Peter Molnar

Self-Organizing Pedestrian Movement

Although pedestrians have individual preferences, aims, and destinations, the dynamics of pedestrian crowds is surprisingly predictable. Pedestrians can move freely only at small pedestrian densities. Otherwise their motion is affected by repulsive interactions with other pedestrians, giving rise to self-organization phenomena. Examples of the resulting patterns of motion are separate lanes of uniform walking direction in crowds of oppositely moving pedestrians or oscillations of the passing direction at bottlenecks. If pedestrians leave footprints on deformable ground (for example, in green spaces such as public parks) this additionally causes attractive interactions which are mediated by modifications of their environment. In such cases, systems of pedestrian trails will evolve over time. The corresponding computer simulations are a valuable tool for developing optimized pedestrian facilities and way systems.

Modelling the evolution of human trail systems.

Many human social phenomena, such as cooperation, the growth of settlements, traffic dynamics and pedestrian movement, appear to be accessible to mathematical descriptions that invoke self-organization. Here we develop a model of pedestrian motion to explore the evolution of trails in urban green spaces such as parks. Our aim is to address such questions as what the topological structures of these trail systems are, and whether optimal path systems can be predicted for urban planning. We use an ‘active walker’ model that takes into account pedestrian motion and orientation and the concomitant feedbacks with the surrounding environment. Such models have previously been applied to the study of complex structure formation in physical, chemical and biological systems. We find that our model is able to reproduce many of the observed large-scale spatial features of trail systems.

Active walker model for the formation of human and animal trail systems

Active walker models have recently proved their great value for describing the formation of clusters, periodic patterns, and spiral waves as well as the development of rivers, dielectric breakdown patterns, and many other structures. It is shown that they also allow to simulate the formation of trail systems by pedestrians and ants, yielding a better understanding of human and animal behavior. A comparison with empirical material shows a good agreement between model and reality. Our trail formation model includes an equation of motion, an equation for environmental changes, and an orientation relation. It contains some model functions, which are specified according to the characteristics of the considered animals or pedestrians. Not only the kind of environmental changes differs: Whereas pedestrians leave footprints on the ground, ants produce chemical markings for their orientation. Nevertheless, it is more important that pedestrians steer towards a certain destination, while ants usually find their food sources by chance, i.e. they reach their destination in a stochastic way. As a consequence, the typical structure of the evolving trail systems depends on the respective species. Some ant species produce a dendritic trail system, whereas pedestrians generate a minimal detour system. The trail formation model can be used as a tool for the optimization of pedestrian facilities: It allows urban planners to design convenient way systems which actually meet the route choice habits of pedestrians.

Bearings-only target localization for an acoustical unattended ground sensor network

This paper extends our development of acoustical bearings-only target localization for the case of multiple moving targets. The resulting techniques can be used to locate and track targets traveling through a network of acoustical sensor arrays. Each array computes and transmits multiple direction-of-arrival (DOA) estimates to a central processor, which employs the target localization technique. In previous work, we developed ML techniques that may or may not account for the fact that a bearing measurement points to the location of a moving target at a retarded time. By inserting a simple bearings association computation in the ML methods, we define quasi-ML techniques that can estimate the location and velocity of multiple targets using multiple bearing estimates per a sensor array.

Control of distributed autonomous robotic systems using principles of pattern formation in nature and pedestrian behavior

Self-organized and error-resistant control of distributed autonomous robotic units in a manufacturing environment with obstacles where the robotic units have to be assigned to manufacturing targets in a cost effective way, is achieved by using two fundamental principles of nature. First, the selection behavior of modes is used which appears in pattern formation of physical, chemical and biological systems. Coupled selection equations based on these pattern formation principles can be used as dynamical system approach to assignment problems. These differential equations guarantee feasibility of the obtained solutions which is of great importance in industrial applications. Second, a model of behavioral forces is used, which has been successfully applied to describe self-organized crowd behavior of pedestrians. This novel approach includes collision avoidance as well as error resistivity. In particular, in systems where failures are of concern, the suggested approach outperforms conventional methods in covering up for sudden external changes like breakdowns of some robotic units. The capability of this system is demonstrated in computer simulations.

Communication Fault Tolerance in Distributed Robotic Systems

The task of assigning a team of mobile robotic systems to individual job-locations has many challenges. We use the dynamical systems approach of coupled selection equations to achieve this problem. This intrinsically distributed algorithm has several advantages over traditional integer programs and other distributed approaches: 1) no backtracking is needed, 2) it can be used for NP-hard problems, such as assigning multiple robots with different capabilities to a certain job (three- or higher-index assignment problems), and 3) feasibility of the obtained solutions can be guaranteed.

Dynamic Robot-Target Assignment — Dependence of Recovering from Breakdowns on the Speed of the Selection Process

The self-organized and fault tolerant behavior of a novel control method for the dynamic assignment of robots to targets using an approach proposed by Starke and Molnar is investigated in detail. Concerning the robot-target assignments the method shows an excellent error resistivity and robustness by using only the local information of each robot. Experimental results verify the dynamic assignment of the mobile robots to the targets and the capability to cope with sudden changes like a breakdown of one of the robots. The dependence of the assignment on the speed of the target-selection dynamics is shown by both experiments and numerical simulations. The results suggest the existence of an optimal value for the speed of the target-selection dynamics.

A statistical approach to quantifying clutter in hyperspectral infrared images

A method to quantify clutter in hyperspectral infrared (HSI) images in a framework similar to work done on single-band images is presented. Hereby, all objects in a scene that may be mistaken for targets by an automatic target recognition (ATR) algorithm are considered clutter. A hyperspectral image contains a number of contiguous discrete bands within the spectrum. The aim is to obtain a measure of complexity for hyperspectral images, which will indicate the inherent difficulty for an ATR to detect targets. We implemented 129 different image clutter metrics, and computed them for a database of synthesized HSI images. A matched filter ATR was used to determine the amount of clutter in the images as a baseline. We developed a method to select a subset of the metrics that in combination correlated best with the amount of clutter in an image, and defined this as the clutter complexity measure (CCM). Multiple runs of this selection procedure for different training image groups show a dominance of a further subset of metrics that best predict the CCM. Our results also show that the CCM obtained from a varying number of random sample images generalizes well for the entire database

Development of undergraduate and graduate programs in computational science

There is a pressing need for a workforce with the modeling and simulation skills associated with computational science. A number of national studies have substantiated those needs with respect to the future competitiveness of USA in research and development, the innovation of new products, and the competitiveness of many industries. Creating computational science programs at academic institutions organized along disciplinary boundaries represents a challenge because aspects of computer science, mathematics, and a science or engineering domain are required parts of any program. Gaining agreement on the associated requirements, integrating the classes with those in the traditional curriculum, and obtaining the necessary support through academic and administrative reviews represent substantial challenges. Clark Atlanta University, the University of Mary Washington, and Southern University are all working on establishing undergraduate or graduate programs in computational science and have had a number of common experiences. Copyright

Adaptive Sampling via Histogram Equalization using an Active Walker Model

We propose a novel, progressive, adaptive sampling method, that efficiently varies the sampling rate in local regions of a function based on the distribution of already collected samples. We show that for many functions, increasing the sampling rate in a region of a function with relatively higher complexity is achieved by the equalization of the histogram of the sampled function values. The sampling scheme thus achieves two purposes that are shown to be equivalent; efficiently adapted sampling rates based on local function complexity, and an improvement in diversity in the sampled function values. We achieve the sampling, progressively, through an active walker model. The sample points are placed based on the location of simulated active walkers whose movement is adapted at each stage to achieve the required histogram equalization. The only requirement by this algorithm is the ability to obtain the value of the function at each sample point; no a priori information on the relative levels of local variation of the function being sampled is required. We illustrate this concept with some examples, and discuss practical applications in the two broad areas of adaptive sampling, and improving diversity in samples