A dynamical view of nonlinear conjugate gradient methods with applications to FFT-based computational micromechanics

For fast Fourier transform (FFT)-based computational micromechanics, solvers need to be fast, memory-efficient, and independent of tedious parameter calibration. In this work, we investigate the benefits of nonlinear conjugate gradient (CG) methods in the context of FFT-based computational micromechanics. Traditionally, nonlinear CG methods require dedicated line-search procedures to be efficient, rendering them not competitive in the FFT-based context. We contribute to nonlinear CG methods devoid of line searches by exploiting similarities between nonlinear CG methods and accelerated gradient methods. More precisely, by letting the step-size go to zero, we exhibit the Fletcher–Reeves nonlinear CG as a dynamical system with state-dependent nonlinear damping. We show how to implement nonlinear CG methods for FFT-based computational micromechanics, and demonstrate by numerical experiments that the Fletcher–Reeves nonlinear CG represents a competitive, memory-efficient and parameter-choice free solution method for linear and nonlinear homogenization problems, which, in addition, decreases the residual monotonically

Modelling and control of lightweight underwater vehicle-manipulator systems

This thesis studies the mathematical description and the low-level control structures for underwater robotic systems performing motion and interaction tasks. The main focus is on the study of lightweight underwater-vehicle manipulator systems. A description of the dynamic and hydrodynamic modelling of the underwater vehicle-manipulator system (UVMS) is presented and a study of the coupling effects between the vehicle and manipulator is given. Through simulation results it is shown that the vehicle’s capabilities are degraded by the motion of the manipulator, when it has a considerable mass with respect to the vehicle. Understanding the interaction effects between the two subsystems is beneficial in developing new control architectures that can improve the performance of the system. A control strategy is proposed for reducing the coupling effects between the two subsystems when motion tasks are required. The method is developed based on the mathematical model of the UVMS and the estimated interaction effects. Simulation results show the validity of the proposed control structure even in the presence of uncertainties in the dynamic model. The problem of autonomous interaction with the underwater environment is further addressed. The thesis proposes a parallel position/force control structure for lightweight underwater vehicle-manipulator systems. Two different strategies for integrating this control law on the vehicle-manipulator structure are proposed. The first strategy uses the parallel control law for the manipulator while a different control law, the Proportional Integral Limited control structure, is used for the vehicle. The second strategy treats the underwater vehicle-manipulator system as a single system and the parallel position/force law is used for the overall system. The low level parallel position/force control law is validated through practical experiments using the HDT-MK3-M electric manipulator. The Proportional Integral Limited control structure is tested using a 5 degrees-of-freedom underwater vehicle in a wave-tank facility. Furthermore, an adaptive tuning method based on interaction theory is proposed for adjusting the gains of the controller. The experimental results show that the method is advantageous as it decreases the complexity of the manual tuning otherwise required and reduces the energy consumption. The main objectives of this thesis are to understand and accurately represent the behaviour of an underwater vehiclemanipulator system, to evaluate this system when in contact with the environment and to design informed low-level control structures based on the observations made through the mathematical study of the system. The concepts presented in this thesis are not restricted to only vehicle-manipulator systems but can be applied to different other multibody robotic systems

Quantum Computing for Fusion Energy Science Applications

This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum computation, and quantum algorithms. Then, we explore the topic of using quantum computers to simulate both linear and nonlinear dynamics in greater detail. Because quantum computers can only efficiently perform linear operations on the quantum state, it is challenging to perform nonlinear operations that are generically required to describe the nonlinear differential equations of interest. In this work, we extend previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator, the Perron-Frobenius evolution operator, and the Koopman-von Neumann evolution (KvN) operator. We also explicitly derive the connection between the Koopman and Carleman approaches to embedding. Extension of the KvN framework to the complex-analytic setting relevant to Carleman embedding, and the proof that different choices of complex analytic reproducing kernel Hilbert spaces depend on the choice of Hilbert space metric are covered in the appendices. Finally, we conclude with a review of recent quantum hardware implementations of algorithms on present-day quantum hardware platforms that may one day be accelerated through Hamiltonian simulation. We discuss the simulation of toy models of wave-particle interactions through the simulation of quantum maps and of wave-wave interactions important in nonlinear plasma dynamics.Comment: 42 pages; 12 figures; invited paper at the 2021-2022 International Sherwood Fusion Theory Conferenc

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

Accelerated algorithms for temporal difference learning methods

L'idée centrale de cette thèse est de comprendre la notion d'accélération dans les algorithmes d'approximation stochastique. Plus précisément, nous tentons de répondre à la question suivante : Comment l'accélération apparaît-elle naturellement dans les algorithmes d'approximation stochastique ? Nous adoptons une approche de systèmes dynamiques et proposons de nouvelles méthodes accélérées pour l'apprentissage par différence temporelle (TD) avec approximation de fonction linéaire : Polyak TD(0) et Nesterov TD(0). Contrairement aux travaux antérieurs, nos méthodes ne reposent pas sur une conception des méthodes de TD comme des méthodes de descente de gradient. Nous étudions l'interaction entre l'accélération, la stabilité et la convergence des méthodes accélérées proposées en temps continu. Pour établir la convergence du système dynamique sous-jacent, nous analysons les modèles en temps continu des méthodes d'approximation stochastique accélérées proposées en dérivant la loi de conservation dans un système de coordonnées dilaté. Nous montrons que le système dynamique sous-jacent des algorithmes proposés converge à un rythme accéléré. Ce cadre nous fournit également des recommandations pour le choix des paramètres d'amortissement afin d'obtenir ce comportement convergent. Enfin, nous discrétisons ces ODE convergentes en utilisant deux schémas de discrétisation différents, Euler explicite et Euler symplectique, et nous analysons leurs performances sur de petites tâches de prédiction linéaire.The central idea of this thesis is to understand the notion of acceleration in stochastic approximation algorithms. Specifically, we attempt to answer the question: How does acceleration naturally show up in SA algorithms? We adopt a dynamical systems approach and propose new accelerated methods for temporal difference (TD) learning with linear function approximation: Polyak TD(0) and Nesterov TD(0). In contrast to earlier works, our methods do not rely on viewing TD methods as gradient descent methods. We study the interplay between acceleration, stability, and convergence of the proposed accelerated methods in continuous time. To establish the convergence of the underlying dynamical system, we analyze continuous-time models of the proposed accelerated stochastic approximation methods by deriving the conservation law in a dilated coordinate system. We show that the underlying dynamical system of our proposed algorithms converges at an accelerated rate. This framework also provides us recommendations for the choice of the damping parameters to obtain this convergent behavior. Finally, we discretize these convergent ODEs using two different discretization schemes, explicit Euler, and symplectic Euler, and analyze their performance on small, linear prediction tasks

Improving aircraft performance using machine learning: a review

This review covers the new developments in machine learning (ML) that are impacting the multi-disciplinary area of aerospace engineering, including fundamental fluid dynamics (experimental and numerical), aerodynamics, acoustics, combustion and structural health monitoring. We review the state of the art, gathering the advantages and challenges of ML methods across different aerospace disciplines and provide our view on future opportunities. The basic concepts and the most relevant strategies for ML are presented together with the most relevant applications in aerospace engineering, revealing that ML is improving aircraft performance and that these techniques will have a large impact in the near future

Contact aware robust semi-autonomous teleoperation of mobile manipulators

In the context of human-robot collaboration, cooperation and teaming, the use of mobile manipulators is widespread on applications involving unpredictable or hazardous environments for humans operators, like space operations, waste management and search and rescue on disaster scenarios. Applications where the manipulator's motion is controlled remotely by specialized operators. Teleoperation of manipulators is not a straightforward task, and in many practical cases represent a common source of failures. Common issues during the remote control of manipulators are: increasing control complexity with respect the mechanical degrees of freedom; inadequate or incomplete feedback to the user (i.e. limited visualization or knowledge of the environment); predefined motion directives may be incompatible with constraints or obstacles imposed by the environment. In the latter case, part of the manipulator may get trapped or blocked by some obstacle in the environment, failure that cannot be easily detected, isolated nor counteracted remotely. While control complexity can be reduced by the introduction of motion directives or by abstraction of the robot motion, the real-time constraint of the teleoperation task requires the transfer of the least possible amount of data over the system's network, thus limiting the number of physical sensors that can be used to model the environment. Therefore, it is of fundamental to define alternative perceptive strategies to accurately characterize different interaction with the environment without relying on specific sensory technologies. In this work, we present a novel approach for safe teleoperation, that takes advantage of model based proprioceptive measurement of the robot dynamics to robustly identify unexpected collisions or contact events with the environment. Each identified collision is translated on-the-fly into a set of local motion constraints, allowing the exploitation of the system redundancies for the computation of intelligent control laws for automatic reaction, without requiring human intervention and minimizing the disturbance of the task execution (or, equivalently, the operator efforts). More precisely, the described system consist in two different building blocks. The first, for detecting unexpected interactions with the environment (perceptive block). The second, for intelligent and autonomous reaction after the stimulus (control block). The perceptive block is responsible of the contact event identification. In short, the approach is based on the claim that a sensorless collision detection method for robot manipulators can be extended to the field of mobile manipulators, by embedding it within a statistical learning framework. The control deals with the intelligent and autonomous reaction after the contact or impact with the environment occurs, and consist on an motion abstraction controller with a prioritized set of constrains, where the highest priority correspond to the robot reconfiguration after a collision is detected; when all related dynamical effects have been compensated, the controller switch again to the basic control mode