In the present study, we develop an iterative scheme that leads to a significant improvement of the overall assimilation performance with respect also to standard AUS. In particular, it boosts the efficiency of regime’s changes tracking, with a low computational cost. Other data assimilation schemes need estimates of ad hoc parameters, which have to be tuned for the specific model at hand. In Numerical Weather Prediction models, tuning of parameters — and in particular an estimate of the model error covariance matrix — may turn out to be quite difficult. Our proposed approach, instead, may be easier to implement in operational models.

New functional and biomechanical assessments for the improvement of the surgical navigation systems for joint replacement in the human lower limb

In case of severe osteoarthritis at the knee causing pain, deformity, and loss of stability and mobility, the clinicians consider that the substitution of these surfaces by means of joint prostheses. The objectives to be pursued by this surgery are: complete pain elimination, restoration of the normal physiological mobility and joint stability, correction of all deformities and, thus, of limping. The knee surgical navigation systems have bee developed in computer-aided surgery in order to improve the surgical final outcome in total knee arthroplasty. These systems provide the surgeon with quantitative and real-time information about each surgical action, like bone cut executions and prosthesis component alignment, by mean of tracking tools rigidly fixed onto the femur and the tibia. Nevertheless, there is still a margin of error due to the incorrect surgical procedures and to the still limited number of kinematic information provided by the current systems. Particularly, patello-femoral joint kinematics is not considered in knee surgical navigation. It is also unclear and, thus, a source of misunderstanding, what the most appropriate methodology is to study the patellar motion. In addition, also the knee ligamentous apparatus is superficially considered in navigated total knee arthroplasty, without taking into account how their physiological behavior is altered by this surgery. The aim of the present research work was to provide new functional and biomechanical assessments for the improvement of the surgical navigation systems for joint replacement in the human lower limb. This was mainly realized by means of the identification and development of new techniques that allow a thorough comprehension of the functioning of the knee joint, with particular attention to the patello-femoral joint and to the main knee soft tissues. A knee surgical navigation system with active markers was used in all research activities presented in this research work. Particularly, preliminary test were performed in order to assess the system accuracy and the robustness of a number of navigation procedures. Four studies were performed in-vivo on patients requiring total knee arthroplasty and randomly implanted by means of traditional and navigated procedures in order to check for the real efficacy of the latter with respect to the former. In order to cope with assessment of patello-femoral joint kinematics in the intact and replaced knees, twenty in-vitro tests were performed by using a prototypal tracking tool also for the patella. In addition to standard anatomical and articular recommendations, original proposals for defining the patellar anatomical-based reference frame and for studying the patello-femoral joint kinematics were reported and used in these tests. These definitions were applied to two further in-vitro tests in which, for the first time, also the implant of patellar component insert was fully navigated. In addition, an original technique to analyze the main knee soft tissues by means of anatomical-based fiber mappings was also reported and used in the same tests. The preliminary instrumental tests revealed a system accuracy within the millimeter and a good inter- and intra-observer repeatability in defining all anatomical reference frames. In in-vivo studies, the general alignments of femoral and tibial prosthesis components and of the lower limb mechanical axis, as measured on radiographs, was more satisfactory, i.e. within ±3°, in those patient in which total knee arthroplasty was performed by navigated procedures. As for in-vitro tests, consistent patello-femoral joint kinematic patterns were observed over specimens throughout the knee flexion arc. Generally, the physiological intact knee patellar motion was not restored after the implant. This restoration was successfully achieved in the two further tests where all component implants, included the patellar insert, were fully navigated, i.e. by means of intra-operative assessment of also patellar component positioning and general tibio-femoral and patello-femoral joint assessment. The tests for assessing the behavior of the main knee ligaments revealed the complexity of the latter and the different functional roles played by the several sub-bundles compounding each ligament. Also in this case, total knee arthroplasty altered the physiological behavior of these knee soft tissues. These results reveal in-vitro the relevance and the feasibility of the applications of new techniques for accurate knee soft tissues monitoring, patellar tracking assessment and navigated patellar resurfacing intra-operatively in the contest of the most modern operative techniques. This present research work gives a contribution to the much controversial knowledge on the normal and replaced of knee kinematics by testing the reported new methodologies. The consistence of these results provides fundamental information for the comprehension and improvements of knee orthopedic treatments. In the future, the reported new techniques can be safely applied in-vivo and also adopted in other joint replacements.

Kinematics of the Sicily and Calabria Subduction System from Elastic Block Modeling of GPS Data

We use data from about 700 GPS stations in the EuroMediterranen region to investigate the present-day behavior of the the Calabrian subduction zone within the Mediterranean-scale plates kinematics and to perform local scale studies about the strain accumulation on active structures. We focus attenction on the Messina Straits and Crati Valley faults where GPS data show extentional velocity gradients of ∼3 mm/yr and ∼2 mm/yr, respectively. We use dislocation model and a non-linear constrained optimization algorithm to invert for fault geometric parameters and slip-rates and evaluate the associated uncertainties adopting a bootstrap approach. Our analysis suggest the presence of two partially locked normal faults. To investigate the impact of elastic strain contributes from other nearby active faults onto the observed velocity gradient we use a block modeling approach. Our models show that the inferred slip-rates on the two analyzed structures are strongly impacted by the assumed locking width of the Calabrian subduction thrust. In order to frame the observed local deformation features within the present- day central Mediterranean kinematics we realyze a statistical analysis testing the indipendent motion (w.r.t. the African and Eurasias plates) of the Adriatic, Cal- abrian and Sicilian blocks. Our preferred model confirms a microplate like behaviour for all the investigated blocks. Within these kinematic boundary conditions we fur- ther investigate the Calabrian Slab interface geometry using a combined approach of block modeling and χ2ν statistic. Almost no information is obtained using only the horizontal GPS velocities that prove to be a not sufficient dataset for a multi-parametric inversion approach. Trying to stronger constrain the slab geometry we estimate the predicted vertical velocities performing suites of forward models of elastic dislocations varying the fault locking depth. Comparison with the observed field suggest a maximum resolved locking depth of 25 km.

Subject-specific musculoskeletal models of the lower limbs for the prediction of skeletal loads during motion

The determination of skeletal loading conditions in vivo and their relationship to the health of bone tissues, remain an open question. Computational modeling of the musculoskeletal system is the only practicable method providing a valuable approach to muscle and joint loading analyses, although crucial shortcomings limit the translation process of computational methods into the orthopedic and neurological practice. A growing attention focused on subject-specific modeling, particularly when pathological musculoskeletal conditions need to be studied. Nevertheless, subject-specific data cannot be always collected in the research and clinical practice, and there is a lack of efficient methods and frameworks for building models and incorporating them in simulations of motion. The overall aim of the present PhD thesis was to introduce improvements to the state-of-the-art musculoskeletal modeling for the prediction of physiological muscle and joint loads during motion. A threefold goal was articulated as follows: (i) develop state-of-the art subject-specific models and analyze skeletal load predictions; (ii) analyze the sensitivity of model predictions to relevant musculotendon model parameters and kinematic uncertainties; (iii) design an efficient software framework simplifying the effort-intensive phases of subject-specific modeling pre-processing. The first goal underlined the relevance of subject-specific musculoskeletal modeling to determine physiological skeletal loads during gait, corroborating the choice of full subject-specific modeling for the analyses of pathological conditions. The second goal characterized the sensitivity of skeletal load predictions to major musculotendon parameters and kinematic uncertainties, and robust probabilistic methods were applied for methodological and clinical purposes. The last goal created an efficient software framework for subject-specific modeling and simulation, which is practical, user friendly and effort effective. Future research development aims at the implementation of more accurate models describing lower-limb joint mechanics and musculotendon paths, and the assessment of an overall scenario of the crucial model parameters affecting the skeletal load predictions through probabilistic modeling.

Intraoperative kinematic evaluation with navigation system and postoperative kinematic evaluation with dynamic RSA of total knee arthroplasty

Restoring a correct implant kinematics and providing a good ligament balance and patellar tracking is mandatory to improve clinical and functional outcome after a Total Knee Replacement. Surgical navigation systems are a reliable and accurate tool to help the surgeon in achieving these goals. The aim of the present study was to use navigation system with an intra-operative surgical protocol to evaluate and determine an optimal implant kinematics during a Total Knee Replacement.

Development Of New Toolkits For Orbit Determination Codes For Precise Radio Tracking Experiments

This thesis describes the developments of new models and toolkits for the orbit determination codes to support and improve the precise radio tracking experiments of the Cassini-Huygens mission, an interplanetary mission to study the Saturn system. The core of the orbit determination process is the comparison between observed observables and computed observables. Disturbances in either the observed or computed observables degrades the orbit determination process. Chapter 2 describes a detailed study of the numerical errors in the Doppler observables computed by NASA's ODP and MONTE, and ESA's AMFIN. A mathematical model of the numerical noise was developed and successfully validated analyzing against the Doppler observables computed by the ODP and MONTE, with typical relative errors smaller than 10%. The numerical noise proved to be, in general, an important source of noise in the orbit determination process and, in some conditions, it may becomes the dominant noise source. Three different approaches to reduce the numerical noise were proposed. Chapter 3 describes the development of the multiarc library, which allows to perform a multi-arc orbit determination with MONTE. The library was developed during the analysis of the Cassini radio science gravity experiments of the Saturn's satellite Rhea. Chapter 4 presents the estimation of the Rhea's gravity field obtained from a joint multi-arc analysis of Cassini R1 and R4 fly-bys, describing in details the spacecraft dynamical model used, the data selection and calibration procedure, and the analysis method followed. In particular, the approach of estimating the full unconstrained quadrupole gravity field was followed, obtaining a solution statistically not compatible with the condition of hydrostatic equilibrium. The solution proved to be stable and reliable. The normalized moment of inertia is in the range 0.37-0.4 indicating that Rhea's may be almost homogeneous, or at least characterized by a small degree of differentiation.

Distributed optimization and games over networks: a system theoretical perspective

Several decision and control tasks involve networks of cyber-physical systems that need to be coordinated and controlled according to a fully-distributed paradigm involving only local communications without any central unit. This thesis focuses on distributed optimization and games over networks from a system theoretical perspective. In the addressed frameworks, we consider agents communicating only with neighbors and running distributed algorithms with optimization-oriented goals. The distinctive feature of this thesis is to interpret these algorithms as dynamical systems and, thus, to resort to powerful system theoretical tools for both their analysis and design. We first address the so-called consensus optimization setup. In this context, we provide an original system theoretical analysis of the well-known Gradient Tracking algorithm in the general case of nonconvex objective functions. Then, inspired by this method, we provide and study a series of extensions to improve the performance and to deal with more challenging settings like, e.g., the derivative-free framework or the online one. Subsequently, we tackle the recently emerged framework named distributed aggregative optimization. For this setup, we develop and analyze novel schemes to handle (i) online instances of the problem, (ii) ``personalized'' optimization frameworks, and (iii) feedback optimization settings. Finally, we adopt a system theoretical approach to address aggregative games over networks both in the presence or absence of linear coupling constraints among the decision variables of the players. In this context, we design and inspect novel fully-distributed algorithms, based on tracking mechanisms, that outperform state-of-the-art methods in finding the Nash equilibrium of the game.

Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators

Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh). A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses. In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data. The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC. Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations. By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community.