Mohamed M. Bayoumi

A survey of modeling and control of hybrid systems

Abstract This survey investigates modeling and control of hybrid systems. These systems exhibit a variety of continuous and discrete behaviour, thus leading to a variety of modeling formalisms. This survey highlights certain characteristics of hybrid systems. A simple three fluid-filled tank system is used to illustrate some modeling approaches. Variations to this example are used to further explore hybrid model characteristics. An expository discussion is presented on analysis and control techniques for hybrid systems.

Modeling the Stochastic Drift of a MEMS-Based Gyroscope in Gyro/Odometer/GPS Integrated Navigation

To have a continuous navigation solution that does not suffer from interruption, GPS is integrated with relative positioning techniques such as odometry and inertial navigation. Targeting a low-cost navigation solution for land vehicles, this paper uses a reduced multisensor system consisting of one microelectromechanical-system (MEMS)-based single-axis gyroscope used together with the vehicles odometer, and the whole system is integrated with GPS. This system provides a 2-D navigation solution, which is adequate for land vehicles. The traditional technique for this multisensor integration problem is Kalman filtering (KF). Due to the inherent errors of MEMS inertial sensors and their stochastic nature, which is difficult to model, the KF with its linearized models has limited capabilities in providing accurate positioning. Particle filtering (PF) has recently been suggested as a nonlinear filtering technique to accommodate arbitrary inertial sensor characteristics, motion dynamics, and noise distributions. An enhanced version of PF is utilized in this paper and is called the Mixture PF. Since PF can accommodate nonlinear models, this paper uses total-state nonlinear system and measurement models. In addition, sophisticated models are used to model the stochastic drift of the MEMS-based gyroscope. A nonlinear system identification technique based on parallel cascade identification (PCI) is used to model this stochastic gyroscope drift. In this paper, the performance of the PCI model is compared with that of higher order autoregressive (AR) stochastic models. Such higher order models are difficult to use with KF since the size of the dynamic matrix and the error-covariance matrix becomes very large and complicates the KF operation. The performance of the proposed 2-D navigation solution using Mixture PF with both PCI and higher order AR models is examined by road-test trajectories in a land vehicle. The two proposed combinations are compared with four other 2-D solutions: a Mixture PF with the Gauss-Markov (GM) model for the gyro drift, a Mixture PF with only white Gaussian noise (WGN) for stochastic gyro errors, and two different KF solutions with GM model for the gyro drift. The experimental results show that the two proposed solutions outperform all the compared counterparts.

Low-Cost Three-Dimensional Navigation Solution for RISS/GPS Integration Using Mixture Particle Filter

Recent technological advances in both GPS and low-cost microelectromechanical-system (MEMS)-based inertial sensors have enabled the monitoring of the location of moving platforms for numerous positioning and navigation (POS/NAV) applications. GPS is presently widely used in land vehicles. However, in some environments, the GPS signal may suffer from signal blockage and multipath effects that deteriorate the positioning accuracy. When miniaturized inside any moving platforms, the MEMS-based inertial navigation system (INS) can be integrated with GPS and enhance the performance in denied GPS environments (like in urban canyons). Targeting a low-cost navigation solution for land vehicles, this paper uses a reduced inertial sensor system (RISS) with MEMS-based inertial sensors. In this paper, the RISS consists of one single-axis gyroscope and a two-axis accelerometer used together with the vehicles odometer, and the whole system is integrated with GPS to obtain a 3-D navigation solution. The traditional technique for this integration problem is Kalman filtering (KF). Due to the inherent errors of MEMS inertial sensors and the relatively high noise levels associated with their measurements, KF has limited capabilities in providing accurate positioning. Particle filtering (PF) was recently suggested as a nonlinear filtering technique to accommodate arbitrary inertial sensor characteristics, motion dynamics, and noise distributions. An enhanced version of PF is utilized in this paper and is called Mixture PF. The performance of the proposed 3-D navigation solution using Mixture PF for RISS/GPS integration is examined by road-test trajectories in a land vehicle. The proposed method is compared with four other solutions: 1) 3-D solution using KF for full INS/GPS integration; 2) 2-D solution using KF for RISS/GPS integration; 3) 2-D solution using Mixture PF for RISS/GPS integration; and 4) 3-D solution using sampling/importance resampling (SIR) PF for RISS/GPS integration. The experimental results show that the proposed solution outperforms all the compared counterparts.

A dyadic wavelet affine invariant function for 2D shape recognition

Dyadic wavelet transform has been used to derive an affine invariant function. First, an invariant function using two dyadic levels is derived. Then, this invariant function is used to derive another invariant function using six dyadic levels. We introduce the wavelet based conic equation. The invariant function is based on analyzing the object boundary using the dyadic wavelet transform. Experimental results on both synthetic and real data are used to demonstrate the discriminating power of the proposed invariant function. It has also been compared with some traditional methods. The stability of the proposed invariant function is examined. In addition, the stability under large perspective transformation is tested.

Robot navigation using a pressure generated mechanical stress field: "the biharmonic potential approach"

This paper suggests a new approach for navigation in a known environment. The approach is based on the biharmonic potential fields which govern mechanical stress fields in homogeneous solids. It is observed that a path generated by such a technique is free of sharp turns that may appear in its counterpart that is generated from an underlying harmonic potential. This in turns makes a path from the former more dynamically suitable for traversal. Also, the navigation field is extracted from the biharmonic potential in a manner that bypass the rapidly vanishing field problem which is encountered in the harmonic potential approach. Development of the biharmonic approach, simulation results, as well as comparison with the Neumann and Dirichlet setting of the harmonic approach are provided.<<ETX>>

Modeling and Control of Hybrid Systems: A Survey

Abstract This survey investigates modeling and control of hybrid systems. The term hybrid systems has come to be used to describe systems exhibiting a variety of continuous/discrete behaviour, thus leading to a variety of modeling formalisms. One of the objectives of this survey is to comparatively study the various modeling formalisms. A second objective is to consider different approaches to control hybrid systems. In order to compare models, groupings are made based on general modeling approaches as well as on classifications of each model in terms of six specific characteristics. The discussion of control focuses on approaches referred to as verification and control synthesis. A fairly simple yet illustrative system is used throughout the paper for demonstration purposes.

Affine invariants for object recognition using the wavelet transform

Dyadic wavelet transform has been used to derive affine invariant functions. The invariant functions are based on the dyadic wavelet transform of the object boundary. Three invariant functions have been calculated using different numbers of dyadic levels. Experimental results show that these invariant functions outperform some traditional invariant functions. The stability of these invariant functions have been tested for a large perspective transformation.

Invariant 2D object recognition using the wavelet modulus maxima

Abstract In this paper, a technique is proposed to recognize 2D objects under translation, rotation, and scale transformations. The technique is based on the continuous wavelet transform and neural networks. Experimental results are presented and compared with some traditional methods. The experimental results showed that this refined technique was successful in classifying the objects under consideration and that it outperformed those traditional methods especially in the presence of noise.

Robot navigation using the vector potential approach

The artificial vector potential is used to construct a navigation control that can drive a manipulator to a target set while avoiding undesired regions in the workspace. It is shown that a vector potential field can better navigate a robot than a scalar potential field. The strategy that is suggested for constructing the navigation control is very flexible in the sense that it allows the addition or deletion of obstacles with minimal adjustment to the control. An efficient technique for generating the navigation field in the N-D space is proposed. Simulation results are provided.<<ETX>>

Digital Phase-Locked Loop for Induction Motor Speed Control

The study of the speed control of induction motor drive using digital phase-locked loop is discussed. The block diagram and the control circuitry have been outlined. A mathematical model has been developed to predict the system performance. Different types of filters have been considered as part of the feedback control system, and their effects on the overall system behavior have been qualitatively studied. The system is tested using a 5-hp induction motor and an integrating type filter. Excellent speed regulation in the order of 0.002 percent has been obtained.