On the motion planning & control of nonlinear robotic systems

In the last decades, we saw a soaring interest in autonomous robots boosted not only by academia and industry, but also by the ever in- creasing demand from civil users. As a matter of fact, autonomous robots are fast spreading in all aspects of human life, we can see them clean houses, navigate through city traffic, or harvest fruits and vegetables. Almost all commercial drones already exhibit unprecedented and sophisticated skills which makes them suitable for these applications, such as obstacle avoidance, simultaneous localisation and mapping, path planning, visual-inertial odometry, and object tracking. The major limitations of such robotic platforms lie in the limited payload that can carry, in their costs, and in the limited autonomy due to finite battery capability. For this reason researchers start to develop new algorithms able to run even on resource constrained platforms both in terms of computation capabilities and limited types of endowed sensors, focusing especially on very cheap sensors and hardware. The possibility to use a limited number of sensors allowed to scale a lot the UAVs size, while the implementation of new efficient algorithms, performing the same task in lower time, allows for lower autonomy. However, the developed robots are not mature enough to completely operate autonomously without human supervision due to still too big dimensions (especially for aerial vehicles), which make these platforms unsafe for humans, and the high probability of numerical, and decision, errors that robots may make. In this perspective, this thesis aims to review and improve the current state-of-the-art solutions for autonomous navigation from a purely practical point of view. In particular, we deeply focused on the problems of robot control, trajectory planning, environments exploration, and obstacle avoidance.

Closed-loop investigation of the dynamical properties of cardiomyocyte electrophysiology by means of Dynamic clamp and Mathematical modelling

The research field of my PhD concerns mathematical modeling and numerical simulation, applied to the cardiac electrophysiology analysis at a single cell level. This is possible thanks to the development of mathematical descriptions of single cellular components, ionic channels, pumps, exchangers and subcellular compartments. Due to the difficulties of vivo experiments on human cells, most of the measurements are acquired in vitro using animal models (e.g. guinea pig, dog, rabbit). Moreover, to study the cardiac action potential and all its features, it is necessary to acquire more specific knowledge about single ionic currents that contribute to the cardiac activity. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behavior of cardiac cells quite well, the models are computationally demanding for numerical simulations and are very difficult to analyze from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. The results presented in this thesis have confirmed that a close integration of computational modeling and experimental recordings in real myocytes, as performed by dynamic clamp, is a useful tool in enhancing our understanding of various components of normal cardiac electrophysiology, but also arrhythmogenic mechanisms in a pathological condition, especially when fully integrated with experimental data.

Homogenization of nonlinear composites for multiscale analysis

A composite is a material made out of two or more constituents (phases) combined together in order to achieve desirable mechanical or thermal properties. Such innovative materials have been widely used in a large variety of engineering fields in the past decades. The design of a composite structure requires the resolution of a multiscale problem that involves a macroscale (i.e. the structural scale) and a microscale. The latter plays a crucial role in the determination of the material behavior at the macroscale, especially when dealing with constituents characterized by nonlinearities. For this reason, numerical tools are required in order to design composite structures by taking into account of their microstructure. These tools need to provide an accurate yet efficient solution in terms of time and memory requirements, due to the large number of internal variables of the problem. This issue is addressed by different methods that overcome this problem by reducing the number of internal variables. Within this framework, this thesis focuses on the development of a new homogenization technique named Mixed TFA (MxTFA) in order to solve the homogenization problem for nonlinear composites. This technique is based on a mixed-stress variational approach involving self-equilibrated stresses and plastic multiplier as independent variables on the Reference Volume Element (RVE). The MxTFA is developed for the case of elastoplasticity and viscoplasticity, and it is implemented into a multiscale analysis for nonlinear composites. Numerical results show the efficiency of the presented techniques, both at microscale and at macroscale level.

Mars delivery service - development of the electro-mechanical systems of the Sample Fetch Rover for the Mars Sample Return Campaign

This thesis describes the development of the Sample Fetch Rover (SFR), studied for Mars Sample Return (MSR), an international campaign carried out in cooperation between the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The focus of this document is the design of the electro-mechanical systems of the rover. After placing this work into the general context of robotic planetary exploration and summarising the state of the art for what concerns Mars rovers, the architecture of the Mars Sample Return Campaign is presented. A complete overview of the current SFR architecture is provided, touching upon all the main subsystems of the spacecraft. For each area, it is discussed what are the design drivers, the chosen solutions and whether they use heritage technology (in particular from the ExoMars Rover) or new developments. This research focuses on two topics of particular interest, due to their relevance for the mission and the novelty of their design: locomotion and sample acquisition, which are discussed in depth. The early SFR locomotion concepts are summarised, covering the initial trade-offs and discarded designs for higher traverse performance. Once a consolidated architecture was reached, the locomotion subsystem was developed further, defining the details of the suspension, actuators, deployment mechanisms and wheels. This technology is presented here in detail, including some key analysis and test results that support the design and demonstrate how it responds to the mission requirements. Another major electro-mechanical system developed as part of this work is the one dedicated to sample tube acquisition. The concept of operations of this machinery was defined to be robust against the unknown conditions that characterise the mission. The design process led to a highly automated robotic system which is described here in its main components: vision system, robotic arm and tube storage.

Meta-models, environment and layers: agent-oriented engineering of complex systems

Traditional software engineering approaches and metaphors fall short when applied to areas of growing relevance such as electronic commerce, enterprise resource planning, and mobile computing: such areas, in fact, generally call for open architectures that may evolve dynamically over time so as to accommodate new components and meet new requirements. This is probably one of the main reasons that the agent metaphor and the agent-oriented paradigm are gaining momentum in these areas. This thesis deals with the engineering of complex software systems in terms of the agent paradigm. This paradigm is based on the notions of agent and systems of interacting agents as fundamental abstractions for designing, developing and managing at runtime typically distributed software systems. However, today the engineer often works with technologies that do not support the abstractions used in the design of the systems. For this reason the research on methodologies becomes the basic point in the scientific activity. Currently most agent-oriented methodologies are supported by small teams of academic researchers, and as a result, most of them are in an early stage and still in the first context of mostly \academic" approaches for agent-oriented systems development. Moreover, such methodologies are not well documented and very often defined and presented only by focusing on specific aspects of the methodology. The role played by meta- models becomes fundamental for comparing and evaluating the methodologies. In fact a meta-model specifies the concepts, rules and relationships used to define methodologies. Although it is possible to describe a methodology without an explicit meta-model, formalising the underpinning ideas of the methodology in question is valuable when checking its consistency or planning extensions or modifications. A good meta-model must address all the different aspects of a methodology, i.e. the process to be followed, the work products to be generated and those responsible for making all this happen. In turn, specifying the work products that must be developed implies dening the basic modelling building blocks from which they are built. As a building block, the agent abstraction alone is not enough to fully model all the aspects related to multi-agent systems in a natural way. In particular, different perspectives exist on the role that environment plays within agent systems: however, it is clear at least that all non-agent elements of a multi-agent system are typically considered to be part of the multi-agent system environment. The key role of environment as a first-class abstraction in the engineering of multi-agent system is today generally acknowledged in the multi-agent system community, so environment should be explicitly accounted for in the engineering of multi-agent system, working as a new design dimension for agent-oriented methodologies. At least two main ingredients shape the environment: environment abstractions - entities of the environment encapsulating some functions -, and topology abstractions - entities of environment that represent the (either logical or physical) spatial structure. In addition, the engineering of non-trivial multi-agent systems requires principles and mechanisms for supporting the management of the system representation complexity. These principles lead to the adoption of a multi-layered description, which could be used by designers to provide different levels of abstraction over multi-agent systems. The research in these fields has lead to the formulation of a new version of the SODA methodology where environment abstractions and layering principles are exploited for en- gineering multi-agent systems.

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

Classical limit of the Nelson model

Since the development of quantum mechanics it has been natural to analyze the connection between classical and quantum mechanical descriptions of physical systems. In particular one should expect that in some sense when quantum mechanical effects becomes negligible the system will behave like it is dictated by classical mechanics. One famous relation between classical and quantum theory is due to Ehrenfest. This result was later developed and put on firm mathematical foundations by Hepp. He proved that matrix elements of bounded functions of quantum observables between suitable coherents states (that depend on Planck's constant h) converge to classical values evolving according to the expected classical equations when h goes to zero. His results were later generalized by Ginibre and Velo to bosonic systems with infinite degrees of freedom and scattering theory. In this thesis we study the classical limit of Nelson model, that describes non relativistic particles, whose evolution is dictated by Schrödinger equation, interacting with a scalar relativistic field, whose evolution is dictated by Klein-Gordon equation, by means of a Yukawa-type potential. The classical limit is a mean field and weak coupling limit. We proved that the transition amplitude of a creation or annihilation operator, between suitable coherent states, converges in the classical limit to the solution of the system of differential equations that describes the classical evolution of the theory. The quantum evolution operator converges to the evolution operator of fluctuations around the classical solution. Transition amplitudes of normal ordered products of creation and annihilation operators between coherent states converge to suitable products of the classical solutions. Transition amplitudes of normal ordered products of creation and annihilation operators between fixed particle states converge to an average of products of classical solutions, corresponding to different initial conditions.

Modeling and simulations of nanoparticles in liquid crystalline systems

The aim of this work is to investigate, using extensive Monte Carlo computer simulations, composite materials consisting of liquid crystals doped with nanoparticles. These systems are currently of great interest as they offer the possibility of tuning the properties of liquid crystals used in displays and other devices as well as providing a way of obtaining regularly organized systems of nanoparticles exploiting the molecular organization of the liquid crystal medium. Surprisingly enough, there is however a lack of fundamental knowledge on the properties and phase behavior of these hybrid materials, making the route to their application an essentially empirical one. Here we wish to contribute to the much needed rationalization of these systems studying some basic effects induced by different nanoparticles on a liquid crystal host. We investigate in particular the effects of nanoparticle shape, size and polarity as well as of their affinity to the liquid crystal solvent on the stability of the system, monitoring phase transitions, order and molecular organizations. To do this we have proposed a coarse grained approach where nanoparticles are modelled as a suitably shaped (spherical, rod and disk like) collection of spherical Lennard-Jones beads, while the mesogens are represented with Gay-Berne particles. We find that the addition of apolar nanoparticles of different shape typically lowers the nematic–isotropic transition of a non-polar nematic, with the destabilization being greater for spherical nanoparticles. For polar mesogens we have studied the effect of solvent affinity of the nanoparticles showing that aggregation takes places for low solvation values. Interestingly, if the nanoparticles are polar the aggregates contribute to stabilizing the system, compensating the shape effect. We thus find the overall effects on stability to be a delicate balance of often contrasting contributions pointing to the relevance of simulations studies for understanding these complex systems.