Jürgen Adamy

Vector norms as Lyapunov functions for linear systems

A unified theory of quadratic and piecewise-linear Lyapunov functions for continuous and discrete-time linear systems is presented. The key to this work is the description of these Lyapunov functions by vector norms. The main results are sufficient and necessary conditions for a vector norm to be a Lyapunov function as well as a method (based on these conditions) of constructing such Lyapunov functions. >

A Probabilistic Model for Binaural Sound Localization

This paper proposes a biologically inspired and technically implemented sound localization system to robustly estimate the position of a sound source in the frontal azimuthal half-plane. For localization, binaural cues are extracted using cochleagrams generated by a cochlear model that serve as input to the system. The basic idea of the model is to separately measure interaural time differences and interaural level differences for a number of frequencies and process these measurements as a whole. This leads to two-dimensional frequency versus time-delay representations of binaural cues, so-called activity maps. A probabilistic evaluation is presented to estimate the position of a sound source over time based on these activity maps. Learned reference maps for different azimuthal positions are integrated into the computation to gain time-dependent discrete conditional probabilities. At every timestep these probabilities are combined over frequencies and binaural cues to estimate the sound source position. In addition, they are propagated over time to improve position estimation. This leads to a system that is able to localize audible signals, for example human speech signals, even in reverberating environments

Regularity and chaos in recurrent fuzzy systems

Abstract In this paper, we shall present a mathematical definition of recurrent fuzzy systems and begin to systematically investigate the underlying theory involved. Unlike static fuzzy systems, recurrent fuzzy systems are equipped with time-delayed feedback of their output and allow representing knowledge-based dynamic processes that may be stated in the form of “if …, then …” rules. We study their relationship to automata and show that they have an automaton-like behavior when appropriately designed. In other cases, recurrent fuzzy system may exhibit chaotic behavior. We present sufficient conditions for the occurrence of chaos in recurrent fuzzy systems that can easily be checked solely on the basis of the qualitative, linguistically formulated models. We also discuss the extent to which state graphs may be used for describing the behaviors of recurrent fuzzy systems.

Consensus for formation control of nonholonomic mobile robots

In this article we present novel formation control laws based on artificial potential fields and consensus algorithms for a group of unicycles enabling arbitrary formation patterns for these nonholonomic vehicles. Given connected and balanced graphs we are able to prove stability of the rendezvous controller by applying the LaSalle-Krasovskii invariance principle. Further, we introduce obstacle avoidance, enabling a reactive behavior of the robotic group in unknown environments. The effectiveness of the proposed controllers is shown using computer simulations and finally, a classification w.r.t. existing solutions is done.

A Biologically Inspired Spiking Neural Network for Sound Source Lateralization

In this paper, a binaural sound source lateralization spiking neural network (NN) will be presented which is inspired by most recent neurophysiological studies on the role of certain nuclei in the superior olivary complex (SOC) and the inferior colliculus (IC). The binaural sound source lateralization neural network (BiSoLaNN) is a spiking NN based on neural mechanisms, utilizing complex neural models, and attempting to simulate certain parts of nuclei of the auditory system in detail. The BiSoLaNN utilizes both excitatory and inhibitory ipsilateral and contralateral influences arrayed in only one delay line originating in the contralateral side to achieve a sharp azimuthal localization. It will be shown that the proposed model can be used both for purposes of understanding the mechanisms of an NN of the auditory system and for sound source lateralization tasks in technical applications, e.g., its use with the Darmstadt robotic head (DRH).

Equilibria of recurrent fuzzy systems

Unlike static fuzzy systems, recurrent fuzzy systems are equipped with feedback loops and thus exhibit dynamic behaviors. The dynamics of a recurrent fuzzy system is largely determined by its rule base. The dynamic behavior of a significant subclass of recurrent fuzzy systems may be immediately deduced from their rule base, without need for analyzing their mathematical description. Their equilibrium points may be readily identified and their stability behaviors investigated based on their rule base. The investigations involved lead to convergence theorems and other statements that preclude chaotic dynamics.

PRORETA 3: An Integrated Approach to Collision Avoidance and Vehicle Automation

Zusammenfassung The article describes first results of the research project PRORETA 3 that aims at the development of an integral driver assistance system for collision avoidance and automated vehicle guidance based on a modular system architecture. For this purpose, relevant information is extracted from a dense environment model and fed into a potential field-based trajectory planner that calculates reference signals for underlying vehicle controllers. In addition, the driver is supported by a human-machine interface. Abstract Der Beitrag beschreibt erste Ergebnisse des Forschungsprojektes PRORETA 3, das die Entwicklung eines integralen Fahrerassistenzsystems zur Kollisionsvermeidung und automatisierten Fahrzeugführung auf Basis einer modularen Systemarchitektur anstrebt. Hierzu werden relevante Informationen aus einem dichten Umfeldmodell extrahiert und in einem potentialfeldbasierten Trajektorienplaner verarbeitet, der Führungsgrößen für unterlagerte Fahrzeugregler generiert. Zusätzlich unterstützt eine Mensch-Maschine-Schnittstelle den Fahrer zielgerichtet bei der Fahrzeugführung.

Implicit Lyapunov functions and isochrones of linear systems

Lyapunovs direct method is based on a Lyapunov function that explicitly depends on the systems state vector. This article describes implicit Lyapunov functions and corresponding stability theorems that are counterparts of the explicit case. We also define isochrones of linear systems and describe their relationship to implicit Lyapunov functions. Determining settling times is considered as an application.

Non-Gaussian velocity distributions integrated over space, time, and scales

Velocity distributions are an enhanced representation of image velocity containing more velocity information than velocity vectors. In particular, non-Gaussian velocity distributions allow for the representation of ambiguous motion information caused by the aperture problem or multiple motions at motion boundaries. To resolve motion ambiguities, discrete non-Gaussian velocity distributions are suggested, which are integrated over space, time, and scales using a joint Bayesian prediction and refinement approach. This leads to a hierarchical velocity-distribution representation from which robust velocity estimates for both slow and high speeds as well as statistical confidence measures rating the velocity estimates can be computed.

Bayesian, maneuver-based, long-term trajectory prediction and criticality assessment for driver assistance systems

We propose a Bayesian trajectory prediction and criticality assessment system that allows to reason about imminent collisions of a vehicle several seconds in advance. We first infer a distribution of high-level, abstract driving maneuvers such as lane changes, turns, road followings, etc. of all vehicles within the driving scene by modeling the domain in a Bayesian network with both causal and diagnostic evidences. This is followed by maneuver-based, long-term trajectory predictions, which themselves contain random components due to the immanent uncertainty of how drivers execute specific maneuvers. Taking all uncertain predictions of all maneuvers of every vehicle into account, the probability of the ego vehicle colliding at least once within a time span is evaluated via Monte-Carlo simulations and given as a function of the prediction horizon. This serves as the basis for calculating a novel criticality measure, the Time-To-Critical-Collision-Probability (TTCCP) - a generalization of the common Time-To-Collision (TTC) in arbitrary, uncertain, multi-object driving environments and valid for longer prediction horizons. The system is applicable from highly-structured to completely non-structured environments and additionally allows the prediction of vehicles not behaving according to a specific maneuver class.