Gaussian processes with linear operator inequality constraints

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence engineering systems, where this kind of information is often made available from phenomenological knowledge. We consider a GP $f$ over functions on $\mathcal{X} \subset \mathbb{R}^{n}$ taking values in $\mathbb{R}$, where the process $\mathcal{L}f$ is still Gaussian when $\mathcal{L}$ is a linear operator. Our goal is to model $f$ under the constraint that realizations of $\mathcal{L}f$ are confined to a convex set of functions. In particular, we require that $a \leq \mathcal{L}f \leq b$, given two functions $a$ and $b$ where $a < b$ pointwise. This formulation provides a consistent way of encoding multiple linear constraints, such as shape-constraints based on e.g. boundedness, monotonicity or convexity. We adopt the approach of using a sufficiently dense set of virtual observation locations where the constraint is required to hold, and derive the exact posterior for a conjugate likelihood. The results needed for stable numerical implementation are derived, together with an efficient sampling scheme for estimating the posterior process.Comment: Published in JMLR: http://jmlr.org/papers/volume20/19-065/19-065.pd

Perception-motivated parallel algorithms for haptics

Negli ultimi anni l\u2019utilizzo di dispositivi aptici, atti cio\ue8 a riprodurre l\u2019interazione fisica con l\u2019ambiente remoto o virtuale, si sta diffondendo in vari ambiti della robotica e dell\u2019informatica, dai videogiochi alla chirurgia robotizzata eseguita in teleoperazione, dai cellulari alla riabilitazione. In questo lavoro di tesi abbiamo voluto considerare nuovi punti di vista sull\u2019argomento, allo scopo di comprendere meglio come riportare l\u2019essere umano, che \ue8 l\u2019unico fruitore del ritorno di forza, tattile e di telepresenza, al centro della ricerca sui dispositivi aptici. Allo scopo ci siamo focalizzati su due aspetti: una manipolazione del segnale di forza mutuata dalla percezione umana e l\u2019utilizzo di architetture multicore per l\u2019implementazione di algoritmi aptici e robotici. Con l\u2019aiuto di un setup sperimentale creato ad hoc e attraverso l\u2019utilizzo di un joystick con ritorno di forza a 6 gradi di libert\ue0, abbiamo progettato degli esperimenti psicofisici atti all\u2019identificazione di soglie differenziali di forze/coppie nel sistema mano-braccio. Sulla base dei risultati ottenuti abbiamo determinato una serie di funzioni di scalatura del segnale di forza, una per ogni grado di libert\ue0, che permettono di aumentare l\u2019abilit\ue0 umana nel discriminare stimoli differenti. L\u2019utilizzo di tali funzioni, ad esempio in teleoperazione, richiede la possibilit\ue0 di variare il segnale di feedback e il controllo del dispositivo sia in relazione al lavoro da svolgere, sia alle peculiari capacit\ue0 dell\u2019utilizzatore. La gestione del dispositivo deve quindi essere in grado di soddisfare due obbiettivi tendenzialmente in contrasto, e cio\ue8 il raggiungimento di alte prestazioni in termini di velocit\ue0, stabilit\ue0 e precisione, abbinato alla flessibilit\ue0 tipica del software. Una soluzione consiste nell\u2019affidare il controllo del dispositivo ai nuovi sistemi multicore che si stanno sempre pi\uf9 prepotentemente affacciando sul panorama informatico. Per far ci\uf2 una serie di algoritmi consolidati deve essere portata su sistemi paralleli. In questo lavoro abbiamo dimostrato che \ue8 possibile convertire facilmente vecchi algoritmi gi\ue0 implementati in hardware, e quindi intrinsecamente paralleli. Un punto da definire rimane per\uf2 quanto costa portare degli algoritmi solitamente descritti in VLSI e schemi in un linguaggio di programmazione ad alto livello. Focalizzando la nostra attenzione su un problema specifico, la pseudoinversione di matrici che \ue8 presente in molti algoritmi di dinamica e cinematica, abbiamo mostrato che un\u2019attenta progettazione e decomposizione del problema permette una mappatura diretta sulle unit\ue0 di calcolo disponibili. In aggiunta, l\u2019uso di parallelismo a livello di dati su macchine SIMD permette di ottenere buone prestazioni utilizzando semplici operazioni vettoriali come addizioni e shift. Dato che di solito tali istruzioni fanno parte delle implementazioni hardware la migrazione del codice risulta agevole. Abbiamo testato il nostro approccio su una Sony PlayStation 3 equipaggiata con un processore IBM Cell Broadband Engine.In the last years the use of haptic feedback has been used in several applications, from mobile phones to rehabilitation, from video games to robotic aided surgery. The haptic devices, that are the interfaces that create the stimulation and reproduce the physical interaction with virtual or remote environments, have been studied, analyzed and developed in many ways. Every innovation in the mechanics, electronics and technical design of the device it is valuable, however it is important to maintain the focus of the haptic interaction on the human being, who is the only user of force feedback. In this thesis we worked on two main topics that are relevant to this aim: a perception based force signal manipulation and the use of modern multicore architectures for the implementation of the haptic controller. With the help of a specific experimental setup and using a 6 dof haptic device we designed a psychophysical experiment aimed at identifying of the force/torque differential thresholds applied to the hand-arm system. On the basis of the results obtained we determined a set of task dependent scaling functions, one for each degree of freedom of the three-dimensional space, that can be used to enhance the human abilities in discriminating different stimuli. The perception based manipulation of the force feedback requires a fast, stable and configurable controller of the haptic interface. Thus a solution is to use new available multicore architectures for the implementation of the controller, but many consolidated algorithms have to be ported to these parallel systems. Focusing on specific problem, i.e. the matrix pseudoinversion, that is part of the robotics dynamic and kinematic computation, we showed that it is possible to migrate code that was already implemented in hardware, and in particular old algorithms that were inherently parallel and thus not competitive on sequential processors. The main question that still lies open is how much effort is required in order to write these algorithms, usually described in VLSI or schematics, in a modern programming language. We show that a careful task decomposition and design permit a mapping of the code on the available cores. In addition, the use of data parallelism on SIMD machines can give good performance when simple vector instructions such as add and shift operations are used. Since these instructions are present also in hardware implementations the migration can be easily performed. We tested our approach on a Sony PlayStation 3 game console equipped with IBM Cell Broadband Engine processor

Model learning for trajectory tracking of robot manipulators

Abstract Model based controllers have drastically improved robot performance, increasing task accuracy while reducing control effort. Nevertheless, all this was realized with a very strong assumption: the exact knowledge of the physical properties of both the robot and the environment that surrounds it. This assertion is often misleading: in fact modern robots are modeled in a very approximate way and, more important, the environment is almost never static and completely known. Also for systems very simple, such as robot manipulators, these assumptions are still too strong and must be relaxed. Many methods were developed which, exploiting previous experiences, are able to refine the nominal model: from classic identification techniques to more modern machine learning based approaches. Indeed, the topic of this thesis is the investigation of these data driven techniques in the context of robot control for trajectory tracking. In the first two chapters, preliminary knowledge is provided on both model based controllers, used in robotics to assure precise trajectory tracking, and model learning techniques. In the following three chapters, are presented the novelties introduced by the author in this context with respect to the state of the art: three works with the same premise (an inaccurate system modeling), an identical goal (accurate trajectory tracking control) but with small differences according to the specific platform of application (fully actuated, underactuated, redundant robots). In all the considered architectures, an online learning scheme has been introduced to correct the nominal feedback linearization control law. Indeed, the method has been primarily introduced in the literature to cope with fully actuated systems, showing its efficacy in the accurate tracking of joint space trajectories also with an inaccurate dynamic model. The main novelty of the technique was the use of only kinematics information, instead of torque measurements (in general very noisy), to online retrieve and compensate the dynamic mismatches. After that the method has been extended to underactuated robots. This new architecture was composed by an online learning correction of the controller, acting on the actuated part of the system (the nominal partial feedback linearization), and an offline planning phase, required to realize a dynamically feasible trajectory also for the zero dynamics of the system. The scheme was iterative: after each trial, according to the collected information, both the phases were improved and then repeated until the task achievement. Also in this case the method showed its capability, both in numerical simulations and on real experiments on a robotics platform. Eventually the method has been applied to redundant systems: differently from before, in this context the task consisted in the accurate tracking of a Cartesian end effector trajectory. In principle very similar to the fully actuated case, the presence of redundancy slowed down drastically the learning machinery convergence, worsening the performance. In order to cope with this, a redundancy resolution was proposed that, exploiting an approximation of the learning algorithm (Gaussian process regression), allowed to locally maximize the information and so select the most convenient self motion for the system; moreover, all of this was realized with just the resolution of a quadratic programming problem. Also in this case the method showed its performance, realizing an accurate online tracking while reducing both the control effort and the joints velocity, obtaining so a natural behaviour. The thesis concludes with summary considerations on the proposed approach and with possible future directions of research

Contributions to Robust Graph Clustering: Spectral Analysis and Algorithms

This dissertation details the design of fast, and parameter free, graph clustering methods to robustly determine set cluster assignments. It provides spectral analysis as well as algorithms that adapt the obtained theoretical results to the implementation of robust graph clustering techniques. Sparsity is of importance in graph clustering and a first contribution of the thesis is the definition of a sparse graph model consistent with the graph clustering objectives. This model is based on an advantageous property, arising from a block diagonal representation, of a matrix that promotes the density of connections within clusters and sparsity between them. Spectral analysis of the sparse graph model including the eigen-decomposition of the Laplacian matrix is conducted. The analysis of the Laplacian matrix is simplified by defining a vector that carries all the relevant information that is contained in the Laplacian matrix. The obtained spectral properties of sparse graphs are adapted to sparsity-aware clustering based on two methods that formulate the determination of the sparsity level as approximations to spectral properties of the sparse graph models. A second contribution of this thesis is to analyze the effects of outliers on graph clustering and to propose algorithms that address robustness and the level of sparsity jointly. The basis for this contribution is to specify fundamental outlier types that occur in the cases of extreme sparsity and the mathematical analysis of their effects on sparse graphs to develop graph clustering algorithms that are robust against the investigated outlier effects. Based on the obtained results, two different robust and sparsity-aware affinity matrix construction methods are proposed. Motivated by the outliers’ effects on eigenvectors, a robust Fiedler vector estimation and a robust spectral clustering methods are proposed. Finally, an outlier detection algorithm that is built upon the vertex degree is proposed and applied to gait analysis. The results of this thesis demonstrate the importance of jointly addressing robustness and the level of sparsity for graph clustering algorithms. Additionally, simplified Laplacian matrix analysis provides promising results to design graph construction methods that may be computed efficiently through the optimization in a vector space instead of the usually used matrix space

THE TOOLS AND MONTE CARLO WORKING GROUP Summary Report from the Les Houches 2009 Workshop on TeV Colliders

This is the summary and introduction to the proceedings contributions for the Les Houches 2009 "Tools and Monte Carlo" working group.Comment: 144 Pages. Workshop site http://wwwlapp.in2p3.fr/conferences/LesHouches/Houches2009/ . Conveners were Butterworth, Maltoni, Moortgat, Richardson, Schumann and Skand

Report / Institute für Physik

The 2017 Report of the Physics Institutes of the Universität Leipzig provides an overview of the structure and research activities of the three institutes. We are happy to announce that Prof. Dr. Caudia Schnohr from Universität Jena will join the Felix Bloch Institute for Solid State Physics beginning 2019 filling the vacant position in the department for Solid State Optics. Dr. Johannes Deiglmayr from ETH Zurich will establish an independent department for Quantum Optics at the same institute