Artur Babiarz

Controllability and minimum energy control of linear fractional discrete-time infinite-dimensional systems

The main purpose of the paper is to discuss controllability problem for infinite-dimensional fractional linear discrete-time control systems. Moreover, the minimum energy control problem of infinite-dimensional fractional-discrete time linear systems is also addressed. Using theory of linear operators necessary and sufficient conditions for the exact controllability of the system are established. Sufficient conditions for the solvability of the minimum energy control of the infinite-dimensional fractional discrete-time systems are given. A procedure for computation of the optimal sequence of inputs minimizing the quadratic performance index is proposed.

An approach to observability analysis and estimation of human arm model

This article presents the analysis of a mathematical model of human arms dynamics in terms of observability. The research is conducted in search of an observer which gives the possibility of arm tracking. The arms model is based on a two-link manipulator able to move in horizontal and vertical planes. Model is analyzed after linearization and omittance of muscles representing part. The experimental part involves simulation of the motion parameters and real IMU measurements. Finally, simulation results concerning the use of observer in the form of Kalman and particle filters are presented.

On mathematical modelling of the human arm using switched linear system

The article presents a novel approach to modelling human arm using switched linear systems. The linear and nonlinear second-order differential equations are shown for two-link arm moving in the horizontal and vertical planes. Linear equations in the state space have been formulated for these two objects. The next step is to present a switched linear system. Switching function is modeled as dependent on the state of the system. Finally, we are shown the division of the state space and linear equations describing the switched system for the vertical and horizontal two-link human arm.

Machine Vision in Autonomous Systems of Detection and Location of Objects in Digital Images

In the article a group of vi libraries (“virtual instrument”) of the simulation – programming LabVIEW environment, enabling the construction of a program that would be the basics of the image programming and analysis system, are presented. Presented libraries are dedicated for the Vivotek, supporting the SDK module (“VitaminCtrl”). They provide the ability to connect the camera that works on the Internet, configuration of the transmission protocol, acquisition parameters and audio and video streaming. In addition, while operating the PTZ (“pan-tilt-zoom”) cameras, suggested module allow to control the camera motion from the client application level which was created in the National Instruments’ firm environment. With the use of the designed libraries, the LabVIEW environments and PTZ cameras of Vivotek a post was made to make algorithm and synthesis of the processing algorithms and for the analysis of digital images. At the stage of the development of the functional modules, a consistent idea of input and output signals definition was also developed. The created modules rely on both the commands of the controlling module SDK and syntax URL format commands. What is more, designed modules enable capturing the video signal frames and their conversation to a LabVIEW variable environment of Image type (“IMAQ Image.ctl”). With the achieved functionality a simple construction of an application for the synthesis and analysis of algorithms for image processing and for the analysis of images acquired in the real time, directly from the camera, is possible.

Controllability of Discrete-Time Linear Switched Systems with Constrains on Switching Signal

In this paper we consider the controllability problem for discrete-time linear switched systems. The problem consists of finding a control signal that steers any initial condition to a given final state regardless of the switching signal. In the paper a necessary and sufficient conditions for this type of controllability are presented. Moreover, we consider problems of controllability from zero initial condition and to zero final state.

Vision System for Group of Mobile Robots

A vision system for group of small mobile robots playing soccer is presented. The whole process of extracting vision information from input images is discussed in detail. The method for correcting radial distortion introduced to the image by camera’s lens is presented, then simple adaptive background subtraction algorithm is described. Next, classical flood fill algorithm is presented together with novel optimization giving better results and shorter calculation time. Later, novel method for calculating object’s orientation, based on the geometrical moments and special shape of color markers on top of each robot, is presented. Then, the color classifier based on the histogram intersection kernel is discussed. Design of the vision system as a central server providing vision information to many clients simultaneously is presented. Experimental results obtained with use of the algorithm presented are also provided.

Schauder's fixed-point theorem in approximate controllability problems

Abstract The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.

Trajectory Controllability of Semilinear Systems with Delay

The finite-dimensional dynamical control system described by scalar semilinear ordinary differential state equation with delay is considered in this paper. The semilinear state equation contains both nonlinear perturbations and pure linear part. The concept of relative controllability on trajectory relative controllability for systems with point delay in control and in nonlinear term was extended. Finally, the remarks and comments on the relationships between different concepts of controllability were presented and the possible extensions proposed.

The mathematical model of the human arm as a switched linear system

The article presents the process of designing a mathematical model of the human arm. Modelling arm consists of two joints connected by the rotational link. Each of them is represented as a rectangular prism which changes shape during the movement. The moment of shape change depends on the two-state coordinates: the angular displacement q1 and q2. Based on the analysis of the arm movement, a mathematical model has been proposed. The design process was made on the basis of switched systems theory. In the first step, we present the transition from the general equation of the two-link arm dynamics to the state equation for stationary linear models. In the second step, a mathematical model has been shown as a switched linear system. The article also shows that the switching rule depends on the two components of the state vector. A switching method was presented in the schematic drawings.

A Distributed Control Group of Mobile Robots in a Limited Area with a Vision System

Digital remote manual control systems are no less complicated than automatic control. Engineers have to overcome number of unique problems. Mechanical parts have to respond to digital signals transferred through wireless connection. Digital control algorithms have to correctly translate the movement of controls at remote station to signals in a way that a operator has a proper feeling of control. The Master Control System presented connects the features of a Drive-By-Wire control system with wireless connection. Main focus is put on the Master controller and its algorithms of input - output translation, that give finer control for an operator. In addition, computer controlled intervention algorithms are proposed that can increase safety of the subject vehicle. All that is done on basis of a small two-wheeled robot and a closed environment of small playground with radio interface allowing wireless connection with the robot, and a vision interface equipped with a camera serving as a visual feedback. Is it a great environment for theoretical considerations, testing and implementation. Modular design of the environment additionally allows the control of whole Mobile Robot Group, not only one robot subject. Moreover sented results can be applied more widely in controllers for cars or other wheeled or tracked vehicles.