Computational Methods for Cognitive and Cooperative Robotics

In the last decades design methods in control engineering made substantial progress in the areas of robotics and computer animation. Nowadays these methods incorporate the newest developments in machine learning and artificial intelligence. But the problems of flexible and online-adaptive combinations of motor behaviors remain challenging for human-like animations and for humanoid robotics. In this context, biologically-motivated methods for the analysis and re-synthesis of human motor programs provide new insights in and models for the anticipatory motion synthesis. This thesis presents the author’s achievements in the areas of cognitive and developmental robotics, cooperative and humanoid robotics and intelligent and machine learning methods in computer graphics. The first part of the thesis in the chapter “Goal-directed Imitation for Robots” considers imitation learning in cognitive and developmental robotics. The work presented here details the author’s progress in the development of hierarchical motion recognition and planning inspired by recent discoveries of the functions of mirror-neuron cortical circuits in primates. The overall architecture is capable of ‘learning for imitation’ and ‘learning by imitation’. The complete system includes a low-level real-time capable path planning subsystem for obstacle avoidance during arm reaching. The learning-based path planning subsystem is universal for all types of anthropomorphic robot arms, and is capable of knowledge transfer at the level of individual motor acts. Next, the problems of learning and synthesis of motor synergies, the spatial and spatio-temporal combinations of motor features in sequential multi-action behavior, and the problems of task-related action transitions are considered in the second part of the thesis “Kinematic Motion Synthesis for Computer Graphics and Robotics”. In this part, a new approach of modeling complex full-body human actions by mixtures of time-shift invariant motor primitives in presented. The online-capable full-body motion generation architecture based on dynamic movement primitives driving the time-shift invariant motor synergies was implemented as an online-reactive adaptive motion synthesis for computer graphics and robotics applications. The last chapter of the thesis entitled “Contraction Theory and Self-organized Scenarios in Computer Graphics and Robotics” is dedicated to optimal control strategies in multi-agent scenarios of large crowds of agents expressing highly nonlinear behaviors. This last part presents new mathematical tools for stability analysis and synthesis of multi-agent cooperative scenarios.In den letzten Jahrzehnten hat die Forschung in den Bereichen der Steuerung und Regelung komplexer Systeme erhebliche Fortschritte gemacht, insbesondere in den Bereichen Robotik und Computeranimation. Die Entwicklung solcher Systeme verwendet heutzutage neueste Methoden und Entwicklungen im Bereich des maschinellen Lernens und der künstlichen Intelligenz. Die flexible und echtzeitfähige Kombination von motorischen Verhaltensweisen ist eine wesentliche Herausforderung für die Generierung menschenähnlicher Animationen und in der humanoiden Robotik. In diesem Zusammenhang liefern biologisch motivierte Methoden zur Analyse und Resynthese menschlicher motorischer Programme neue Erkenntnisse und Modelle für die antizipatorische Bewegungssynthese. Diese Dissertation präsentiert die Ergebnisse der Arbeiten des Autors im Gebiet der kognitiven und Entwicklungsrobotik, kooperativer und humanoider Robotersysteme sowie intelligenter und maschineller Lernmethoden in der Computergrafik. Der erste Teil der Dissertation im Kapitel “Zielgerichtete Nachahmung für Roboter” behandelt das Imitationslernen in der kognitiven und Entwicklungsrobotik. Die vorgestellten Arbeiten beschreiben neue Methoden für die hierarchische Bewegungserkennung und -planung, die durch Erkenntnisse zur Funktion der kortikalen Spiegelneuronen-Schaltkreise bei Primaten inspiriert wurden. Die entwickelte Architektur ist in der Lage, ‘durch Imitation zu lernen’ und ‘zu lernen zu imitieren’. Das komplette entwickelte System enthält ein echtzeitfähiges Pfadplanungssubsystem zur Hindernisvermeidung während der Durchführung von Armbewegungen. Das lernbasierte Pfadplanungssubsystem ist universell und für alle Arten von anthropomorphen Roboterarmen in der Lage, Wissen auf der Ebene einzelner motorischer Handlungen zu übertragen. Im zweiten Teil der Arbeit “Kinematische Bewegungssynthese für Computergrafik und Robotik” werden die Probleme des Lernens und der Synthese motorischer Synergien, d.h. von räumlichen und räumlich-zeitlichen Kombinationen motorischer Bewegungselemente bei Bewegungssequenzen und bei aufgabenbezogenen Handlungs übergängen behandelt. Es wird ein neuer Ansatz zur Modellierung komplexer menschlicher Ganzkörperaktionen durch Mischungen von zeitverschiebungsinvarianten Motorprimitiven vorgestellt. Zudem wurde ein online-fähiger Synthesealgorithmus für Ganzköperbewegungen entwickelt, der auf dynamischen Bewegungsprimitiven basiert, die wiederum auf der Basis der gelernten verschiebungsinvarianten Primitive konstruiert werden. Dieser Algorithmus wurde für verschiedene Probleme der Bewegungssynthese für die Computergrafik- und Roboteranwendungen implementiert. Das letzte Kapitel der Dissertation mit dem Titel “Kontraktionstheorie und selbstorganisierte Szenarien in der Computergrafik und Robotik” widmet sich optimalen Kontrollstrategien in Multi-Agenten-Szenarien, wobei die Agenten durch eine hochgradig nichtlineare Kinematik gekennzeichnet sind. Dieser letzte Teil präsentiert neue mathematische Werkzeuge für die Stabilitätsanalyse und Synthese von kooperativen Multi-Agenten-Szenarien

Slow collective variables and molecular kinetics from short off-equilibrium simulations

Markov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach conformation dynamics/molecular kinetics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters. While it is known how to estimate MSMs from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VAC. Previous estimates from short trajectories have been strongly biased and thus not variationally optimal. Here, we employ the Koopman operator theory and the ideas from dynamic mode decomposition to extend the VAC and TICA to non-equilibrium data. The main insight is that the VAC and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provides estimates of relaxation time scales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA, and the linear VAC and allow molecular kinetics to be described without a cluster discretization

Adaptive blind signal separation.

by Chi-Chiu Cheung.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 124-131).Abstract --- p.iAcknowledgments --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- The Blind Signal Separation Problem --- p.1Chapter 1.2 --- Contributions of this Thesis --- p.3Chapter 1.3 --- Applications of the Problem --- p.4Chapter 1.4 --- Organization of the Thesis --- p.5Chapter 2 --- The Blind Signal Separation Problem --- p.7Chapter 2.1 --- The General Blind Signal Separation Problem --- p.7Chapter 2.2 --- Convolutive Linear Mixing Process --- p.8Chapter 2.3 --- Instantaneous Linear Mixing Process --- p.9Chapter 2.4 --- Problem Definition and Assumptions in this Thesis --- p.9Chapter 3 --- Literature Review --- p.13Chapter 3.1 --- Previous Works on Blind Signal Separation with Instantaneous Mixture --- p.13Chapter 3.1.1 --- Algebraic Approaches --- p.14Chapter 3.1.2 --- Neural approaches --- p.15Chapter 3.2 --- Previous Works on Blind Signal Separation with Convolutive Mixture --- p.20Chapter 4 --- The Information-theoretic ICA Scheme --- p.22Chapter 4.1 --- The Bayesian YING-YANG Learning Scheme --- p.22Chapter 4.2 --- The Information-theoretic ICA Scheme --- p.25Chapter 4.2.1 --- Derivation of the cost function from YING-YANG Machine --- p.25Chapter 4.2.2 --- Connections to previous information-theoretic approaches --- p.26Chapter 4.2.3 --- Derivation of the Algorithms --- p.27Chapter 4.2.4 --- Roles and Constraints on the Nonlinearities --- p.30Chapter 4.3 --- Direction and Motivation for the Analysis of the Nonlinearity --- p.30Chapter 5 --- Properties of the Cost Function and the Algorithms --- p.32Chapter 5.1 --- Lemmas and Corollaries --- p.32Chapter 5.1.1 --- Singularity of J(V) --- p.33Chapter 5.1.2 --- Continuity of J(V) --- p.34Chapter 5.1.3 --- Behavior of J(V) along a radially outward line --- p.35Chapter 5.1.4 --- Impossibility of divergence of the information-theoretic ICA al- gorithms with a large class of nonlinearities --- p.36Chapter 5.1.5 --- Number and stability of correct solutions in the 2-channel case --- p.37Chapter 5.1.6 --- Scale for the equilibrium points --- p.39Chapter 5.1.7 --- Absence of local maximum of J(V) --- p.43Chapter 6 --- The Algorithms with Cubic Nonlinearity --- p.44Chapter 6.1 --- The Cubic Nonlinearity --- p.44Chapter 6.2 --- Theoretical Results on the 2-Channel Case --- p.46Chapter 6.2.1 --- Equilibrium points --- p.46Chapter 6.2.2 --- Stability of the equilibrium points --- p.49Chapter 6.2.3 --- An alternative proof for the stability of the equilibrium points --- p.50Chapter 6.2.4 --- Convergence Analysis --- p.52Chapter 6.3 --- Experiments on the 2-Channel Case --- p.53Chapter 6.3.1 --- Experiments on two sub-Gaussian sources --- p.54Chapter 6.3.2 --- Experiments on two super-Gaussian sources --- p.55Chapter 6.3.3 --- Experiments on one super-Gaussian source and one sub-Gaussian source which are globally sub-Gaussian --- p.57Chapter 6.3.4 --- Experiments on one super-Gaussian source and one sub-Gaussian source which are globally super-Gaussian --- p.59Chapter 6.3.5 --- Experiments on asymmetric exponentially distributed signals .。 --- p.60Chapter 6.3.6 --- Demonstration on exactly and nearly singular initial points --- p.61Chapter 6.4 --- Theoretical Results on the 3-Channel Case --- p.63Chapter 6.4.1 --- Equilibrium points --- p.63Chapter 6.4.2 --- Stability --- p.66Chapter 6.5 --- Experiments on the 3-Channel Case --- p.66Chapter 6.5.1 --- Experiments on three pairwise globally sub-Gaussian sources --- p.67Chapter 6.5.2 --- Experiments on three sources consisting of globally sub-Gaussian and globally super-Gaussian pairs --- p.67Chapter 6.5.3 --- Experiments on three pairwise globally super-Gaussian sources --- p.69Chapter 7 --- Nonlinearity and Separation Capability --- p.71Chapter 7.1 --- Theoretical Argument --- p.71Chapter 7.1.1 --- Nonlinearities that strictly match the source distribution --- p.72Chapter 7.1.2 --- Nonlinearities that loosely match the source distribution --- p.72Chapter 7.2 --- Experiment Verification --- p.76Chapter 7.2.1 --- Experiments on reversed sigmoid --- p.76Chapter 7.2.2 --- Experiments on the cubic root nonlinearity --- p.77Chapter 7.2.3 --- Experimental verification of Theorem 2 --- p.77Chapter 7.2.4 --- Experiments on the MMI algorithm --- p.78Chapter 8 --- Implementation with Mixture of Densities --- p.80Chapter 8.1 --- Implementation of the Information-theoretic ICA scheme with Mixture of Densities --- p.80Chapter 8.1.1 --- The mixture of densities --- p.81Chapter 8.1.2 --- Derivation of the algorithms --- p.82Chapter 8.2 --- Experimental Verification on the Nonlinearity Adaptation --- p.84Chapter 8.2.1 --- Experiment 1: Two channels of sub-Gaussian sources --- p.84Chapter 8.2.2 --- Experiment 2: Two channels of super-Gaussian sources --- p.85Chapter 8.2.3 --- Experiment 3: Three channels of different signals --- p.89Chapter 8.3 --- Seeking the Simplest Workable Mixtures of Densities ......... .。 --- p.91Chapter 8.3.1 --- Number of components --- p.91Chapter 8.3.2 --- Mixture of two densities with only biases changeable --- p.93Chapter 9 --- ICA with Non-Kullback Cost Function --- p.97Chapter 9.1 --- Derivation of ICA Algorithms from Non-Kullback Separation Functionals --- p.97Chapter 9.1.1 --- Positive Convex Divergence --- p.97Chapter 9.1.2 --- Lp Divergence --- p.100Chapter 9.1.3 --- De-correlation Index --- p.102Chapter 9.2 --- Experiments on the ICA Algorithm Based on Positive Convex Divergence --- p.103Chapter 9.2.1 --- Experiments on the algorithm with fixed nonlinearities --- p.103Chapter 9.2.2 --- Experiments on the algorithm with mixture of densities --- p.106Chapter 10 --- Conclusions --- p.107Chapter A --- Proof for Stability of the Equilibrium Points of the Algorithm with Cubic Nonlinearity on Two Channels of Signals --- p.110Chapter A.1 --- Stability of Solution Group A --- p.110Chapter A.2 --- Stability of Solution Group B --- p.111Chapter B --- Proof for Stability of the Equilibrium Points of the Algorithm with Cubic Nonlinearity on Three Channels of Signals --- p.119Chapter C --- Proof for Theorem2 --- p.122Bibliography --- p.12

Particle filtering in high-dimensional chaotic systems

We present an efficient particle filtering algorithm for multiscale systems, that is adapted for simple atmospheric dynamics models which are inherently chaotic. Particle filters represent the posterior conditional distribution of the state variables by a collection of particles, which evolves and adapts recursively as new information becomes available. The difference between the estimated state and the true state of the system constitutes the error in specifying or forecasting the state, which is amplified in chaotic systems that have a number of positive Lyapunov exponents. The purpose of the present paper is to show that the homogenization method developed in Imkeller et al. (2011), which is applicable to high dimensional multi-scale filtering problems, along with important sampling and control methods can be used as a basic and flexible tool for the construction of the proposal density inherent in particle filtering. Finally, we apply the general homogenized particle filtering algorithm developed here to the Lorenz'96 atmospheric model that mimics mid-latitude atmospheric dynamics with microscopic convective processes.Comment: 28 pages, 12 figure

A survey of random processes with reinforcement

The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Advanced optimization algorithms for sensor arrays and multi-antenna communications

Optimization problems arise frequently in sensor array and multi-channel signal processing applications. Often, optimization needs to be performed subject to a matrix constraint. In particular, unitary matrices play a crucial role in communications and sensor array signal processing. They are involved in almost all modern multi-antenna transceiver techniques, as well as sensor array applications in biomedicine, machine learning and vision, astronomy and radars. In this thesis, algorithms for optimization under unitary matrix constraint stemming from Riemannian geometry are developed. Steepest descent (SD) and conjugate gradient (CG) algorithms operating on the Lie group of unitary matrices are derived. They have the ability to find the optimal solution in a numerically efficient manner and satisfy the constraint accurately. Novel line search methods specially tailored for this type of optimization are also introduced. The proposed approaches exploit the geometrical properties of the constraint space in order to reduce the computational complexity. Array and multi-channel signal processing techniques are key technologies in wireless communication systems. High capacity and link reliability may be achieved by using multiple transmit and receive antennas. Combining multi-antenna techniques with multicarrier transmission leads to high the spectral efficiency and helps to cope with severe multipath propagation. The problem of channel equalization in MIMO-OFDM systems is also addressed in this thesis. A blind algorithm that optimizes of a combined criterion in order to be cancel both inter-symbol and co-channel interference is proposed. The algorithm local converge properties are established as well

Dark Energy Survey Year 3 results: Galaxy clustering and systematics treatment for lens galaxy samples

DES Collaboration: M. Rodríguez-Monroy, N. Weaverdyck, J. Elvin-Poole et al.In this work, we present the galaxy clustering measurements of the two DES lens galaxy samples: a magnitude-limited sample optimized for the measurement of cosmological parameters, MAGLIM, and a sample of luminous red galaxies selected with the REDMAGIC algorithm. MAGLIM/REDMAGIC sample contains over 10 million/2.5 million galaxies and is divided into six/five photometric redshift bins spanning the range z ∈ [0.20, 1.05]/z ∈ [0.15, 0.90]. Both samples cover 4143 deg2 over which we perform our analysis blind, measuring the angular correlation function with an S/N ∼ 63 for both samples. In a companion paper, these measurements of galaxy clustering are combined with the correlation functions of cosmic shear and galaxy–galaxy lensing of each sample to place cosmological constraints with a 3 × 2pt analysis. We conduct a thorough study of the mitigation of systematic effects caused by the spatially varying survey properties and we correct the measurements to remove artificial clustering signals. We employ several decontamination methods with different configurations to ensure the robustness of our corrections and to determine the systematic uncertainty that needs to be considered for the final cosmology analyses. We validate our fiducial methodology using lognormal mocks, showing that our decontamination procedure induces biases no greater than 0.5σ in the (Ωm, b) plane, where b is the galaxy bias.Funding for the Dark Energy Survey Projects has been provided by the US Department of Energy, the US National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, NFS’s NOIRLab, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas A&M University, and the OzDES Membership Consortium. This paper is based in part on observations at Cerro Tololo Inter-American Observatory at NSF’s NOIRLab (NOIRLab Prop. ID 2012B-0001; PI: J. Frieman), which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. The DES data management system is supported by the National Science Foundation under Grant Numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MICINN under grants ESP2017-89838, PGC2018-094773, PGC2018-102021, SEV-2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007-2013) including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Brazilian Instituto Nacional de Ciência e Tecnologia (INCT) do e-Universo (CNPq grant 465376/2014-2). This paper has been authored by Fermi Research Alliance, LLC under Contract No. DE-AC02-07CH11359 with the US Department of Energy, Office of Science, Office of High Energy Physics.Peer reviewe

Freeform Reflector Design With Extended Sources

Reflector design stemmed from the need to shape the light emitted by candles or lamps. Over 2,000 years ago people realized that a mirror shaped as a parabola can concentrate light, and thus significantly boosts its intensity, to the point where objects can be set afire. Nowadays many applications require an accurate control of light, such as automotive headlights, streetlights, projection displays, and medical illuminators. In all cases light emitted from a light source can be shaped into a desired target distribution with a reflective surface. Design methods for systems with rotational and translational symmetry were devised in the 1930s. However, the freeform reflector shapes required to illuminate targets with no such symmetries proved to be much more challenging to design. Even when the source is assumed to be a point, the reflector shape is governed by a set of second-order partial non-linear differential equations that cannot be solved with standard numerical integration techniques. An iterative approach to solve the problem for a discrete target, known as the method of supporting ellipsoids, was recently proposed by Oliker. In this research we report several efficient implementations of the method of supporting ellipsoids, based on the point source approximation, and we propose new reflector design techniques that take into account the extent of the source. More specifically, this work has led to three major achievements. First, a thorough analysis of the method of supporting ellipsoids was performed that resulted in two alternative implementations of the algorithm, which enable a fast generation of freeform reflector shapes within the point source approximation. We tailored the algorithm in order to provide control over the parameters of interest to the designers, such as the reflector scale and geometry. Second, the shape generation algorithm was used to analyze how source flux can be mapped onto the target. We derived the condition under which a given source-target mapping can be achieved with a smooth continuous surface, referred as the integrability condition. We proposed a method to derive mappings that satisfy the integrability condition. We then use these mappings to quickly generate reflector shapes that create continuous target distributions as opposed to reflectors generated with the method of supporting ellipsoids that create discrete sets of points on the target. We also show how mappings that do not satisfy the integrability condition can be achieved by introducing step discontinuities in the reflector surface. Third, we investigated two methods to design reflectors with extended sources. The first method uses a compensation approach where the prescribed target distribution is adjusted iteratively. This method is effective for compact sources and systems with rotational or translational symmetry. The second method tiles the source images created by a reflector designed with the method of supporting ellipsoids and then blends the source images together using scattering in order to obtain a continuous target distribution. This latter method is effective for freeform reflectors and target distributions with no sharp variations. Finally, several case studies illustrate how these methods can be successfully applied to design reflectors for general illumination applications such as street lighting or luminaires. We show that the proposed design methods can ease the design of freeform reflectors and provide efficient, cost-effective solutions that avoid unnecessary energy consumption and light pollution