Samuel A. Burden

Bio: Samuel A. Burden is an academic researcher from University of Washington. The author has contributed to research in topics: Hybrid system & Dynamical systems theory. The author has an hindex of 21, co-authored 65 publications receiving 1261 citations. Previous affiliations of Samuel A. Burden include University of California, Berkeley.

Characterization and computation of local Nash equilibria in continuous games

Abstract: We present derivative-based necessary and sufficient conditions ensuring player strategies constitute local Nash equilibria in non-cooperative continuous games. Our results can be interpreted as generalizations of analogous second-order conditions for local optimality from nonlinear programming and optimal control theory. Drawing on this analogy, we propose an iterative steepest descent algorithm for numerical approximation of local Nash equilibria and provide a sufficient condition ensuring local convergence of the algorithm. We demonstrate our analytical and computational techniques by computing local Nash equilibria in games played on a finite-dimensional differentiable manifold or an infinite-dimensional Hilbert space.

Bio-inspired design and dynamic maneuverability of a minimally actuated six-legged robot

Abstract: Rapidly running arthropods like cockroaches make use of passive dynamics to achieve remarkable locomotion performance with regard to stability, speed, and maneuverability In this work, we take inspiration from these organisms to design, fabricate, and control a 10cm, 24 gram underactuated hexapedal robot capable of running at 14 body lengths per second and performing dynamic turning maneuvers Our design relies on parallel kinematic mechanisms fabricated using the scaled smart composite microstructures (SCM) process and viscoelastic polymer legs with tunable stiffness In addition to the novel robot design, we present experimental validation of the lateral leg spring (LLS) locomotion model's prediction that dynamic turning can be achieved by modulating leg stiffness Finally, we present and validate a leg design for active stiffness control using shape memory alloy and demonstrate the ability of the robot to execute near-gymnastic 90° turns in the span of five strides

On the Characterization of Local Nash Equilibria in Continuous Games

Abstract: We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and second-order conditions ensuring strategies constitute local Nash equilibria. We term points satisfying the sufficient conditions differential Nash equilibria . Further, we provide a sufficient condition (non-degeneracy) guaranteeing differential Nash equilibria are isolated and show that such equilibria are structurally stable. We present tutorial examples to illustrate our results and highlight degeneracies that can arise in continuous games.

Programmable parts: a demonstration of the grammatical approach to self-organization

Abstract: In this paper, we introduce a robotic implementation of the theory of graph grammars (Klavins et al., 2005), which we use to model and direct self-organization in a formal, predictable and provably-correct fashion. The robots, which we call programmable parts, float passively on an air table and bind to each other upon random collisions. Once attached, they execute local rules that determine how their internal states change and whether they should remain bound. We demonstrate through experiments how they can self-organize into a global structure by executing a common graph grammar in a completely distributed fashion. The system also presents a challenge to the grammatical method (and to distributed systems approaches in general) due to the stochastic nature of its dynamics. We conclude by discussing these challenges and our initial approach to addressing them.

A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems

Abstract: Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment.

Stochastic Processes in Physics and Chemistry

Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

Generative adversarial networks

Abstract: Generative adversarial networks are a kind of artificial intelligence algorithm designed to solve the generative modeling problem. The goal of a generative model is to study a collection of training examples and learn the probability distribution that generated them. Generative Adversarial Networks (GANs) are then able to generate more examples from the estimated probability distribution. Generative models based on deep learning are common, but GANs are among the most successful generative models (especially in terms of their ability to generate realistic high-resolution images). GANs have been successfully applied to a wide variety of tasks (mostly in research settings) but continue to present unique challenges and research opportunities because they are based on game theory while most other approaches to generative modeling are based on optimization.

Coverage control for mobile sensing networks

Abstract: This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

NIPS 2016 Tutorial: Generative Adversarial Networks

Abstract: This report summarizes the tutorial presented by the author at NIPS 2016 on generative adversarial networks (GANs). The tutorial describes: (1) Why generative modeling is a topic worth studying, (2) how generative models work, and how GANs compare to other generative models, (3) the details of how GANs work, (4) research frontiers in GANs, and (5) state-of-the-art image models that combine GANs with other methods. Finally, the tutorial contains three exercises for readers to complete, and the solutions to these exercises.