Recent advancements in time-optimal trajectory planning, control, and state estimation for autonomous vehicles have paved the way for the emerging field of autonomous racing. In the last 5-10 years, this form of racing has become a popular and challenging testbed for autonomous driving algorithms, aiming to enhance the safety and performance of future intelligent vehicles. In autonomous racing, the main goal is to develop real-time algorithms capable of autonomously maneuvering a vehicle around a racetrack, even in the presence of moving opponents. However, as a vehicle approaches its handling limits, several challenges arise for online trajectory planning and control. The vehicle dynamics become nonlinear and hard to capture with low-complexity models, while fast re-planning and good generalization capabilities are crucial to execute optimal maneuvers in unforeseen scenarios. These challenges leave several open research questions, three of which will be addressed in this thesis. The first explores developing accurate yet computationally efficient vehicle models for online time-optimal trajectory planning. The second focuses on enhancing learning-based methods for trajectory planning, control, and state estimation, overcoming issues like poor generalization and the need for large amounts of training data. The third investigates the optimality of online-executed trajectories with simplified vehicle models, compared to offline solutions of minimum-lap-time optimal control problems using high-fidelity vehicle models. This thesis consists of four parts, each of which addresses one or more of the aforementioned research questions, in the fields of time-optimal vehicle trajectory planning, control and state estimation. The first part of the thesis presents a novel artificial race driver (ARD), which autonomously learns to drive a vehicle around an obstacle-free circuit, performing online time-optimal vehicle trajectory planning and control. The following research questions are addressed in this part: How optimal is the trajectory executed online by an artificial agent that drives a high-fidelity vehicle model, in comparison with a minimum-lap-time optimal control problem (MLT-OCP), based on the same vehicle model and solved offline? Can the artificial agent generalize to circuits and conditions not seen during training? ARD employs an original neural network with a physics-driven internal structure (PhS-NN) for steering control, and a novel kineto-dynamical vehicle model for time-optimal trajectory planning. A new learning scheme enables ARD to progressively learn the nonlinear dynamics of an unknown vehicle. When tested on a high-fidelity model of a high-performance car, ARD achieves very similar results as an MLT-OCP, based on the same vehicle model and solved offline. When tested on a 1:8 vehicle prototype, ARD achieves similar lap times as an offline optimization problem. Thanks to its physics-driven architecture, ARD generalizes well to unseen circuits and scenarios, and is robust to unmodeled changes in the vehicle’s mass. The second part of the thesis deals with online time-optimal trajectory planning for dynamic obstacle avoidance. The research questions addressed in this part are: Can time-optimal trajectory planning for dynamic obstacle avoidance be performed online and with low computational times? How optimal is the resulting trajectory? Can the planner generalize to unseen circuits and scenarios? At each planning step, the proposed approach builds a tree of time-optimal motion primitives, by performing a sampling-based exploration in a local mesh of waypoints. The novel planner is validated in challenging scenarios with multiple dynamic opponents, and is shown to be computationally efficient, to return near-time-optimal trajectories, and to generalize well to new circuits and scenarios. The third part of the thesis shows an application of time-optimal trajectory planning with optimal control and PhS-NNs in the context of autonomous parking. The research questions addressed in this part are: Can an autonomous parking framework perform fast online trajectory planning and tracking in real-life parking scenarios, such as parallel, reverse and angle parking spots, and unstructured environments? Can the framework generalize to unknown variations in the vehicle’s parameters and road adherence, and operate with measurement noise? The autonomous parking framework employs a novel penalty function for collision avoidance with optimal control, a new warm-start strategy and an original PhS-NN for steering control. The framework executes complex maneuvers in a wide range of parking scenarios, and is validated with a high-fidelity vehicle model. The framework is shown to be robust to variations in the vehicle’s mass and road adherence, and to operate with realistic measurement noise. The fourth and last part of the thesis develops novel kinematics-structured neural networks (KS-NNs) to estimate the vehicle’s lateral velocity, which is a key quantity for time-optimal trajectory planning and control. The KS-NNs are a special type of PhS-NNs: their internal structure is designed to incorporate the kinematic principles, which enhances the generalization capabilities and physical explainability. The research questions addressed in this part are: Can a neural network-based lateral velocity estimator generalize well when tested on a vehicle not used for training? Can the network’s parameters be physically explainable? The approach is validated using an open dataset with two race cars. In comparison with traditional and neural network estimators of the literature, the KS-NNs improve noise rejection, exhibit better generalization capacity, are more sample-efficient, and their structure is physically explainable.

La description détaillée des systèmes désordonnés et vitreux représente un défi central en physique statistique et de la matière condensée, puisqu'à ce jour il n'existe pas de théorie unique et établie permettant de comprendre ces systèmes, pourtant omniprésents.Ce travail de recherche est lié en particulier à l'étude des matériaux vitreux à basse température. Plus précisément, si l'on considère des systèmes formés par un ensemble de particules athermiques avec des interactions répulsives de portée finie, en augmentant la densité, on peut observer une transition dite d'encombrement ("jamming"). Celle-ci consiste en un blocage des degrés de liberté accompagné par une augmentation spectaculaire de la rigidité du matériau.Nous étudierons ce problème à l’aide d’une analogie formelle entre des modèles de sphères et le perceptron, un modèle théorique qui développe une transition d'encombrement et des phénomènes de frustration typiques des systèmes désordonnés.En tant que modèle en champ moyen, il permet d'obtenir des résultats analytiques précis et généralisables à des systèmes à haute dimension.L'enjeu majeur de cette étude est de reconstruire le spectre des modes de vibration et toutes les propriétés pertinentes d'une phase spécifique (correspondant au régime dit des sphères dures).Dans ce cadre, nous dériverons le potentiel effectif en fonction des paramètres d'ordre du modèle et nous montrerons qu'il est dominé à proximité du point de jamming par une interaction logarithmique non triviale, qui clarifiera le lien entre les forces de contact et les distances moyennes entre les particules, dans la région critique et au-delà.Comprendre pleinement la transition d'encombrement et les propriétés du perceptron nous permettra de faire des progrès dans plusieurs domaines reliés. En premier lieu, cela peut conduire à une théorie complète des systèmes amorphes, à la fois en dimension infinie et en dimension finie.De plus, le modèle du perceptron semble avoir un lien étroit avec des problèmes dits de Von Neumann. En effet, les systèmes biologiques et écologiques développent souvent des propriétés liées à une condition pseudo-critique en mettant en oeuvre des mécanismes d'optimisation de ressource-consommation.Est-il possible d'identifier un régime caractérisé par une brisure de symétrie? Quel serait le spectre de fluctuations d'énergie dans ces systèmes?Ce ne sont que quelques-unes des questions auxquelles nous essayerons de répondre dans cette thèse.Cependant, l'approximation de champ moyen peut parfois fournir des informationsincorrectes ou trompeuses, en particulier dans l'étude de certaines transitions de phase et la détermination des dimensions critiques inférieure et supérieure.Afin d'avoir une vue d'ensemble et pouvoir manipuler correctement des systèmes en dimension finie, dans la suite de la thèse nous discuterons comment obtenir un développement perturbatif systématique, applicable à tout modèle, à condition que ce dernier soit défini sur un réseau ou un graphe biparti.Notre motivation est en particulier liée à la possibilité d'étudier certaines transitions de phase du second ordre qui existent sur le réseau de Bethe - c'est-à-dire un réseau en arbre sans boucles dont chaque noeud a une connectivité fixe - mais qui sont qualitativement différentes ou absentes dans le modèle entièrement connecté correspondant. / The detailed description of disordered and glassy systems represents an open problem in statistical physics and condensed matter. As yet, there is no single, well-established theory allowing to understand such systems. The research presented in this thesis is related in particular to the study of glassy materials in the low-temperature regime. More precisely, considering systems formed by athermal particles subject to repulsive short-range interactions, upon progressively increasing the density, a so-called jamming transition can be detected. It entails a freezing of the degrees of freedom and hence a huge increase of the material rigidity.We shall study this problem in view of a formal analogy between sphere models and the perceptron, a theoretical model undergoing a jamming transition and frustration phenomena typical of disordered systems. Being a mean-field model, it allows to obtain exact analytical results, which are generalizable to more complex high-dimensional settings.The main aim is to reconstruct the vibrational spectrum and all the relevant properties of a specific phase of the perceptron, corresponding to the hard-sphere regime.In this framework, we will derive the effective potential as a function of the gaps between and forces among the particles, and we will show that it is dominated by a non-trivial logarithmic interaction near the jamming point. This interaction in turn will clarify the relations existing between the relevant variables of the system, in the critical jamming region and beyond.Understanding the jamming transition and the perceptron properties will allow us to make progress in several related fields. First, this study could lay part of the groundwork towards a complete theory of amorphous systems, in both infinite and finite dimensions. Furthermore, the perceptron model seems to a have a close connection with the so-called Von Neumann problems. Indeed, biological and ecological systems often develop pseudo-critical properties and give rise to general mechanisms of resource-consumption optimisation.Is the identification of a broken symmetry regime possible? What would it yield in terms of the spectrum of the energy fluctuations?These are just a few questions we shall attempt to answer in this context.However, the mean-field approximation can sometimes provide wrong or misleading information, especially in studying certain phase transitions and determining the exact lower and upper critical dimensions. To have a broad perspective and correctly deal with finite-dimensional systems, in the second part of the thesis we will discuss obtaining a systematic perturbative expansion which can be applied to any model, as long as defined on a lattice or a bipartite graph.Our motivation is in particular due to the possibility of studying relevant second-order phase transitions which exist on the Bethe lattice — a lattice with a locally tree-like structure and fixed connectivity for each node — but which are qualitatively different or absent in the corresponding fully-connected version.

Mobile assistive robotics can play a key role to improve the autonomy and lifestyle of patients. In this context, RoboEye project aims to support people affected by mobility problems that range from very impairing pathologies (like ALS, amyotrophic lateral sclerosis) to old age. Any severe motor disability is a condition that limits the capability of interacting with the environment, even the domestic one, caused by the loss of the control on our own mobility. Although these pathologies are relatively rare, the number of people affected by this disease are increasing during the years. The focus of this project is the restore of persons’ mobility using novel technologies based on the gaze on a power wheelchair designed to enable the user to move easily and autonomously inside his home. A novel and intuitive control system was designed to achieve such a goal, in which a non-invasive eye tracker, a monitor, and a 3D camera represent some of the core elements. The developed prototype integrates, on a standard power wheelchair, functionalities from the mobile robotics field, with the main benefit of providing to the user two driving options and comfortable navigation. The most intuitive, and direct, modality foresees the continuous control of the frontal and angular velocities of the wheelchair by gazing at different areas of the monitor. The second, semi-autonomous, enables the navigation toward a selected point in the environment by just pointing and activating the wished destination while the system autonomously plans and follows the trajectory that brings the wheelchair there. The main goal is the development of shared control, combining direct control by the user with the comfort of autonomous navigation based on augmented reality markers. A first evaluation has been performed on a real test bed where specific motion metrics are evaluated. The designs of the control structure and driving interfaces were tuned thanks to the testing of some volunteers, habitual users of standard power wheelchairs. The driving modalities, especially the semi-autonomous one, were modelled and qualified to verify their efficiency, reliability, and safety for domestic usage.