Lutz Gröll

Interpretability issues in data-based learning of fuzzy systems

This paper presents a method for an automatic and complete design of fuzzy systems from data. The main objective is to build fuzzy systems with a user-controllable trade-off between accuracy and interpretability. Whereas criteria for accuracy mostly follow straightforwardly from the application, definition of interpretability and its criteria are subject to controversial discussion. For this reason, a set of interpretability criteria is given which guide the design process. Consequently, interpretability is maintained by structural choices regarding the type of membership functions, rules, and inference mechanism, on the one hand, and by including interpretability criteria in the rule/rule base evaluation, on the other hand. An application in Instrumented Gait Analysis, to characterize a certain group of patients in comparison to healthy subjects, illustrates the proposed algorithm.

Source localization by spatially distributed electronic noses for advection and diffusion

Based on continuous concentration measurements from spatially distributed electronic noses, the location of a point source is to be determined. It is assumed that the emitted substance is transported by advection caused by a known homogeneous wind field and by isotropic diffusion. A new two-step approach for solving the source localization problem is presented. In the first step, for each sensor i, the set of points P/sub i/ is determined, on which the source can lie, taking only the specific concentration measurement C/sub i/ at sensor i into account. In the second step, an estimate for the source position is evaluated by intersecting the sets P/sub i/. The new approach overcomes the problem of poor convergence of iterative algorithms, which try to minimize the least squares output error. Finally, experimental results showing the capability of the new approach are presented.

A New Convergence Proof of Fuzzy c-Means

In this letter, we give a new, more direct derivation of the convergence properties of the fuzzy c-means (FCM) algorithm, using the equivalence between the original and reduced FCM criterion. From the point of view of the reduced criterion, the FCM algorithm is simply a steepest descent algorithm with variable steplength. We prove that steplength adjustment follows from the majorization principle for steplength. By applying the majorization principle we give a straightforward proof of global convergence. Further convergence properties follow immediately using known results of optimization theory

Optimal trajectories for time-critical street scenarios using discretized terminal manifolds

This paper deals with the trajectory generation problem faced by an autonomous vehicle in moving traffic. Being given the predicted motion of the traffic flow, the proposed semi-reactive planning strategy realizes all required long-term maneuver tasks (lane-changing, merging, distance-keeping, velocity-keeping, precise stopping, etc.) while providing short-term collision avoidance. The key to comfortable, human-like as well as physically feasible trajectories is the combined optimization of the lateral and longitudinal movements in street-relative coordinates with carefully chosen cost functionals and terminal state sets (manifolds). The performance of the approach is demonstrated in simulated traffic scenarios.

A robust algorithm for handling moving traffic in urban scenarios

This paper describes an algorithm for handling moving traffic which was deployed on AnnieWAY, an autonomous vehicle successfully entering the finals of the DARPA Urban Challenge 2007 competition. The algorithm allows for a robust and effective collision check for a variety of maneuvers including turning at intersections with oncoming traffic, merging into moving traffic, changing lanes, as well as dynamic passing and can easily be integrated into a high-level decision process, such as a state machine.

EMG-control of prostheses by switch signals: extraction and classification of features

This work examines the process of grasp type classification based on electromyographic (EMG-) signals by a recently presented multifunctional control scheme. For the latter the online feature extraction out of EMG-signals is described. Features are used to teach the corresponding signal to the system. The teaching process is based on statistical classifiers, fuzzy rulebases and artificial neural networks, respectively. Since there is no knowledge about which classifier serves best for EMG-data several classifiers are compared using data of seven amputated subjects. Subsequently, a routine is presented which generates source code for a microcontroller implementation.

Low-level controllers realizing high-level decisions in an autonomous vehicle

The urban challenge 2007 is a research program conducted in a competitive format to address the challenging aspects of letting vehicles accomplish missions in urban scenarios fully autonomously. AnnieWAY is one out of eleven autonomous vehicles that entered the finals. As it turned out, one of the major difficulties is the combination of different algorithms for different tasks to a functioning unit. This contribution describes AnnieWAYpsilas interface between high-level decision making (path planning) and low-level control and provides herewith a simple but robust solution to handling the vehiclepsilas physics. Additionally, the longitudinal and lateral controller, which convert the interfacepsilas values ultimately to the manipulated variables are described in detail.

Takagi--Sugeno--Kang Fuzzy Classifiers for a Special Class of Time-Varying Systems

This paper proposes new design strategies for Takagi-Sugeno-Kang classifiers to solve a special class of time-varying classification problems with known or estimated trigger events. The resulting classifiers have lower classification errors than time-invariant classifiers, as well as a lower computational effort and a better interpretability than other multiple classifiers with a time-varying fusion. The strategies are applied to several benchmark datasets and to a real-world application to design a brain-machine interface.

Optimal estimation of line segments in noisy lidar data

Lidar data usually is obtained by independently measuring distance r and angle ϕ. Therefore, measurements of r and ϕ are statistically independent. However, in most approaches measurements in x and y are assumed to be uncorrelated thus not taking properly into account the noise characteristic.This article investigates the application of least squares (LS), total least squares (TLS), mixed-LS-TLS (MTLS), structured total least norm (STLN) and maximum-likelihood (ML) estimators to the problem of estimating line segments in noisy lidar data and compares their performance from a theoretical point of view. This analysis is supported by simulation results. A new approach of estimating an arbitrary line segment without the need of parametric constraints is proposed.

Constrained Ellipse Fitting with Center on a Line

Fitting an ellipse to given data points is a common optimization task in computer vision problems. However, the possibility of incorporating the prior constraint “the ellipse’s center is located on a given line” into the optimization algorithm has not been examined so far. This problem arises, for example, by fitting an ellipse to data points representing the path of the image positions of an adhesion inside a rotating vessel whose position of the rotational axis in the image is known. Our new method makes use of a constrained algebraic cost function with the incorporated “ellipse center on given line”-prior condition in a global convergent one-dimensional optimization approach. Further advantages of the algorithm are computational efficiency and numerical stability.